diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/README.md b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/README.md index e930cb19e737..5ece81421b68 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/README.md +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/README.md @@ -68,8 +68,10 @@ y = kernelBetaincinv( 1.0, 6.0, 0.8, 0.2 ); ```javascript var randu = require( '@stdlib/random/base/randu' ); +var EPS = require( '@stdlib/constants/float64/eps' ); var kernelBetaincinv = require( '@stdlib/math/base/special/kernel-betaincinv' ); +var out; var i; var p; var a; @@ -77,9 +79,10 @@ var b; for ( i = 0; i < 100; i++ ) { p = randu(); - a = randu() * 10.0; - b = randu() * 10.0; - console.log( 'p: %d, \t a: %d, \t b: %d, \t f(p,a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), kernelBetaincinv( a, b, p, 1.0-p )[ 0 ] ); + a = ( randu() * 10.0 ) + EPS; + b = ( randu() * 10.0 ) + EPS; + out = kernelBetaincinv( a, b, p, 1.0-p ); + console.log( 'p: %d, \t a: %d, \t b: %d, \t y: %d, \t 1-y: %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) ); } ``` @@ -87,6 +90,110 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/kernel_betaincinv.h" +``` + +#### stdlib_base_kernel_betaincinv( a, b, p, q, &out1, &out2 ) + +Computes the inverse of the lower incomplete beta function. + +```c +double out1; +double out2; + +stdlib_base_kernel_betaincinv( 3.0, 3.0, 0.2, 0.8, &out1, &out2 ); +``` + +The function accepts the following arguments: + +- **a**: `[in] double` first function parameter (a positive number). +- **b**: `[in] double` second function parameter (a positive number). +- **p**: `[in] double` probability. +- **q**: `[in] double` probability equal to `1-p`. +- **out1**: `[out] double*` destination pointer to store the function value `y`. +- **out2**: `[out] double*` destination pointer to store `1-y`. + +```c +void stdlib_base_kernel_betaincinv( const double a, const double b, const double p, const double q, double *out1, double *out2 ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/kernel_betaincinv.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/random/base/randu.h" +#include +#include + +int main( void ) { + struct BasePRNGObject *obj = stdlib_base_random_randu_allocate( 0 ); + double out1; + double out2; + int32_t i; + double p; + double a; + double b; + + for ( i = 0; i < 100; i++ ) { + p = stdlib_base_random_randu( obj ); + a = ( stdlib_base_random_randu( obj ) * 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS; + b = ( stdlib_base_random_randu( obj ) * 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS; + stdlib_base_kernel_betaincinv( a, b, p, 1.0-p, &out1, &out2 ); + printf( "p: %lf, a: %lf, b: %lf, y: %lf, 1-y: %lf\n", p, a, b, out1, out2 ); + } + + stdlib_base_random_randu_free( obj ); +} +``` + +
+ + + +
+ + +
diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.js index 297558ad974d..b0b57c2a5e0b 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.js @@ -22,7 +22,7 @@ var bench = require( '@stdlib/bench' ); var uniform = require( '@stdlib/random/array/uniform' ); -var isNumberArray = require( '@stdlib/assert/is-number-array' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); var EPS = require( '@stdlib/constants/float64/eps' ); var pkg = require( './../package.json' ).name; var kernelBetaincinv = require( './../lib' ); @@ -32,6 +32,7 @@ var kernelBetaincinv = require( './../lib' ); bench( pkg, function benchmark( assert ) { var p; + var q; var y; var a; var b; @@ -43,14 +44,15 @@ bench( pkg, function benchmark( assert ) { assert.tic(); for ( i = 0; i < assert.iterations; i++ ) { - y = kernelBetaincinv( a[ i%a.length ], b[ i%b.length ], p[ i%p.length ], 1.0-p ); - if ( !isNumberArray( y ) ) { - assert.fail( 'should return an array of numbers' ); + q = p[ i%p.length ]; + y = kernelBetaincinv( a[ i%a.length ], b[ i%b.length ], q, 1.0-q ); + if ( isnan( y[ 0 ] ) || isnan( y[ 1 ] ) ) { + assert.fail( 'should not return NaN' ); } } assert.toc(); - if ( !isNumberArray( y ) ) { - assert.fail( 'should return an array of numbers' ); + if ( isnan( y[ 0 ] ) || isnan( y[ 1 ] ) ) { + assert.fail( 'should not return NaN' ); } assert.pass( 'benchmark finished' ); assert.end(); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.native.js new file mode 100644 index 000000000000..a1750c79e332 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/benchmark.native.js @@ -0,0 +1,69 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var format = require( '@stdlib/string/format' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var kernelBetaincinv = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( kernelBetaincinv instanceof Error ) +}; + + +// MAIN // + +bench( format( '%s::native', pkg ), opts, function benchmark( assert ) { + var p; + var q; + var y; + var a; + var b; + var i; + + p = uniform( 100, 0.0, 1.0 ); + a = uniform( 100, EPS, 1000.0 ); + b = uniform( 100, EPS, 1000.0 ); + + assert.tic(); + for ( i = 0; i < assert.iterations; i++ ) { + q = p[ i%p.length ]; + y = kernelBetaincinv( a[ i%a.length ], b[ i%b.length ], q, 1.0-q ); + if ( isnan( y[ 0 ] ) || isnan( y[ 1 ] ) ) { + assert.fail( 'should not return NaN' ); + } + } + assert.toc(); + if ( isnan( y[ 0 ] ) || isnan( y[ 1 ] ) ) { + assert.fail( 'should not return NaN' ); + } + assert.pass( 'benchmark finished' ); + assert.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/c/native/Makefile new file mode 100644 index 000000000000..979768abbcec --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled benchmarks. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/c/native/benchmark.c new file mode 100644 index 000000000000..ec71bbc6870b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/benchmark/c/native/benchmark.c @@ -0,0 +1,144 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/kernel_betaincinv.h" +#include "stdlib/constants/float64/eps.h" +#include +#include +#include +#include +#include + +#define NAME "kernel-betaincinv" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +static void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec / 1.0e6; +} + +/** +* Generates a random number on the interval [min,max). +* +* @param min minimum value (inclusive) +* @param max maximum value (exclusive) +* @return random number +*/ +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double p[ 100 ]; + double a[ 100 ]; + double b[ 100 ]; + double elapsed; + double out1; + double out2; + double t; + int i; + + for ( i = 0; i < 100; i++ ) { + p[ i ] = random_uniform( 0.0, 1.0 ); + a[ i ] = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 100.0 ); + b[ i ] = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 100.0 ); + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + stdlib_base_kernel_betaincinv( a[ i % 100 ], b[ i % 100 ], p[ i % 100 ], 1.0 - p[ i % 100 ], &out1, &out2 ); + if ( out1 != out1 || out2 != out2 ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( out1 != out1 || out2 != out2 ) { + printf( "should not return NaN\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/binding.gyp b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/binding.gyp new file mode 100644 index 000000000000..0d6508a12e99 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A `.gyp` file for building a Node.js native add-on. +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # List of files to include in this file: + 'includes': [ + './include.gypi', + ], + + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Target name should match the add-on export name: + 'addon_target_name%': 'addon', + + # Set variables based on the host OS: + 'conditions': [ + [ + 'OS=="win"', + { + # Define the object file suffix: + 'obj': 'obj', + }, + { + # Define the object file suffix: + 'obj': 'o', + } + ], # end condition (OS=="win") + ], # end conditions + }, # end variables + + # Define compile targets: + 'targets': [ + + # Target to generate an add-on: + { + # The target name should match the add-on export name: + 'target_name': '<(addon_target_name)', + + # Define dependencies: + 'dependencies': [], + + # Define directories which contain relevant include headers: + 'include_dirs': [ + # Local include directory: + '<@(include_dirs)', + ], + + # List of source files: + 'sources': [ + '<@(src_files)', + ], + + # Settings which should be applied when a target's object files are used as linker input: + 'link_settings': { + # Define libraries: + 'libraries': [ + '<@(libraries)', + ], + + # Define library directories: + 'library_dirs': [ + '<@(library_dirs)', + ], + }, + + # C/C++ compiler flags: + 'cflags': [ + # Enable commonly used warning options: + '-Wall', + + # Aggressive optimization: + '-O3', + ], + + # C specific compiler flags: + 'cflags_c': [ + # Specify the C standard to which a program is expected to conform: + '-std=c99', + ], + + # C++ specific compiler flags: + 'cflags_cpp': [ + # Specify the C++ standard to which a program is expected to conform: + '-std=c++11', + ], + + # Linker flags: + 'ldflags': [], + + # Apply conditions based on the host OS: + 'conditions': [ + [ + 'OS=="mac"', + { + # Linker flags: + 'ldflags': [ + '-undefined dynamic_lookup', + '-Wl,-no-pie', + '-Wl,-search_paths_first', + ], + }, + ], # end condition (OS=="mac") + [ + 'OS!="win"', + { + # C/C++ flags: + 'cflags': [ + # Generate platform-independent code: + '-fPIC', + ], + }, + ], # end condition (OS!="win") + ], # end conditions + }, # end target <(addon_target_name) + + # Target to copy a generated add-on to a standard location: + { + 'target_name': 'copy_addon', + + # Declare that the output of this target is not linked: + 'type': 'none', + + # Define dependencies: + 'dependencies': [ + # Require that the add-on be generated before building this target: + '<(addon_target_name)', + ], + + # Define a list of actions: + 'actions': [ + { + 'action_name': 'copy_addon', + 'message': 'Copying addon...', + + # Explicitly list the inputs in the command-line invocation below: + 'inputs': [], + + # Declare the expected outputs: + 'outputs': [ + '<(addon_output_dir)/<(addon_target_name).node', + ], + + # Define the command-line invocation: + 'action': [ + 'cp', + '<(PRODUCT_DIR)/<(addon_target_name).node', + '<(addon_output_dir)/<(addon_target_name).node', + ], + }, + ], # end actions + }, # end target copy_addon + ], # end targets +} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/repl.txt index c0b4e323ccc5..05c517c2cb20 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/repl.txt +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/repl.txt @@ -20,7 +20,7 @@ Returns ------- - out: Array + y: Array Two-element array holding function value `y` and `1-y`. Examples diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/types/index.d.ts index 7c8a32517cfc..ccf7ad817cc8 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/docs/types/index.d.ts @@ -19,7 +19,7 @@ // TypeScript Version: 4.1 /** -* Calculates the inverse of the incomplete beta function. +* Computes the inverse of the lower incomplete beta function. * * ## Notes * @@ -28,7 +28,7 @@ * @param a - function parameter * @param b - function parameter * @param p - function parameter -* @param q - probability equal to `1 - p` +* @param q - probability equal to `1-p` * @returns two-element array holding function value `y` and `1-y` * * @example diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/c/Makefile new file mode 100644 index 000000000000..c8f8e9a1517b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := example.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled examples. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/c/example.c new file mode 100644 index 000000000000..4f9035edeef6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/c/example.c @@ -0,0 +1,43 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/kernel_betaincinv.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/random/base/randu.h" +#include +#include + +int main( void ) { + struct BasePRNGObject *obj = stdlib_base_random_randu_allocate( 0 ); + double out1; + double out2; + int32_t i; + double p; + double a; + double b; + + for ( i = 0; i < 100; i++ ) { + p = stdlib_base_random_randu( obj ); + a = ( stdlib_base_random_randu( obj ) * 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS; + b = ( stdlib_base_random_randu( obj ) * 10.0 ) + STDLIB_CONSTANT_FLOAT64_EPS; + stdlib_base_kernel_betaincinv( a, b, p, 1.0-p, &out1, &out2 ); + printf( "p: %lf, a: %lf, b: %lf, y: %lf, 1-y: %lf\n", p, a, b, out1, out2 ); + } + + stdlib_base_random_randu_free( obj ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/index.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/index.js index 8de06a107273..b91142bcfcd3 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/index.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/examples/index.js @@ -19,8 +19,10 @@ 'use strict'; var randu = require( '@stdlib/random/base/randu' ); +var EPS = require( '@stdlib/constants/float64/eps' ); var kernelBetaincinv = require( './../lib' ); +var out; var i; var p; var a; @@ -28,7 +30,8 @@ var b; for ( i = 0; i < 100; i++ ) { p = randu(); - a = randu() * 10.0; - b = randu() * 10.0; - console.log( 'p: %d, \t a: %d, \t b: %d, \t f(p,a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), kernelBetaincinv( a, b, p, 1.0-p )[ 0 ] ); + a = ( randu() * 10.0 ) + EPS; + b = ( randu() * 10.0 ) + EPS; + out = kernelBetaincinv( a, b, p, 1.0-p ); + console.log( 'p: %d, \t a: %d, \t b: %d, \t y: %d, \t 1-y: %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/include.gypi b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/include.gypi new file mode 100644 index 000000000000..bee8d41a2caf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A GYP include file for building a Node.js native add-on. +# +# Main documentation: +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Source directory: + 'src_dir': './src', + + # Include directories: + 'include_dirs': [ + ' 1024 ) ? 8.0 : 2.0; + fc = fun( xc )[ 0 ]; + state[ 2 ] -= 1; + } + } else { + // If the brackets are negative we have to multiply to head towards the lower bracket: + while ( state[ 2 ] !== 0 && ( ( fc < 0.0 ) === ( fx < 0.0 ) ) ) { + state[ 1 ] = xc; + xc *= multiplier; + if ( xc < state[ 0 ] ) { + xc = state[ 0 ]; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + fc = fun( xc )[ 0 ]; + state[ 2 ] -= 1; + } + } + if ( state[ 2 ] !== 0 ) { + state[ 0 ] = xc; + if ( multiplier > 16.0 ) { + return ( guess0-xc ) + bracketRootTowardsMax( fun, xc, fc, state ); + } + } + return guess0 - ( ( state[ 1 ] + state[ 0 ] ) / 2.0 ); +} + +/** +* Moves the current best guess toward the upper bracket until the root is bracketed, updating the brackets along the way. +* +* @private +* @param {Function} fun - function which returns the function value and its first two derivatives +* @param {number} x - current best guess +* @param {number} fx - function value at the position from which bracketing begins +* @param {NumericArray} state - bracket state (`[ min, max, count ]`), updated in place +* @returns {number} step which should be subtracted from the current best guess +*/ +function bracketRootTowardsMax( fun, x, fx, state ) { + var multiplier; + var guess0; + var xc; + var fc; + var fe; + var e; + + if ( state[ 2 ] < 2 ) { + // Not enough iterations left to do anything! + return x - ( ( state[ 1 ] + state[ 0 ] ) / 2.0 ); + } + // Move `x` towards the upper bracket until we bracket the root, updating the brackets as we go: + fe = frexp( state[ 1 ] / x ); + e = abs( fe[ 1 ] ); + guess0 = x; + xc = x; + multiplier = ( e < 64 ) ? 2.0 : ldexp( 1.0, floor( e / 32 ) ); + fc = fx; + state[ 2 ] -= 1; + if ( abs( state[ 0 ] ) < abs( state[ 1 ] ) ) { + while ( state[ 2 ] !== 0 && ( ( fc < 0.0 ) === ( fx < 0.0 ) ) ) { + state[ 0 ] = xc; + xc *= multiplier; + if ( xc > state[ 1 ] ) { + xc = state[ 1 ]; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + fc = fun( xc )[ 0 ]; + state[ 2 ] -= 1; + } + } else { + // If the brackets are negative we have to divide to head towards the upper bracket: + while ( state[ 2 ] !== 0 && ( ( fc < 0.0 ) === ( fx < 0.0 ) ) ) { + state[ 0 ] = xc; + xc /= multiplier; + if ( xc > state[ 1 ] ) { + xc = state[ 1 ]; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + fc = fun( xc )[ 0 ]; + state[ 2 ] -= 1; + } + } + if ( state[ 2 ] !== 0 ) { + state[ 1 ] = xc; + if ( multiplier > 16.0 ) { + return ( guess0-xc ) + bracketRootTowardsMin( fun, xc, fc, state ); + } + } + return guess0 - ( ( state[ 1 ] + state[ 0 ] ) / 2.0 ); +} // MAIN // @@ -46,7 +197,7 @@ var MAX_VALUE = require( '@stdlib/constants/float64/max' ); * Performs root finding via third order Halley iteration. * * @private -* @param {Array} fun - array of function and its first two derivatives +* @param {Function} fun - function which returns the function value and its first two derivatives * @param {number} guess - initial starting value * @param {number} minimum - minimum possible value for the result, used as initial lower bracket * @param {number} maximum - maximum possible value for the result, used as initial upper bracket @@ -57,6 +208,9 @@ var MAX_VALUE = require( '@stdlib/constants/float64/max' ); function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { var convergence; var outOfBounds; + var maxRangeF; + var minRangeF; + var bigRange; var delta1; var delta2; var factor; @@ -81,6 +235,10 @@ function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { delta1 = delta; delta2 = delta; + // We use these to sanity check that we do actually bracket a root; if we update both ends of the brackets and the function value has the same sign at both ends, then there is no root to be found: + maxRangeF = 0.0; + minRangeF = 0.0; + count = maxIter; do { f0Last = f0; @@ -104,7 +262,7 @@ function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { } else { guess = minimum; } - f0Last = fun( guess ); + f0Last = fun( guess )[ 0 ]; delta = guess - result; } if ( sign( f0Last ) * sign( f0 ) < 0 ) { @@ -134,20 +292,45 @@ function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { if ( delta * f1 / f0 < 0.0 ) { // Probably cancellation error, try a Newton step instead: delta = f0 / f1; - if ( abs(delta) > 2.0 * abs(guess) ) { - delta = ( (delta < 0.0) ? -1.0 : 1.0 ) * 2.0 * abs( guess ); + if ( abs(delta) > 2.0 * abs(result) ) { + delta = ( ( delta < 0.0 ) ? -2.0 : 2.0 ) * abs( result ); } } } - convergence = abs( delta / delta2 ); + // We need to avoid delta/delta2 overflowing here: + if ( abs(delta2) > 1.0 || abs( MAX_VALUE*delta2 ) > abs( delta ) ) { + convergence = abs( delta / delta2 ); + } else { + convergence = MAX_VALUE; + } if ( convergence > 0.8 && convergence < 2.0 ) { - // Last two steps haven't converged, try bisection: - delta = ( delta > 0.0 ) ? ( result-minimum )/2.0 : ( result-maximum )/2.0; // eslint-disable-line max-len - if ( abs(delta) > result ) { - delta = sign( delta ) * result; // Protect against huge jumps! + // Last two steps haven't converged... + if ( abs( minimum ) < 1.0 ) { + bigRange = ( abs( 1000.0*minimum ) < abs( maximum ) ); + } else { + bigRange = ( abs( maximum/minimum ) > 1000.0 ); + } + if ( bigRange ) { + STATE[ 0 ] = minimum; + STATE[ 1 ] = maximum; + STATE[ 2 ] = count; + if ( delta > 0.0 ) { + delta = bracketRootTowardsMin( fun, result, f0, STATE ); + } else { + delta = bracketRootTowardsMax( fun, result, f0, STATE ); + } + minimum = STATE[ 0 ]; + maximum = STATE[ 1 ]; + count = STATE[ 2 ]; + } else { + delta = ( delta > 0.0 ) ? ( result-minimum )/2.0 : ( result-maximum )/2.0; // eslint-disable-line max-len + if ( result !== 0.0 && abs(delta) > result ) { + delta = sign( delta ) * abs( result ) * 0.9; // Protect against huge jumps! + } } - // Reset delta2 so that this branch will *not* be taken on the next iteration: + // Reset delta1/delta2 so that this branch will *not* be taken on the next iteration: delta2 = delta * 3.0; + delta1 = delta * 3.0; } guess = result; result -= delta; @@ -155,11 +338,16 @@ function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { // Check for out of bounds step: if ( result < minimum ) { if ( - abs(minimum) < 1 && - abs(result) > 1 && + abs(minimum) < 1.0 && + abs(result) > 1.0 && ( MAX_VALUE / abs(result) < abs(minimum) ) ) { diff = 1000.0; + } else if ( + abs(minimum) < 1.0 && + ( abs( MAX_VALUE*minimum ) < abs(result) ) + ) { + diff = ( ( minimum < 0.0 ) === ( result < 0.0 ) ) ? MAX_VALUE : -MAX_VALUE; // eslint-disable-line max-len } else { diff = result / minimum; } @@ -172,11 +360,27 @@ function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { result = guess - delta; outOfBounds = true; // Only take this branch once! } else { - delta = (guess - minimum) / 2.0; - result = guess - delta; - if ( result === minimum || result === maximum ) { + if ( ulpDifference( minimum, maximum ) < 2.0 ) { + result = ( minimum + maximum ) / 2.0; + guess = result; break; } + STATE[ 0 ] = minimum; + STATE[ 1 ] = maximum; + STATE[ 2 ] = count; + delta = bracketRootTowardsMin( fun, guess, f0, STATE ); + minimum = STATE[ 0 ]; + maximum = STATE[ 1 ]; + count = STATE[ 2 ]; + result = guess - delta; + if ( result <= minimum ) { + result = floatNext( minimum ); + } + if ( result >= maximum ) { + result = floatPrior( maximum ); + } + guess = minimum; + continue; } } else if ( result > maximum ) { if ( @@ -197,18 +401,41 @@ function halleyIterate( fun, guess, minimum, maximum, digits, maxIter ) { result = guess - delta; outOfBounds = true; // Only take this branch once! } else { - delta = ( guess - maximum ) / 2.0; - result = guess - delta; - if ( result === minimum || result === maximum ) { + if ( ulpDifference( minimum, maximum ) < 2.0 ) { + result = ( minimum + maximum ) / 2.0; + guess = result; break; } + STATE[ 0 ] = minimum; + STATE[ 1 ] = maximum; + STATE[ 2 ] = count; + delta = bracketRootTowardsMax( fun, guess, f0, STATE ); + minimum = STATE[ 0 ]; + maximum = STATE[ 1 ]; + count = STATE[ 2 ]; + result = guess - delta; + if ( result >= maximum ) { + result = floatPrior( maximum ); + } + if ( result <= minimum ) { + result = floatNext( minimum ); + } + guess = minimum; + continue; } } // Update brackets: if ( delta > 0.0 ) { maximum = guess; + maxRangeF = f0; } else { minimum = guess; + minRangeF = f0; + } + // Sanity check that we bracket the root: + if ( maxRangeF * minRangeF > 0.0 ) { + // There appears to be no root to be found (the original C++ implementation raises an evaluation error; we instead return the current best guess): + return guess; } } while ( count && ( abs(result * factor) < abs(delta) ) ); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/ibeta_roots.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/ibeta_roots.js index 0aae6376e41e..93589063fef2 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/ibeta_roots.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/ibeta_roots.js @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/index.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/index.js index 74926baed4ee..91e42d48167d 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/index.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/index.js @@ -19,7 +19,7 @@ 'use strict'; /** -* Evaluate the inverse of the incomplete beta function. +* Evaluate the inverse of the lower incomplete beta function. * * @module @stdlib/math/base/special/kernel-betaincinv * diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t.js index 9a701353e67a..d61fb2ec6ad7 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t.js @@ -18,10 +18,10 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. * * ```text -* Copyright John Maddock 2006. +* Copyright John Maddock 2007. * Copyright Paul A. Bristow 2007. * * Use, modification and distribution are subject to the @@ -37,12 +37,12 @@ var erfcinv = require( '@stdlib/math/base/special/erfcinv' ); var floor = require( '@stdlib/math/base/special/floor' ); var ldexp = require( '@stdlib/math/base/special/ldexp' ); -var round = require( '@stdlib/math/base/special/round' ); +var frexp = require( '@stdlib/math/base/special/frexp' ); var acos = require( '@stdlib/math/base/special/acos' ); var sqrt = require( '@stdlib/math/base/special/sqrt' ); var abs = require( '@stdlib/math/base/special/abs' ); var cos = require( '@stdlib/math/base/special/cos' ); -var pow = require( '@stdlib/math/base/special/pow' ); +var cbrt = require( '@stdlib/math/base/special/cbrt' ); var sin = require( '@stdlib/math/base/special/sin' ); var SQRT2 = require( '@stdlib/constants/float64/sqrt-two' ); var PI = require( '@stdlib/constants/float64/pi' ); @@ -54,7 +54,6 @@ var inverseStudentsTHill = require( './inverse_students_t_hill.js' ); // VARIABLES // var DF_THRESHOLD = 0x10000000; // 2^28 -var ONE_THIRD = 1.0 / 3.0; var EXP = ( 2.0 * 53.0 ) / 3.0; var C = 0.85498797333834849467655443627193; @@ -78,6 +77,7 @@ function inverseStudentsT( df, u, v ) { var result; var alpha; var tmp; + var fe; var p0; var p2; var p4; @@ -130,7 +130,7 @@ function inverseStudentsT( df, u, v ) { } // Newton-Raphson iteration of a polynomial case, choice of seed value is taken from Shaw's online supplement: a = 4.0 * ( u - (u*u) ); // 1 - 4 * (u - 0.5f) * (u - 0.5f); - b = pow( a, ONE_THIRD ); + b = cbrt( a ); p = 6.0 * ( 1.0 + ( C * ( (1.0/b) - 1.0 ) ) ); do { p2 = p * p; @@ -149,7 +149,7 @@ function inverseStudentsT( df, u, v ) { break; default: if ( df > DF_THRESHOLD ) { // 2^28 - result = erfcinv( 2.0 * u ) * SQRT2; + result = -erfcinv( 2.0 * u ) * SQRT2; } else if ( df < 3 ) { // Use a roughly linear scheme to choose between Shaw's tail series and body series: crossover = 0.2742 - ( df * 0.0242143 ); @@ -159,9 +159,10 @@ function inverseStudentsT( df, u, v ) { result = inverseStudentsTTailSeries( df, u ); } } else { - // Use Hill's method except in the extreme tails where we use Shaw's tail series. The crossover point is roughly exponential in -df: - crossover = ldexp( 1.0, round( df / -0.654 ) ); - if ( u > crossover ) { + // Use Hill's method except in the extreme tails where we use Shaw's tail series. The crossover point is roughly exponential in -df (i.e., use Hill's method when `u > 2^(-df/0.654)`), which we evaluate via the binary exponent of `u` in order to avoid underflow for large `df`. + // NOTE: the Boost implementation tests `u_exp < df / 0.654`, which contradicts the stated intent (the tail series would never be selected); we implement the stated intent, which reproduces the behavior of earlier Boost versions: + fe = frexp( u ); + if ( fe[ 0 ] > 0.0 && fe[ 1 ] > df / -0.654 ) { result = inverseStudentsTHill( df, u ); } else { result = inverseStudentsTTailSeries( df, u ); @@ -179,9 +180,10 @@ function inverseStudentsT( df, u, v ) { result = inverseStudentsTTailSeries( df, u ); } } else { - // Use Hill's method except in the extreme tails where we use Shaw's tail series. The crossover point is roughly exponential in -df: - crossover = ldexp( 1.0, round( df / -0.654 ) ); - if ( u > crossover ) { + // Use Hill's method except in the extreme tails where we use Shaw's tail series. The crossover point is roughly exponential in -df (i.e., use Hill's method when `u > 2^(-df/0.654)`), which we evaluate via the binary exponent of `u` in order to avoid underflow for large `df`. + // NOTE: the Boost implementation tests `u_exp < df / 0.654`, which contradicts the stated intent (the tail series would never be selected); we implement the stated intent, which reproduces the behavior of earlier Boost versions: + fe = frexp( u ); + if ( fe[ 0 ] > 0.0 && fe[ 1 ] > df / -0.654 ) { result = inverseStudentsTHill( df, u ); } else { result = inverseStudentsTTailSeries( df, u ); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_body_series.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_body_series.js index f36bb787661f..b419367c6a5f 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_body_series.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_body_series.js @@ -18,10 +18,10 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. * * ```text -* Copyright John Maddock 2006. +* Copyright John Maddock 2007. * Copyright Paul A. Bristow 2007. * * Use, modification and distribution are subject to the diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_hill.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_hill.js index 287475680007..4bb39624420a 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_hill.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_hill.js @@ -18,10 +18,10 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_61_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. * * ```text -* Copyright John Maddock 2006. +* Copyright John Maddock 2007. * Copyright Paul A. Bristow 2007. * * Use, modification and distribution are subject to the diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_tail_series.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_tail_series.js index 95c00abe3244..cd4edc83a77d 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_tail_series.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/inverse_students_t_tail_series.js @@ -18,10 +18,10 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_61_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/t_distribution_inv.hpp}. The implementation has been modified for JavaScript. * * ```text -* Copyright John Maddock 2006. +* Copyright John Maddock 2007. * Copyright Paul A. Bristow 2007. * * Use, modification and distribution are subject to the diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/lower_gamma_series.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/lower_gamma_series.js deleted file mode 100644 index 5b0781e71db0..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/lower_gamma_series.js +++ /dev/null @@ -1,80 +0,0 @@ -/** -* @license Apache-2.0 -* -* Copyright (c) 2018 The Stdlib Authors. -* -* Licensed under the Apache License, Version 2.0 (the "License"); -* you may not use this file except in compliance with the License. -* You may obtain a copy of the License at -* -* http://www.apache.org/licenses/LICENSE-2.0 -* -* Unless required by applicable law or agreed to in writing, software -* distributed under the License is distributed on an "AS IS" BASIS, -* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -* See the License for the specific language governing permissions and -* limitations under the License. -* -* -* ## Notice -* -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_61_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. -* -* ```text -* Copyright John Maddock 2006-7, 2013-14. -* Copyright Paul A. Bristow 2007, 2013-14. -* Copyright Nikhar Agrawal 2013-14. -* Copyright Christopher Kormanyos 2013-14. -* -* Use, modification and distribution are subject to the -* Boost Software License, Version 1.0. (See accompanying file -* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) -* ``` -*/ - -'use strict'; - -// MODULES // - -var sumSeries = require( '@stdlib/math/base/tools/sum-series' ); -var lowerIncompleteGammaSeries = require( './lower_incomplete_gamma_series.js' ); - - -// VARIABLES // - -var opts = { - 'maxIter': 1000 -}; - - -// MAIN // - -/** -* Sums elements of the series expansion of the lower incomplete gamma function. -* -* ## Method -* -* - Multiply result by `(z^a)*(e^-z) / a` to get the full lower incomplete integral. -* - Divide by `tgamma(a)` to get the normalized value. -* -* @private -* @param {number} a - function parameter -* @param {number} z - function parameter -* @param {number} initialValue - initial value of the resulting sum -* @returns {number} sum of terms of lower gamma series -*/ -function lowerGammaSeries( a, z, initialValue ) { - var result; - var s; - - initialValue = initialValue || 0.0; - s = lowerIncompleteGammaSeries( a, z ); - opts.initialValue = initialValue; - result = sumSeries( s, opts ); - return result; -} - - -// EXPORTS // - -module.exports = lowerGammaSeries; diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/lower_incomplete_gamma_series.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/lower_incomplete_gamma_series.js deleted file mode 100644 index 46afc4bfbfeb..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/lower_incomplete_gamma_series.js +++ /dev/null @@ -1,68 +0,0 @@ -/** -* @license Apache-2.0 -* -* Copyright (c) 2018 The Stdlib Authors. -* -* Licensed under the Apache License, Version 2.0 (the "License"); -* you may not use this file except in compliance with the License. -* You may obtain a copy of the License at -* -* http://www.apache.org/licenses/LICENSE-2.0 -* -* Unless required by applicable law or agreed to in writing, software -* distributed under the License is distributed on an "AS IS" BASIS, -* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -* See the License for the specific language governing permissions and -* limitations under the License. -* -* -* ## Notice -* -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_61_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. -* -* ```text -* Copyright John Maddock 2006-7, 2013-14. -* Copyright Paul A. Bristow 2007, 2013-14. -* Copyright Nikhar Agrawal 2013-14. -* Copyright Christopher Kormanyos 2013-14. -* -* Use, modification and distribution are subject to the -* Boost Software License, Version 1.0. (See accompanying file -* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) -* ``` -*/ - -'use strict'; - -// MAIN // - -/** -* Creates a function to evaluate a series expansion of the incomplete gamma function. -* -* @private -* @param {number} a - function parameter -* @param {number} z - function parameter -* @returns {Function} series function -*/ -function lowerIncompleteGammaSeries( a, z ) { // eslint-disable-line id-length - var result = 1.0; - return next; - - /** - * Calculate the next term of the series. - * - * @private - * @returns {number} series expansion term - */ - function next() { - var r = result; - a += 1.0; - result *= z/a; - return r; - } -} - - -// EXPORTS // - -module.exports = lowerIncompleteGammaSeries; diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/main.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/main.js index 751187a3bde0..9bf1e064d13a 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/main.js @@ -1,5 +1,3 @@ -/* eslint-disable max-statements, max-lines */ - /** * @license Apache-2.0 * @@ -20,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. @@ -32,12 +30,15 @@ * ``` */ +/* eslint-disable max-statements, max-lines */ + 'use strict'; // MODULES // var evalpoly = require( '@stdlib/math/base/tools/evalpoly' ); var betainc = require( '@stdlib/math/base/special/betainc' ); +var gammaln = require( '@stdlib/math/base/special/gammaln' ); var expm1 = require( '@stdlib/math/base/special/expm1' ); var log1p = require( '@stdlib/math/base/special/log1p' ); var asin = require( '@stdlib/math/base/special/asin' ); @@ -51,8 +52,10 @@ var max = require( '@stdlib/math/base/special/max' ); var min = require( '@stdlib/math/base/special/min' ); var ln = require( '@stdlib/math/base/special/ln' ); var FLOAT64_MIN_NORM = require( '@stdlib/constants/float64/smallest-normal' ); +var FLOAT64_MAX = require( '@stdlib/constants/float64/max' ); var HALF_PI = require( '@stdlib/constants/float64/half-pi' ); var EPSILON = require( '@stdlib/constants/float64/eps' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); var findIBetaInvFromTDist = require( './find_ibeta_inv_from_t_dist.js' ); var temme1 = require( './temme1.js' ); var temme2 = require( './temme2.js' ); @@ -73,16 +76,23 @@ var terms = [ 0.0, 0.0, 0.0, 0.0, 0.0 ]; // WARNING: not thread safe // MAIN // /** -* Calculates the inverse of the incomplete beta function. +* Computes the inverse of the lower incomplete beta function. * -* @private * @param {PositiveNumber} a - function parameter * @param {PositiveNumber} b - function parameter * @param {Probability} p - function parameter -* @param {Probability} q - probability equal to `1 - p` +* @param {Probability} q - probability equal to `1-p` * @returns {Array} two-element array holding function value `y` and `1-y` +* +* @example +* var y = kernelBetaincinv( 3.0, 3.0, 0.2, 0.8 ); +* // returns [ ~0.327, ~0.673 ] +* +* @example +* var y = kernelBetaincinv( 1.0, 6.0, 0.4, 0.6 ); +* // returns [ ~0.082, ~0.918 ] */ -function ibetaInvImp( a, b, p, q ) { +function kernelBetaincinv( a, b, p, q ) { var digits; var invert; var lambda; @@ -245,6 +255,9 @@ function ibetaInvImp( a, b, p, q ) { bet = 0.0; if ( b < 2.0 ) { bet = beta( a, b ); + if ( bet === PINF ) { + bet = FLOAT64_MAX; + } } if ( bet === 0.0 ) { y = 1.0; @@ -252,10 +265,14 @@ function ibetaInvImp( a, b, p, q ) { y = pow( b*q*bet, 1.0/b ); x = 1.0 - y; } - } - if ( y > 1.0e-5 ) { - x = temme3( a, b, p, q ); - y = 1.0 - x; + if ( y > 1.0e-5 && min( a, b ) < 1000.0 ) { + x = temme3( a, b, p, q ); + y = 1.0 - x; + } else if ( y > 1.0e-5 && min( a, b ) > 1000.0 ) { + // All options have failed, so use the saddle point as a starting location: + x = max( a, b ) / ( a+b ); + y = min( a, b ) / ( a+b ); + } } } } @@ -284,7 +301,23 @@ function ibetaInvImp( a, b, p, q ) { invert = !invert; xs = 1.0 - xs; } - xg = pow( a*p*beta( a, b ), 1.0/a ); + if ( a < FLOAT64_MIN_NORM && b > FLOAT64_MIN_NORM ) { + // Nothing interesting is going on here: + if ( invert ) { + return [ 1.0, 0.0 ]; + } + return [ 0.0, 1.0 ]; + } + // The computation of `beta` may overflow to infinity, in which case we compute the estimate via logarithms: + bet = beta( a, b ); + if ( bet === PINF ) { + xg = exp( ( gammaln( a+1.0 ) + gammaln( b ) - gammaln( a+b ) + ln( p ) ) / a ); // eslint-disable-line max-len + if ( xg > 2.0/EPSILON ) { + xg = 2.0 / EPSILON; + } + } else { + xg = pow( a*p*bet, 1.0/a ); + } x = xg / ( 1.0+xg ); y = 1.0 / ( 1.0+xg ); @@ -354,8 +387,20 @@ function ibetaInvImp( a, b, p, q ) { p = tmp; invert = !invert; } - if ( pow( p, 1.0/a ) < 0.5 ) { + if ( a < FLOAT64_MIN_NORM ) { + // Avoid spurious overflows for denormalized `a`: + if ( p < 1.0 ) { + x = 1.0; + y = 0.0; + } else { + x = 0.0; + y = 1.0; + } + } else if ( pow( p, 1.0/a ) < 0.5 ) { x = pow( p*a*beta( a, b ), 1.0/a ); + if ( x > 1.0 || x === PINF ) { + x = 1.0; + } if ( x === 0.0 ) { x = FLOAT64_MIN_NORM; } @@ -365,6 +410,9 @@ function ibetaInvImp( a, b, p, q ) { else { // Model a distorted quarter circle: y = pow( 1.0-pow( p, b*beta( a, b ) ), 1.0/b ); + if ( y > 1.0 || y === PINF ) { + y = 1.0; + } if ( y === 0 ) { y = FLOAT64_MIN_NORM; } @@ -393,15 +441,7 @@ function ibetaInvImp( a, b, p, q ) { } // Lower bound for our search: We're not interested in denormalized answers as these tend to take up lots of iterations, given that we can't get accurate derivatives in this area (they tend to be infinite). if ( lower === 0 ) { - if ( invert ) { - // We're not interested in answers smaller than machine epsilon: - lower = EPSILON; - if ( x < lower ) { - x = lower; - } - } else { - lower = FLOAT64_MIN_NORM; - } + lower = FLOAT64_MIN_NORM; if ( x < lower ) { x = lower; } @@ -430,4 +470,4 @@ function ibetaInvImp( a, b, p, q ) { // EXPORTS // -module.exports = ibetaInvImp; +module.exports = kernelBetaincinv; diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/native.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/native.js new file mode 100644 index 000000000000..8954c7a7ec22 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/native.js @@ -0,0 +1,64 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var Float64Array = require( '@stdlib/array/float64' ); +var addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the inverse of the lower incomplete beta function. +* +* @private +* @param {PositiveNumber} a - function parameter +* @param {PositiveNumber} b - function parameter +* @param {Probability} p - function parameter +* @param {Probability} q - probability equal to `1-p` +* @returns {Float64Array} two-element array holding function value `y` and `1-y` +* +* @example +* var out = kernelBetaincinv( 3.0, 3.0, 0.2, 0.8 ); +* // returns [ ~0.327, ~0.673 ] +* +* @example +* var out = kernelBetaincinv( 3.0, 3.0, 0.4, 0.6 ); +* // returns [ ~0.446, ~0.554 ] +* +* @example +* var out = kernelBetaincinv( 1.0, 6.0, 0.4, 0.6 ); +* // returns [ ~0.082, ~0.918 ] +* +* @example +* var out = kernelBetaincinv( 1.0, 6.0, 0.8, 0.2 ); +* // returns [ ~0.235, ~0.765 ] +*/ +function kernelBetaincinv( a, b, p, q ) { + var out = new Float64Array( 2 ); + addon( a, b, p, q, out ); + return out; +} + + +// EXPORTS // + +module.exports = kernelBetaincinv; diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/newton_raphson.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/newton_raphson.js index 0ba075ded239..e0622cb7979d 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/newton_raphson.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/newton_raphson.js @@ -18,10 +18,11 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/tools/roots.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/tools/roots.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. +* Copyright Matt Borland 2024. * * Use, modification and distribution are subject to the * Boost Software License, Version 1.0. (See accompanying file @@ -45,15 +46,17 @@ var MAX_VALUE = require( '@stdlib/constants/float64/max' ); * Performs root finding via second order Newton-Raphson iteration. * * @private -* @param {Array} fun - two-element array of the function and its first derivative -* @param {number} guess - initial starting value. -* @param {number} min - minimum possible value for the result,used as initial lower bracket. -* @param {number} max - maximum possible value for the result, used as initial upper bracket. +* @param {Function} fun - function which returns the function value and its first derivative +* @param {number} guess - initial starting value +* @param {number} min - minimum possible value for the result, used as initial lower bracket +* @param {number} max - maximum possible value for the result, used as initial upper bracket * @param {PositiveInteger} digits - desired number of binary digits * @param {PositiveInteger} maxIter - maximum number of iterations * @returns {number} function value */ function newtonRaphsonIterate( fun, guess, min, max, digits, maxIter ) { + var maxRangeF; + var minRangeF; var f0last; var delta1; var delta2; @@ -61,6 +64,7 @@ function newtonRaphsonIterate( fun, guess, min, max, digits, maxIter ) { var result; var count; var delta; + var shift; var res; var f0; var f1; @@ -74,6 +78,10 @@ function newtonRaphsonIterate( fun, guess, min, max, digits, maxIter ) { delta1 = MAX_VALUE; delta2 = MAX_VALUE; + // We use these to sanity check that we do actually bracket a root; if we update both ends of the brackets and the function value has the same sign at both ends, then there is no root to be found: + maxRangeF = 0.0; + minRangeF = 0.0; + count = maxIter; do { f0last = f0; @@ -95,7 +103,7 @@ function newtonRaphsonIterate( fun, guess, min, max, digits, maxIter ) { } else { guess = min; } - f0last = fun( guess ); + f0last = fun( guess )[ 0 ]; delta = guess - result; } if ( sign(f0last) * sign(f0) < 0 ) { @@ -114,8 +122,16 @@ function newtonRaphsonIterate( fun, guess, min, max, digits, maxIter ) { delta = f0 / f1; } if ( abs(delta * 2.0) > abs(delta2) ) { - // Last two steps haven't converged, try bisection: - delta = ( delta > 0.0 ) ? (result-min) / 2.0 : (result-max) / 2.0; + // Last two steps haven't converged: + shift = ( delta > 0.0 ) ? (result-min) / 2.0 : (result-max) / 2.0; + if ( result !== 0.0 && abs(shift) > abs(result) ) { + delta = sign( delta ) * abs( result ); // Protect against huge jumps! + } else { + delta = shift; + } + // Reset delta1/delta2 so that this branch will *not* be taken on the next iteration: + delta1 = 3.0 * delta; + delta2 = 3.0 * delta; } guess = result; result -= delta; @@ -135,8 +151,15 @@ function newtonRaphsonIterate( fun, guess, min, max, digits, maxIter ) { // Update brackets: if ( delta > 0.0 ) { max = guess; + maxRangeF = f0; } else { min = guess; + minRangeF = f0; + } + // Sanity check that we bracket the root: + if ( maxRangeF * minRangeF > 0.0 ) { + // There appears to be no root to be found (the original C++ implementation raises an evaluation error; we instead return the current best guess): + return guess; } } while ( count && ( abs(result * factor) < abs(delta) ) ); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/root_finder.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/root_finder.js index 00f31339a9ae..92434e5b8a16 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/root_finder.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/root_finder.js @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_62_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. @@ -69,11 +69,13 @@ function temmeRootFinder( t, a ) { var y; y = 1.0 - x; + + // NOTE: the most recent Boost versions omit the following two guards (in favor of a debug assertion in the functor constructor); we retain them defensively, matching earlier Boost versions: if ( y === 0.0 ) { return [ -BIG, -BIG ]; } if ( x === 0.0 ) { - return [ -BIG, -BIG ]; + return [ -BIG, BIG ]; } f = ln( x ) + ( a * ln( y ) ) + t; f1 = ( 1.0 / x ) - ( a / y ); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme1.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme1.js index 2870c3001caa..ae07bc1ca417 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme1.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme1.js @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. @@ -55,7 +55,7 @@ var terms = [ 0.0, 0.0, 0.0, 0.0 ]; * * ## References * -* - Temme, N. M. 1992. "Incomplete Laplace Integrals: Uniform Asymptotic Expansion with Application to the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 1638–63. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). +* - Temme, N. M. 1992. "Asymptotic Inversion of the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 145–57. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). * * @private * @param {PositiveNumber} a - function parameter @@ -69,6 +69,7 @@ function temme1( a, b, z ) { var eta; var B2; var B3; + var x; var B; var c; @@ -122,9 +123,17 @@ function temme1( a, b, z ) { eta2 = eta * eta; c = -exp( -eta2 / 2.0 ); if ( eta2 === 0.0 ) { - return 0.5; + x = 0.5; + } else { + x = ( 1.0 + ( eta * sqrt( ( 1.0+c ) / eta2 ) ) ) / 2.0; } - return ( 1.0 + ( eta * sqrt( ( 1.0+c ) / eta2 ) ) ) / 2.0; + // The addition above may result in us being out by one ulp on either side of the boundary, so just check that we are in bounds and adjust as needed: + if ( x < 0.0 ) { + x = 0.0; + } else if ( x > 1.0 ) { + x = 1.0; + } + return x; } diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme2.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme2.js index cac92a7c38d7..3b7320f0758c 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme2.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme2.js @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. @@ -73,7 +73,7 @@ var terms = [ 0.0, 0.0, 0.0, 0.0 ]; * * ## References * -* - Temme, N. M. 1992. "Incomplete Laplace Integrals: Uniform Asymptotic Expansion with Application to the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 1638–63. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). +* - Temme, N. M. 1992. "Asymptotic Inversion of the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 145–57. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). * * @private * @param {number} z - function parameter @@ -127,7 +127,7 @@ function temme2( z, r, theta ) { workspace[ 0 ] = ((2.0*s2) - 1.0) / ( 3.0*sc ); workspace[ 1 ] = -polyval1( s2 ) / (36.0*sc2); workspace[ 2 ] = polyval2( s2 ) / (1620.0*sc3); - workspace[ 3 ] = polyval3( s2 ) / (6480.0*sc4); + workspace[ 3 ] = -polyval3( s2 ) / (6480.0*sc4); workspace[ 4 ] = polyval4( s2 ) / (90720.0*sc5); workspace[ 5 ] = 0.0; terms[ 1 ] = evalpoly( workspace, eta0 ); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme3.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme3.js index 7d6d6dfa597a..1569c61fd11c 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme3.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/temme3.js @@ -18,7 +18,7 @@ * * ## Notice * -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. +* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}. The implementation has been modified for JavaScript. * * ```text * Copyright John Maddock 2006. @@ -39,7 +39,7 @@ var gammaincinv = require( '@stdlib/math/base/special/gammaincinv' ); var ln = require( '@stdlib/math/base/special/ln' ); var sqrt = require( '@stdlib/math/base/special/sqrt' ); -var SMALLEST_SUBNORMAL = require( '@stdlib/constants/float64/smallest-subnormal' ); +var FLOAT64_MIN_NORM = require( '@stdlib/constants/float64/smallest-normal' ); var temmeRootFinder = require( './root_finder.js' ); var newtonRaphsonIterate = require( './newton_raphson.js' ); @@ -51,7 +51,7 @@ var newtonRaphsonIterate = require( './newton_raphson.js' ); * * ## References * -* - Temme, N. M. 1992. "Incomplete Laplace Integrals: Uniform Asymptotic Expansion with Application to the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 1638–63. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). +* - Temme, N. M. 1992. "Asymptotic Inversion of the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 145–57. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). * * @private * @param {PositiveNumber} a - function parameter @@ -154,13 +154,18 @@ function temme3( a, b, p, q ) { Many thanks to Prof Temme for clarifying this point. Therefore we'll just jump straight into Newton iterations to solve Eq 4.2 using these bounds, and simple bisection as the first guess, in practice this converges pretty quickly and we only need a few digits correct anyway: */ if ( eta <= 0 ) { - eta = SMALLEST_SUBNORMAL; + eta = FLOAT64_MIN_NORM; } u = eta - ( mu*ln(eta) ) + ( ( 1.0+mu ) * ln( 1.0+mu ) ) - mu; cross = 1.0 / ( 1.0+mu ); lower = (eta < mu) ? cross : 0.0; upper = (eta < mu) ? 1.0 : cross; x = (lower+upper) / 2.0; + + // Early exit for cases with numerical precision issues: + if ( cross === 0.0 || cross === 1.0 ) { + return cross; + } roots = temmeRootFinder( u, mu ); return newtonRaphsonIterate( roots, x, lower, upper, 32, 100 ); } diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/upper_gamma_fraction.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/upper_gamma_fraction.js deleted file mode 100644 index 9e912877e595..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/upper_gamma_fraction.js +++ /dev/null @@ -1,59 +0,0 @@ -/** -* @license Apache-2.0 -* -* Copyright (c) 2018 The Stdlib Authors. -* -* Licensed under the Apache License, Version 2.0 (the "License"); -* you may not use this file except in compliance with the License. -* You may obtain a copy of the License at -* -* http://www.apache.org/licenses/LICENSE-2.0 -* -* Unless required by applicable law or agreed to in writing, software -* distributed under the License is distributed on an "AS IS" BASIS, -* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -* See the License for the specific language governing permissions and -* limitations under the License. -* -* -* ## Notice -* -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_37_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. -* -* ```text -* (C) Copyright John Maddock 2006. -* (C) Copyright Paul A. Bristow 2007. -* -* Use, modification and distribution are subject to the -* Boost Software License, Version 1.0. (See accompanying file -* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) -* ``` -*/ - -'use strict'; - -// MODULES // - -var continuedFraction = require( '@stdlib/math/base/tools/continued-fraction' ); -var upperIncompleteGammaFract = require( './upper_incomplete_gamma_fract.js' ); - - -// MAIN // - -/** -* Evaluate the lower incomplete gamma integral via a series expansion and divide by gamma(z) to normalize. -* -* @private -* @param {number} a - function parameter -* @param {number} z - function parameter -* @returns {number} function value -*/ -function upperGammaFraction( a, z ) { - var f = upperIncompleteGammaFract( a, z ); - return 1.0 / ( z - a + 1.0 + continuedFraction( f ) ); -} - - -// EXPORTS // - -module.exports = upperGammaFraction; diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/upper_incomplete_gamma_fract.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/upper_incomplete_gamma_fract.js deleted file mode 100644 index 0fd0301b8eb3..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/lib/upper_incomplete_gamma_fract.js +++ /dev/null @@ -1,68 +0,0 @@ -/** -* @license Apache-2.0 -* -* Copyright (c) 2018 The Stdlib Authors. -* -* Licensed under the Apache License, Version 2.0 (the "License"); -* you may not use this file except in compliance with the License. -* You may obtain a copy of the License at -* -* http://www.apache.org/licenses/LICENSE-2.0 -* -* Unless required by applicable law or agreed to in writing, software -* distributed under the License is distributed on an "AS IS" BASIS, -* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -* See the License for the specific language governing permissions and -* limitations under the License. -* -* -* ## Notice -* -* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_61_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. -* -* ```text -* Copyright John Maddock 2006-7, 2013-14. -* Copyright Paul A. Bristow 2007, 2013-14. -* Copyright Nikhar Agrawal 2013-14. -* Copyright Christopher Kormanyos 2013-14. -* -* Use, modification and distribution are subject to the -* Boost Software License, Version 1.0. (See accompanying file -* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) -* ``` -*/ - -'use strict'; - -// MAIN // - -/** -* Creates a function to evaluate a series expansion of the upper incomplete gamma fraction. -* -* @private -* @param {number} a - function parameter -* @param {number} z - function parameter -* @returns {Function} series function -*/ -function upperIncompleteGammaFract( a, z ) { - var k = 0; - z = z - a + 1.0; - return next; - - /** - * Calculate the next term of the series. - * - * @private - * @returns {Array} series expansion terms - */ - function next() { - k += 1; - z += 2.0; - return [ k * (a - k), z ]; - } -} - - -// EXPORTS // - -module.exports = upperIncompleteGammaFract; diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/manifest.json b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/manifest.json new file mode 100644 index 000000000000..3ac1e2e67927 --- /dev/null +++ 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"@stdlib/constants/float64/sqrt-two" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/acos", + "@stdlib/math/base/special/asin", + "@stdlib/math/base/special/beta", + "@stdlib/math/base/special/cbrt", + "@stdlib/math/base/special/cos", + "@stdlib/math/base/special/erfcinv", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/frexp", + "@stdlib/math/base/special/gamma-delta-ratio", + "@stdlib/math/base/special/gammaincinv", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/kernel-betainc", + "@stdlib/math/base/special/ldexp", + "@stdlib/math/base/special/ln", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/signum", + "@stdlib/math/base/special/sin", + "@stdlib/math/base/special/sqrt", + "@stdlib/number/float64/base/from-words", + "@stdlib/number/float64/base/to-words", + "@stdlib/number/float64/base/ulp-difference", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/half-pi", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/smallest-normal", + "@stdlib/constants/float64/sqrt-two" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/random/base/randu", + "@stdlib/math/base/special/abs", + "@stdlib/math/base/special/acos", + "@stdlib/math/base/special/asin", + "@stdlib/math/base/special/beta", + "@stdlib/math/base/special/cbrt", + "@stdlib/math/base/special/cos", + "@stdlib/math/base/special/erfcinv", + "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/floor", + "@stdlib/math/base/special/frexp", + "@stdlib/math/base/special/gamma-delta-ratio", + "@stdlib/math/base/special/gammaincinv", + "@stdlib/math/base/special/gammaln", + "@stdlib/math/base/special/kernel-betainc", + "@stdlib/math/base/special/ldexp", + "@stdlib/math/base/special/ln", + "@stdlib/math/base/special/log1p", + "@stdlib/math/base/special/max", + "@stdlib/math/base/special/min", + "@stdlib/math/base/special/pow", + "@stdlib/math/base/special/signum", + "@stdlib/math/base/special/sin", + "@stdlib/math/base/special/sqrt", + "@stdlib/number/float64/base/from-words", + "@stdlib/number/float64/base/to-words", + "@stdlib/number/float64/base/ulp-difference", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/half-pi", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/pinf", + "@stdlib/constants/float64/pi", + "@stdlib/constants/float64/smallest-normal", + "@stdlib/constants/float64/sqrt-two" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/package.json b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/package.json index 2405a0594d4b..06e0298ef654 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/package.json +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/package.json @@ -1,7 +1,7 @@ { "name": "@stdlib/math/base/special/kernel-betaincinv", "version": "0.0.0", - "description": "Inverse incomplete beta function.", + "description": "Inverse of the lower incomplete beta function.", "license": "Apache-2.0 AND BSL-1.0", "author": { "name": "The Stdlib Authors", @@ -14,12 +14,15 @@ } ], "main": "./lib", + "gypfile": true, "directories": { "benchmark": "./benchmark", "doc": "./docs", "example": "./examples", + "include": "./include", "lib": "./lib", "scripts": "./scripts", + "src": "./src", "test": "./test" }, "types": "./docs/types", diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/scripts/evalpoly.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/scripts/evalpoly.js index 108a622d67c6..4320adb596bf 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/scripts/evalpoly.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/scripts/evalpoly.js @@ -24,10 +24,15 @@ // MODULES // var resolve = require( 'path' ).resolve; +var readFileSync = require( '@stdlib/fs/read-file' ).sync; var writeFileSync = require( '@stdlib/fs/write-file' ).sync; var currentYear = require( '@stdlib/time/current-year' ); +var substringBefore = require( '@stdlib/string/substring-before' ); +var substringAfter = require( '@stdlib/string/substring-after' ); +var format = require( '@stdlib/string/format' ); var licenseHeader = require( '@stdlib/_tools/licenses/header' ); var compile = require( '@stdlib/math/base/tools/evalpoly-compile' ); +var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' ); // VARIABLES // @@ -208,6 +213,33 @@ var header = licenseHeader( 'Apache-2.0', 'js', { header += '\n/* This is a generated file. Do not edit directly. */\n'; +// FUNCTIONS // + +/** +* Inserts a compiled function into file content. +* +* @private +* @param {string} text - source content +* @param {string} id - function identifier +* @param {string} str - function string +* @returns {string} updated content +*/ +function insert( text, id, str ) { + var before; + var after; + var begin; + var end; + + begin = '// BEGIN: '+id; + end = '// END: '+id; + + before = substringBefore( text, begin ); + after = substringAfter( text, end ); + + return format( '%s// BEGIN: %s\n\n%s\n%s%s', before, id, str, end, after ); +} + + // MAIN // /** @@ -218,7 +250,9 @@ header += '\n/* This is a generated file. Do not edit directly. */\n'; function main() { var fpath; var coefs; + var copts; var opts; + var file; var str; var i; @@ -255,6 +289,22 @@ function main() { str = header + compile( coefs[i][0] ); writeFileSync( fpath, str, opts ); } + + copts = { + 'dtype': 'double', + 'name': '' + }; + + fpath = resolve( __dirname, '..', 'src', 'main.c' ); + file = readFileSync( fpath, opts ); + + for ( i = 0; i < coefs.length; i++ ) { + copts.name = 'polyval_'+coefs[i][1]; + str = compileC( coefs[i][0], copts ); + file = insert( file, copts.name, str ); + } + + writeFileSync( fpath, file, opts ); } main(); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/Makefile b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/Makefile new file mode 100644 index 000000000000..2caf905cedbe --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + + +# RULES # + +#/ +# Removes generated files for building an add-on. +# +# @example +# make clean-addon +#/ +clean-addon: + $(QUIET) -rm -f *.o *.node + +.PHONY: clean-addon + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: clean-addon + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/addon.c b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/addon.c new file mode 100644 index 000000000000..2318b00d509f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/addon.c @@ -0,0 +1,44 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/kernel_betaincinv.h" +#include "stdlib/napi/argv.h" +#include "stdlib/napi/argv_double.h" +#include "stdlib/napi/argv_float64array.h" +#include "stdlib/napi/export.h" +#include + +/** +* Receives JavaScript callback invocation data. +* +* @param env environment under which the function is invoked +* @param info callback data +* @return Node-API value +*/ +static napi_value addon( napi_env env, napi_callback_info info ) { + STDLIB_NAPI_ARGV( env, info, argv, argc, 5 ); + STDLIB_NAPI_ARGV_DOUBLE( env, a, argv, 0 ); + STDLIB_NAPI_ARGV_DOUBLE( env, b, argv, 1 ); + STDLIB_NAPI_ARGV_DOUBLE( env, p, argv, 2 ); + STDLIB_NAPI_ARGV_DOUBLE( env, q, argv, 3 ); + STDLIB_NAPI_ARGV_FLOAT64ARRAY( env, y, ylen, argv, 4 ); + stdlib_base_kernel_betaincinv( a, b, p, q, &y[ 0 ], &y[ 1 ] ); + return NULL; +} + +STDLIB_NAPI_MODULE_EXPORT_FCN( addon ) diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/main.c b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/main.c new file mode 100644 index 000000000000..d9bb5bb9862e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/src/main.c @@ -0,0 +1,2325 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +* +* +* ## Notice +* +* The original C++ code and copyright notice are from the Boost library ([ibeta_inverse.hpp]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/ibeta_inverse.hpp}, [t_distribution_inv.hpp]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/special_functions/detail/t_distribution_inv.hpp}, and [roots.hpp]{@link http://www.boost.org/doc/libs/1_92_0/boost/math/tools/roots.hpp}). The implementation has been modified according to stdlib conventions. +* +* ```text +* Copyright John Maddock 2006. +* Copyright Paul A. Bristow 2007. +* Copyright Matt Borland 2024. +* +* Use, modification and distribution are subject to the +* Boost Software License, Version 1.0. (See accompanying file +* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) +* ``` +*/ + +#include "stdlib/math/base/special/kernel_betaincinv.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/constants/float64/half_pi.h" +#include "stdlib/constants/float64/max.h" +#include "stdlib/constants/float64/pi.h" +#include "stdlib/constants/float64/pinf.h" +#include "stdlib/constants/float64/smallest_normal.h" +#include "stdlib/constants/float64/sqrt_two.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/math/base/special/acos.h" +#include "stdlib/math/base/special/asin.h" +#include "stdlib/math/base/special/beta.h" +#include "stdlib/math/base/special/cbrt.h" +#include "stdlib/math/base/special/cos.h" +#include "stdlib/math/base/special/erfcinv.h" +#include "stdlib/math/base/special/exp.h" +#include "stdlib/math/base/special/expm1.h" +#include "stdlib/math/base/special/floor.h" +#include "stdlib/math/base/special/frexp.h" +#include "stdlib/math/base/special/gamma_delta_ratio.h" +#include "stdlib/math/base/special/gammaincinv.h" +#include "stdlib/math/base/special/gammaln.h" +#include "stdlib/math/base/special/kernel_betainc.h" +#include "stdlib/math/base/special/ldexp.h" +#include "stdlib/math/base/special/ln.h" +#include "stdlib/math/base/special/log1p.h" +#include "stdlib/math/base/special/max.h" +#include "stdlib/math/base/special/min.h" +#include "stdlib/math/base/special/pow.h" +#include "stdlib/math/base/special/signum.h" +#include "stdlib/math/base/special/sin.h" +#include "stdlib/math/base/special/sqrt.h" +#include "stdlib/number/float64/base/from_words.h" +#include "stdlib/number/float64/base/to_words.h" +#include "stdlib/number/float64/base/ulp_difference.h" +#include +#include + +static const double EPSILON = STDLIB_CONSTANT_FLOAT64_EPS; +static const double HALF_PI = STDLIB_CONSTANT_FLOAT64_HALF_PI; +static const double FLOAT64_MAX = STDLIB_CONSTANT_FLOAT64_MAX; +static const double PI = STDLIB_CONSTANT_FLOAT64_PI; +static const double FLOAT64_MIN_NORM = STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL; +static const double PINF = STDLIB_CONSTANT_FLOAT64_PINF; +static const double SQRT2 = STDLIB_CONSTANT_FLOAT64_SQRT2; + +// Maximum tolerable search bound (see `root_finder.js`): +static const double BIG = STDLIB_CONSTANT_FLOAT64_MAX / 4.0; + +// Degrees-of-freedom threshold (see `inverse_students_t.js`): +static const double DF_THRESHOLD = 0x10000000; // 2^28 + +// Constant used when finding the inverse of the Student's t-distribution via Hill's approach (JS: `C` in `inverse_students_t.js`): +static const double CONST_C = 0.85498797333834849467655443627193; + +// Number of binary digits which determines the tolerance for Halley iteration (see `main.js`): +static const int32_t DIGITS = 32; + +// Maximum number of iterations when performing Halley iteration (see `main.js`): +static const int32_t MAX_ITERATIONS = 1000; + +/* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ + +// BEGIN: polyval_co1 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co1( const double x ) { + return -1.0 + (x * (-5.0 + (x * 5.0))); +} + +// END: polyval_co1 + +// BEGIN: polyval_co2 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co2( const double x ) { + return 1.0 + (x * (21.0 + (x * (-69.0 + (x * 46.0))))); +} + +// END: polyval_co2 + +// BEGIN: polyval_co3 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co3( const double x ) { + return 7.0 + (x * (-2.0 + (x * (33.0 + (x * (-62.0 + (x * 31.0))))))); +} + +// END: polyval_co3 + +// BEGIN: polyval_co4 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co4( const double x ) { + return 25.0 + (x * (-52.0 + (x * (-17.0 + (x * (88.0 + (x * (-115.0 + (x * 46.0))))))))); +} + +// END: polyval_co4 + +// BEGIN: polyval_co5 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co5( const double x ) { + return 7.0 + (x * (12.0 + (x * (-78.0 + (x * 52.0))))); +} + +// END: polyval_co5 + +// BEGIN: polyval_co6 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co6( const double x ) { + return -7.0 + (x * (2.0 + (x * (183.0 + (x * (-370.0 + (x * 185.0))))))); +} + +// END: polyval_co6 + +// BEGIN: polyval_co7 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co7( const double x ) { + return -533.0 + (x * (776.0 + (x * (-1835.0 + (x * (10240.0 + (x * (-13525.0 + (x * 5410.0))))))))); +} + +// END: polyval_co7 + +// BEGIN: polyval_co8 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co8( const double x ) { + return -1579.0 + (x * (3747.0 + (x * (-3372.0 + (x * (-15821.0 + (x * (45588.0 + (x * (-45213.0 + (x * 15071.0))))))))))); +} + +// END: polyval_co8 + +// BEGIN: polyval_co9 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co9( const double x ) { + return 449.0 + (x * (-1259.0 + (x * (-769.0 + (x * (6686.0 + (x * (-9260.0 + (x * 3704.0))))))))); +} + +// END: polyval_co9 + +// BEGIN: polyval_co10 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co10( const double x ) { + return 63149.0 + (x * (-151557.0 + (x * (140052.0 + (x * (-727469.0 + (x * (2239932.0 + (x * (-2251437.0 + (x * 750479.0))))))))))); +} + +// END: polyval_co10 + +// BEGIN: polyval_co11 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co11( const double x ) { + return 29233.0 + (x * (-78755.0 + (x * (105222.0 + (x * (146879.0 + (x * (-1602610.0 + (x * (3195183.0 + (x * (-2554139.0 + (x * 729754.0))))))))))))); +} + +// END: polyval_co11 + +// BEGIN: polyval_co12 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co12( const double x ) { + return 1.0 + (x * (-13.0 + (x * 13.0))); +} + +// END: polyval_co12 + +// BEGIN: polyval_co13 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co13( const double x ) { + return 1.0 + (x * (21.0 + (x * (-69.0 + (x * 46.0))))); +} + +// END: polyval_co13 + +// BEGIN: polyval_co14 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co14( const double x ) { + return 0.16666666666666666 + (x * 0.16666666666666666); +} + +// END: polyval_co14 + +// BEGIN: polyval_co15 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co15( const double x ) { + return 0.058333333333333334 + (x * (0.06666666666666667 + (x * 0.008333333333333333))); +} + +// END: polyval_co15 + +// BEGIN: polyval_co16 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co16( const double x ) { + return 0.0251984126984127 + (x * (0.026785714285714284 + (x * (0.0017857142857142857 + (x * 0.0001984126984126984))))); +} + +// END: polyval_co16 + +// BEGIN: polyval_co17 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co17( const double x ) { + return 0.012039792768959435 + (x * (0.010559964726631394 + (x * (-0.0011078042328042327 + (x * (0.0003747795414462081 + (x * 0.0000027557319223985893))))))); +} + +// END: polyval_co17 + +// BEGIN: polyval_co18 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co18( const double x ) { + return 0.003837005972422639 + (x * (0.00610392115600449 + (x * (-0.0016095979637646305 + (x * (0.0005945867404200738 + (x * (-0.00006270542728876062 + (x * 2.505210838544172e-8))))))))); +} + +// END: polyval_co18 + +// BEGIN: polyval_co19 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co19( const double x ) { + return 0.0032177478835464946 + (x * (0.0010898206731540065 + (x * (-0.0012579159844784845 + (x * (0.0006908420797309686 + (x * (-0.00016376804137220805 + (x * (0.0000154012654012654 + (x * 1.6059043836821613e-10))))))))))); +} + +// END: polyval_co19 + +// BEGIN: polyval_co20 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co20( const double x ) { + return 0.001743826229834001 + (x * (0.00003353097688001788 + (x * (-0.0007624513544032393 + (x * (0.0006451304695145635 + (x * (-0.000249472580470431 + (x * (0.000049255746366361444 + (x * (-0.0000039851014346715405 + (x * 7.647163731819816e-13))))))))))))); +} + +// END: polyval_co20 + +// BEGIN: polyval_co21 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co21( const double x ) { + return 0.0009647274732138864 + (x * (-0.0003110108632631878 + (x * (-0.00036307660358786886 + (x * (0.0005140660578834113 + (x * (-0.00029133414466938067 + (x * (0.00009086710793521991 + (x * (-0.000015303004486655377 + (x * (0.0000010914179173496788 + (x * 2.8114572543455206e-15))))))))))))))); +} + +// END: polyval_co21 + +// BEGIN: polyval_co22 + +/** +* Evaluates a polynomial. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double polyval_co22( const double x ) { + return 0.0005422926281312969 + (x * (-0.0003694266780000966 + (x * (-0.00010230378073700413 + (x * (0.00035764655430568635 + (x * (-0.00028690924218514614 + (x * (0.00012645437628698076 + (x * (-0.000033202652391372056 + (x * (0.000004890304529197534 + (x * (-3.123956959982987e-7 + (x * 8.22063524662433e-18))))))))))))))))); +} + +// END: polyval_co22 + +/* End auto-generated functions. */ + +/** +* Evaluates a polynomial using double-precision floating-point arithmetic. +* +* ## Notes +* +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param c polynomial coefficients sorted in ascending degree +* @param len number of coefficients +* @param x value at which to evaluate the polynomial +* @return evaluated polynomial +*/ +static double evalpoly( const double *c, const int32_t len, const double x ) { + int32_t i; + double p; + + i = len; + if ( i < 2 || x == 0.0 ) { + return ( i == 0 ) ? 0.0 : c[ 0 ]; + } + i -= 1; + p = ( c[ i ] * x ) + c[ i-1 ]; + i -= 2; + while ( i >= 0 ) { + p = ( p * x ) + c[ i ]; + i -= 1; + } + return p; +} + +/** +* Returns the next representable double-precision floating-point number greater than the input value. +* +* ## Notes +* +* - The input value is assumed to be a nonnegative finite number, as these are the only values arising in the root-finding brackets of this file. +* +* @param x input value +* @return next representable value toward positive infinity +*/ +static double floatNext( const double x ) { + uint32_t high; + uint32_t low; + double out; + + stdlib_base_float64_to_words( x, &high, &low ); + if ( low == 0xffffffff ) { + high += 1; + low = 0; + } else { + low += 1; + } + stdlib_base_float64_from_words( high, low, &out ); + return out; +} + +/** +* Returns the next representable double-precision floating-point number less than the input value. +* +* ## Notes +* +* - The input value is assumed to be a positive finite number, as these are the only values arising in the root-finding brackets of this file. +* +* @param x input value +* @return next representable value toward negative infinity +*/ +static double floatPrior( const double x ) { + uint32_t high; + uint32_t low; + double out; + + stdlib_base_float64_to_words( x, &high, &low ); + if ( low == 0 ) { + high -= 1; + low = 0xffffffff; + } else { + low -= 1; + } + stdlib_base_float64_from_words( high, low, &out ); + return out; +} + +/** +* Helper function used by root finding code to convert `eta` to `x`. +* +* ## Notes +* +* - The function writes the function value and its first derivative to the two-element output array `out`. +* +* @param t first parameter +* @param a second parameter +* @param x function value +* @param out output array +*/ +static void temmeRoots( const double t, const double a, const double x, double *out ) { + double f1; + double f; + double y; + + y = 1.0 - x; + + // NOTE: the most recent Boost versions omit the following two guards (in favor of a debug assertion in the functor constructor); we retain them defensively, matching earlier Boost versions: + if ( y == 0.0 ) { + out[ 0 ] = -BIG; + out[ 1 ] = -BIG; + return; + } + if ( x == 0.0 ) { + out[ 0 ] = -BIG; + out[ 1 ] = BIG; + return; + } + f = stdlib_base_ln( x ) + ( a * stdlib_base_ln( y ) ) + t; + f1 = ( 1.0 / x ) - ( a / y ); + out[ 0 ] = f; + out[ 1 ] = f1; + return; +} + +/** +* Calculates the roots of the (upper or lower) incomplete beta function together with its first and second derivatives. +* +* ## Notes +* +* - The function writes the function value and its first and second derivatives to the three-element output array `out`. +* +* @param a function parameter +* @param b function parameter +* @param target probability value +* @param invert boolean indicating whether to find the roots of the upper or lower incomplete beta function +* @param x input value +* @param out output array +*/ +static void ibetaRoots( const double a, const double b, const double target, const bool invert, const double x, double *out ) { + double buf[ 2 ]; + double f1; + double f2; + double xc; + double f; + double y; + + xc = x; + y = 1.0 - xc; + + buf[ 0 ] = 0.0; + buf[ 1 ] = 0.0; + stdlib_base_kernel_betainc( xc, a, b, true, invert, &buf[ 0 ], &buf[ 1 ] ); + f = buf[ 0 ] - target; + f1 = buf[ 1 ]; + if ( invert ) { + f1 = -f1; + } + if ( y == 0.0 ) { + y = FLOAT64_MIN_NORM * 64.0; + } + if ( xc == 0.0 ) { + xc = FLOAT64_MIN_NORM * 64.0; + } + f2 = f1 * ( -( y * a ) + ( ( b - 2.0 ) * xc ) + 1.0 ); + if ( stdlib_base_abs( f2 ) < y * xc * FLOAT64_MAX ) { + f2 /= ( y * xc ); + } + if ( invert ) { + f2 = -f2; + } + // Make sure we don't have a zero derivative: + if ( f1 == 0.0 ) { + f1 = ( ( invert ) ? -1.0 : 1.0 ) * FLOAT64_MIN_NORM * 64.0; + } + out[ 0 ] = f; + out[ 1 ] = f1; + out[ 2 ] = f2; + return; +} + +/** +* Performs root finding via second order Newton-Raphson iteration. +* +* ## Notes +* +* - In the original Boost/JavaScript implementations, the routine accepts a functor returning a two-element array of the function and its first derivative. As the functor is always `temmeRoots`, the functor parameters `t` and `a` are passed directly. +* - When no root can be bracketed, the original C++ implementation raises an evaluation error; this implementation instead returns the current best guess. +* +* @param t first `temmeRoots` parameter +* @param a second `temmeRoots` parameter +* @param guess initial starting value +* @param minimum minimum possible value for the result, used as initial lower bracket +* @param maximum maximum possible value for the result, used as initial upper bracket +* @param digits desired number of binary digits +* @param maxIter maximum number of iterations +* @return function value +*/ +static double newtonRaphsonIterate( const double t, const double a, const double guess, const double minimum, const double maximum, const int32_t digits, const int32_t maxIter ) { + double maxRangeF; + double minRangeF; + double res[ 2 ]; + double f0last; + double delta1; + double delta2; + double factor; + double result; + double guessc; + int32_t count; + double delta; + double shift; + double min; + double max; + double f0; + double f1; + + guessc = guess; + min = minimum; + max = maximum; + + f0 = 0.0; + f0last = 0.0; // cppcheck-suppress unreadVariable + result = guessc; + + factor = stdlib_base_ldexp( 1.0, 1 - digits ); + delta = FLOAT64_MAX; + delta1 = FLOAT64_MAX; + delta2 = FLOAT64_MAX; // cppcheck-suppress unreadVariable + + // We use these to sanity check that we do actually bracket a root; if we update both ends of the brackets and the function value has the same sign at both ends, then there is no root to be found: + maxRangeF = 0.0; + minRangeF = 0.0; + + count = maxIter; + do { + f0last = f0; + delta2 = delta1; + delta1 = delta; + temmeRoots( t, a, result, res ); + f0 = res[ 0 ]; + f1 = res[ 1 ]; + count -= 1; + if ( f0 == 0.0 ) { + break; + } + if ( f1 == 0.0 ) { + // Oops zero derivative!!! + if ( f0last == 0.0 ) { + // Must be the first iteration, pretend that we had a previous one at either min or max: + if ( result == min ) { + guessc = max; + } else { + guessc = min; + } + temmeRoots( t, a, guessc, res ); + f0last = res[ 0 ]; + delta = guessc - result; + } + if ( stdlib_base_signum( f0last ) * stdlib_base_signum( f0 ) < 0.0 ) { + // We've crossed over so move in opposite direction to last step: + if ( delta < 0.0 ) { + delta = ( result - min ) / 2.0; + } else { + delta = ( result - max ) / 2.0; + } + } else if ( delta < 0.0 ) { + delta = ( result - max ) / 2.0; + } else { + delta = ( result - min ) / 2.0; + } + } else { + delta = f0 / f1; + } + if ( stdlib_base_abs( delta * 2.0 ) > stdlib_base_abs( delta2 ) ) { + // Last two steps haven't converged: + shift = ( delta > 0.0 ) ? ( result - min ) / 2.0 : ( result - max ) / 2.0; + if ( result != 0.0 && stdlib_base_abs( shift ) > stdlib_base_abs( result ) ) { + delta = stdlib_base_signum( delta ) * stdlib_base_abs( result ); // Protect against huge jumps! + } else { + delta = shift; + } + // Reset delta1/delta2 so that this branch will *not* be taken on the next iteration: + delta1 = 3.0 * delta; + delta2 = 3.0 * delta; // cppcheck-suppress unreadVariable + } + guessc = result; + result -= delta; + if ( result <= min ) { + delta = 0.5 * ( guessc - min ); + result = guessc - delta; + if ( result == min || result == max ) { + break; + } + } else if ( result >= max ) { + delta = 0.5 * ( guessc - max ); + result = guessc - delta; + if ( result == min || result == max ) { + break; + } + } + // Update brackets: + if ( delta > 0.0 ) { + max = guessc; + maxRangeF = f0; + } else { + min = guessc; + minRangeF = f0; + } + // Sanity check that we bracket the root: + if ( maxRangeF * minRangeF > 0.0 ) { + // There appears to be no root to be found (the original C++ implementation raises an evaluation error; we instead return the current best guess): + return guessc; + } + } + while ( count && ( stdlib_base_abs( result * factor ) < stdlib_base_abs( delta ) ) ); + + return result; +} + +/** +* Moves the current best guess toward the upper bracket until the root is bracketed, updating the brackets along the way. +* +* @param a function parameter of the incomplete beta function +* @param b function parameter of the incomplete beta function +* @param target probability value +* @param invert boolean indicating whether to find the roots of the upper or lower incomplete beta function +* @param x current best guess +* @param fx function value at the position from which bracketing begins +* @param min pointer to the lower bracket +* @param max pointer to the upper bracket +* @param count pointer to the remaining number of iterations +* @return step which should be subtracted from the current best guess +*/ +static double bracketRootTowardsMax( const double a, const double b, const double target, const bool invert, const double x, const double fx, double *min, double *max, int32_t *count ); + +/** +* Moves the current best guess toward the lower bracket until the root is bracketed, updating the brackets along the way. +* +* @param a function parameter of the incomplete beta function +* @param b function parameter of the incomplete beta function +* @param target probability value +* @param invert boolean indicating whether to find the roots of the upper or lower incomplete beta function +* @param x current best guess +* @param fx function value at the position from which bracketing begins +* @param min pointer to the lower bracket +* @param max pointer to the upper bracket +* @param count pointer to the remaining number of iterations +* @return step which should be subtracted from the current best guess +*/ +static double bracketRootTowardsMin( const double a, const double b, const double target, const bool invert, const double x, const double fx, double *min, double *max, int32_t *count ) { + double multiplier; + double res[ 3 ]; + double guess0; + double frac; + int32_t e; + double xc; + double fc; + + if ( *count < 2 ) { + // Not enough iterations left to do anything! + return x - ( ( *max + *min ) / 2.0 ); + } + // Move `x` towards the lower bracket until we bracket the root, updating the brackets as we go: + stdlib_base_frexp( x / *min, &frac, &e ); + if ( e < 0 ) { + e = -e; + } + guess0 = x; + xc = x; + multiplier = ( e < 64 ) ? 2.0 : stdlib_base_ldexp( 1.0, e / 32 ); + fc = fx; + *count -= 1; + if ( stdlib_base_abs( *min ) < stdlib_base_abs( *max ) ) { + while ( *count != 0 && ( ( fc < 0.0 ) == ( fx < 0.0 ) ) ) { + *max = xc; + xc /= multiplier; + if ( xc < *min ) { + xc = *min; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + ibetaRoots( a, b, target, invert, xc, res ); + fc = res[ 0 ]; + *count -= 1; + } + } else { + // If the brackets are negative we have to multiply to head towards the lower bracket: + while ( *count != 0 && ( ( fc < 0.0 ) == ( fx < 0.0 ) ) ) { + *max = xc; + xc *= multiplier; + if ( xc < *min ) { + xc = *min; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + ibetaRoots( a, b, target, invert, xc, res ); + fc = res[ 0 ]; + *count -= 1; + } + } + if ( *count != 0 ) { + *min = xc; + if ( multiplier > 16.0 ) { + return ( guess0 - xc ) + bracketRootTowardsMax( a, b, target, invert, xc, fc, min, max, count ); + } + } + return guess0 - ( ( *max + *min ) / 2.0 ); +} + +static double bracketRootTowardsMax( const double a, const double b, const double target, const bool invert, const double x, const double fx, double *min, double *max, int32_t *count ) { + double multiplier; + double res[ 3 ]; + double guess0; + double frac; + int32_t e; + double xc; + double fc; + + if ( *count < 2 ) { + // Not enough iterations left to do anything! + return x - ( ( *max + *min ) / 2.0 ); + } + // Move `x` towards the upper bracket until we bracket the root, updating the brackets as we go: + stdlib_base_frexp( *max / x, &frac, &e ); + if ( e < 0 ) { + e = -e; + } + guess0 = x; + xc = x; + multiplier = ( e < 64 ) ? 2.0 : stdlib_base_ldexp( 1.0, e / 32 ); + fc = fx; + *count -= 1; + if ( stdlib_base_abs( *min ) < stdlib_base_abs( *max ) ) { + while ( *count != 0 && ( ( fc < 0.0 ) == ( fx < 0.0 ) ) ) { + *min = xc; + xc *= multiplier; + if ( xc > *max ) { + xc = *max; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + ibetaRoots( a, b, target, invert, xc, res ); + fc = res[ 0 ]; + *count -= 1; + } + } else { + // If the brackets are negative we have to divide to head towards the upper bracket: + while ( *count != 0 && ( ( fc < 0.0 ) == ( fx < 0.0 ) ) ) { + *min = xc; + xc /= multiplier; + if ( xc > *max ) { + xc = *max; + fc = -fc; // there must be a change of sign! + break; + } + multiplier *= ( e > 1024 ) ? 8.0 : 2.0; + ibetaRoots( a, b, target, invert, xc, res ); + fc = res[ 0 ]; + *count -= 1; + } + } + if ( *count != 0 ) { + *max = xc; + if ( multiplier > 16.0 ) { + return ( guess0 - xc ) + bracketRootTowardsMin( a, b, target, invert, xc, fc, min, max, count ); + } + } + return guess0 - ( ( *max + *min ) / 2.0 ); +} + +/** +* Performs root finding via third order Halley iteration. +* +* ## Notes +* +* - In the original Boost/JavaScript implementations, the routine accepts a functor returning a three-element array of the function and its first two derivatives. As the functor is always `ibetaRoots`, the functor parameters `a`, `b`, `target`, and `invert` are passed directly. +* - When no root can be bracketed, the original C++ implementation raises an evaluation error; this implementation instead returns the current best guess. +* +* @param a function parameter of the incomplete beta function +* @param b function parameter of the incomplete beta function +* @param target probability value +* @param invert boolean indicating whether to find the roots of the upper or lower incomplete beta function +* @param guess initial starting value +* @param minimum minimum possible value for the result, used as initial lower bracket +* @param maximum maximum possible value for the result, used as initial upper bracket +* @param digits desired number of binary digits +* @param maxIter maximum number of iterations +* @return function value +*/ +static double halleyIterate( const double a, const double b, const double target, const bool invert, const double guess, const double minimum, const double maximum, const int32_t digits, const int32_t maxIter ) { + double convergence; + bool outOfBounds; + double maxRangeF; + double minRangeF; + double res[ 3 ]; + bool bigRange; + double delta1; + double delta2; + double factor; + double result; + double f0Last; + double guessc; + int32_t count; + double delta; + double denom; + double diff; + double min; + double max; + double num; + double f0; + double f1; + double f2; + + guessc = guess; + min = minimum; + max = maximum; + + f0 = 0.0; + outOfBounds = false; + result = guessc; + factor = stdlib_base_ldexp( 1.0, 1 - digits ); + delta = stdlib_base_max( 10000000.0 * guessc, 10000000.0 ); // Arbitrarily large delta... + f0Last = 0.0; // cppcheck-suppress unreadVariable + delta1 = delta; + delta2 = delta; // cppcheck-suppress unreadVariable + + // We use these to sanity check that we do actually bracket a root; if we update both ends of the brackets and the function value has the same sign at both ends, then there is no root to be found: + maxRangeF = 0.0; + minRangeF = 0.0; + + count = maxIter; + do { + f0Last = f0; + delta2 = delta1; + delta1 = delta; + ibetaRoots( a, b, target, invert, result, res ); + f0 = res[ 0 ]; + f1 = res[ 1 ]; + f2 = res[ 2 ]; + count -= 1; + + if ( f0 == 0.0 ) { + break; + } + if ( f1 == 0.0 ) { + // Oops zero derivative!!! + if ( f0Last == 0.0 ) { + // Must be the first iteration, pretend that we had a previous one at either min or max: + if ( result == min ) { + guessc = max; + } else { + guessc = min; + } + ibetaRoots( a, b, target, invert, guessc, res ); + f0Last = res[ 0 ]; + delta = guessc - result; + } + if ( stdlib_base_signum( f0Last ) * stdlib_base_signum( f0 ) < 0.0 ) { + // We've crossed over so move in opposite direction to last step: + if ( delta < 0.0 ) { + delta = ( result - min ) / 2.0; + } else { + delta = ( result - max ) / 2.0; + } + // Move in same direction as last step: + } else if ( delta < 0.0 ) { + delta = ( result - max ) / 2.0; + } else { + delta = ( result - min ) / 2.0; + } + } else if ( f2 != 0.0 ) { + denom = 2.0 * f0; + num = ( 2.0 * f1 ) - ( f0 * ( f2 / f1 ) ); + if ( stdlib_base_abs( num ) < 1.0 && ( stdlib_base_abs( denom ) >= stdlib_base_abs( num ) * FLOAT64_MAX ) ) { + // Possible overflow, use Newton step: + delta = f0 / f1; + } else { + delta = denom / num; + } + if ( delta * f1 / f0 < 0.0 ) { + // Probably cancellation error, try a Newton step instead: + delta = f0 / f1; + if ( stdlib_base_abs( delta ) > 2.0 * stdlib_base_abs( result ) ) { + delta = ( ( delta < 0.0 ) ? -1.0 : 1.0 ) * 2.0 * stdlib_base_abs( result ); + } + } + } else { + delta = f0 / f1; + } + // We need to avoid delta/delta2 overflowing here: + if ( stdlib_base_abs( delta2 ) > 1.0 || stdlib_base_abs( FLOAT64_MAX * delta2 ) > stdlib_base_abs( delta ) ) { + convergence = stdlib_base_abs( delta / delta2 ); + } else { + convergence = FLOAT64_MAX; + } + if ( convergence > 0.8 && convergence < 2.0 ) { + // Last two steps haven't converged... + if ( stdlib_base_abs( min ) < 1.0 ) { + bigRange = ( stdlib_base_abs( 1000.0 * min ) < stdlib_base_abs( max ) ); + } else { + bigRange = ( stdlib_base_abs( max / min ) > 1000.0 ); + } + if ( bigRange ) { + if ( delta > 0.0 ) { + delta = bracketRootTowardsMin( a, b, target, invert, result, f0, &min, &max, &count ); + } else { + delta = bracketRootTowardsMax( a, b, target, invert, result, f0, &min, &max, &count ); + } + } else { + delta = ( delta > 0.0 ) ? ( result - min ) / 2.0 : ( result - max ) / 2.0; + if ( result != 0.0 && stdlib_base_abs( delta ) > result ) { + delta = stdlib_base_signum( delta ) * stdlib_base_abs( result ) * 0.9; // Protect against huge jumps! + } + } + // Reset delta1/delta2 so that this branch will *not* be taken on the next iteration: + delta2 = delta * 3.0; // cppcheck-suppress unreadVariable + delta1 = delta * 3.0; // cppcheck-suppress unreadVariable + } + guessc = result; + result -= delta; + + // Check for out of bounds step: + if ( result < min ) { + if ( + stdlib_base_abs( min ) < 1.0 && + stdlib_base_abs( result ) > 1.0 && + ( FLOAT64_MAX / stdlib_base_abs( result ) < stdlib_base_abs( min ) ) + ) { + diff = 1000.0; + } else if ( + stdlib_base_abs( min ) < 1.0 && + ( stdlib_base_abs( FLOAT64_MAX * min ) < stdlib_base_abs( result ) ) + ) { + diff = ( ( min < 0.0 ) != ( result < 0.0 ) ) ? -FLOAT64_MAX : FLOAT64_MAX; + } else { + diff = result / min; + } + if ( stdlib_base_abs( diff ) < 1.0 ) { + diff = 1.0 / diff; + } + if ( !outOfBounds && diff > 0.0 && diff < 3.0 ) { + // Only a small out of bounds step, let's assume that the result is probably approximately at minimum: + delta = 0.99 * ( guessc - min ); + result = guessc - delta; + outOfBounds = true; // Only take this branch once! + } else { + if ( stdlib_base_float64_ulp_difference( min, max ) < 2.0 ) { + result = ( min + max ) / 2.0; + guessc = result; // cppcheck-suppress unreadVariable + break; + } + delta = bracketRootTowardsMin( a, b, target, invert, guessc, f0, &min, &max, &count ); + result = guessc - delta; + if ( result <= min ) { + result = floatNext( min ); + } + if ( result >= max ) { + result = floatPrior( max ); + } + guessc = min; + continue; + } + } else if ( result > max ) { + if ( + stdlib_base_abs( max ) < 1.0 && + stdlib_base_abs( result ) > 1.0 && + ( FLOAT64_MAX / stdlib_base_abs( result ) < stdlib_base_abs( max ) ) + ) { + diff = 1000.0; + } else { + diff = result / max; + } + if ( stdlib_base_abs( diff ) < 1.0 ) { + diff = 1.0 / diff; + } + if ( !outOfBounds && diff > 0.0 && diff < 3.0 ) { + // Only a small out of bounds step, let's assume that the result is probably approximately at minimum: + delta = 0.99 * ( guessc - max ); + result = guessc - delta; + outOfBounds = true; // Only take this branch once! + } else { + if ( stdlib_base_float64_ulp_difference( min, max ) < 2.0 ) { + result = ( min + max ) / 2.0; + guessc = result; // cppcheck-suppress unreadVariable + break; + } + delta = bracketRootTowardsMax( a, b, target, invert, guessc, f0, &min, &max, &count ); + result = guessc - delta; + if ( result >= max ) { + result = floatPrior( max ); + } + if ( result <= min ) { + result = floatNext( min ); + } + guessc = min; + continue; + } + } + // Update brackets: + if ( delta > 0.0 ) { + max = guessc; + maxRangeF = f0; + } else { + min = guessc; + minRangeF = f0; + } + // Sanity check that we bracket the root: + if ( maxRangeF * minRangeF > 0.0 ) { + // There appears to be no root to be found (the original C++ implementation raises an evaluation error; we instead return the current best guess): + return guessc; + } + } while ( count && ( stdlib_base_abs( result * factor ) < stdlib_base_abs( delta ) ) ); + + return result; +} + +/** +* Carries out the first method by Temme (described in section 2). +* +* ## References +* +* - Temme, N. M. 1992. "Asymptotic Inversion of the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 145–57. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). +* +* @param a function parameter +* @param b function parameter +* @param z function parameter +* @return function value +*/ +static double temme1( const double a, const double b, const double z ) { + double workspace[ 7 ]; + double terms[ 4 ]; + double eta0; + double eta2; + double eta; + double B2; + double B3; + double B; + double c; + double x; + + // Get the first approximation for eta from the inverse error function (Eq: 2.9 and 2.10): + eta0 = stdlib_base_erfcinv( 2.0 * z ); + eta0 /= -stdlib_base_sqrt( a / 2.0 ); + + terms[ 0 ] = eta0; + + // Calculate powers: + B = b - a; + B2 = B * B; + B3 = B2 * B; + + // Calculate correction terms: + + // See eq following 2.15: + workspace[ 0 ] = -B * SQRT2 / 2.0; + workspace[ 1 ] = ( 1.0 - ( 2.0 * B ) ) / 8.0; + workspace[ 2 ] = -( B * SQRT2 / 48.0 ); + workspace[ 3 ] = -1.0 / 192.0; + workspace[ 4 ] = -B * SQRT2 / 3840.0; + workspace[ 5 ] = 0.0; + workspace[ 6 ] = 0.0; + terms[ 1 ] = evalpoly( workspace, 7, eta0 ); + + // Eq Following 2.17: + workspace[ 0 ] = B * SQRT2 * ( ( 3.0 * B ) - 2.0 ) / 12.0; + workspace[ 1 ] = ( ( 20.0 * B2 ) - ( 12.0 * B ) + 1.0 ) / 128.0; + workspace[ 2 ] = B * SQRT2 * ( ( 20.0 * B ) - 1.0 ) / 960.0; + workspace[ 3 ] = ( ( 16.0 * B2 ) + ( 30.0 * B ) - 15.0 ) / 4608.0; + workspace[ 4 ] = B * SQRT2 * ( ( 21.0 * B ) + 32.0 ) / 53760.0; + workspace[ 5 ] = ( -( 32.0 * B2 ) + 63.0 ) / 368640.0; + workspace[ 6 ] = -B * SQRT2 * ( ( 120.0 * B ) + 17.0 ) / 25804480.0; + terms[ 2 ] = evalpoly( workspace, 7, eta0 ); + + // Eq Following 2.17: + workspace[ 0 ] = B * SQRT2 * ( ( -75.0 * B2 ) + ( 80.0 * B ) - 16.0 ) / 480.0; + workspace[ 1 ] = ( ( -1080.0 * B3 ) + ( 868.0 * B2 ) - ( 90.0 * B ) - 45.0 ) / 9216.0; + workspace[ 2 ] = B * SQRT2 * ( ( -1190.0 * B2 ) + ( 84.0 * B ) + 373.0 ) / 53760.0; + workspace[ 3 ] = ( ( -2240.0 * B3 ) - ( 2508.0 * B2 ) + ( 2100.0 * B ) - 165.0 ) / 368640.0; + workspace[ 4 ] = 0.0; + workspace[ 5 ] = 0.0; + workspace[ 6 ] = 0.0; + terms[ 3 ] = evalpoly( workspace, 7, eta0 ); + + // Bring them together to get a final estimate for eta: + eta = evalpoly( terms, 4, 1.0 / a ); + + // Now we need to convert eta to the return value `x`, by solving the appropriate quadratic equation: + eta2 = eta * eta; + c = -stdlib_base_exp( -eta2 / 2.0 ); + if ( eta2 == 0.0 ) { + x = 0.5; + } else { + x = ( 1.0 + ( eta * stdlib_base_sqrt( ( 1.0 + c ) / eta2 ) ) ) / 2.0; + } + // The addition above may result in us being out by one ulp on either side of the boundary, so just check that we are in bounds and adjust as needed: + if ( x < 0.0 ) { + x = 0.0; + } else if ( x > 1.0 ) { + x = 1.0; + } + return x; +} + +/** +* Carries out the second method by Temme (described in section 3). +* +* ## References +* +* - Temme, N. M. 1992. "Asymptotic Inversion of the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 145–57. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). +* +* @param z function parameter +* @param r function parameter +* @param theta function parameter +* @return function value +*/ +static double temme2( const double z, const double r, const double theta ) { + double workspace[ 6 ]; + double terms[ 4 ]; + double upper; + double lower; + double alpha; + double eta0; + double eta; + double sc7; + double sc6; + double sc5; + double sc4; + double sc3; + double sc2; + double sc; + double lu; + double s2; + double c2; + double c; + double s; + double u; + double x; + + // Get first estimate for eta, see Eq 3.9 and 3.10, but note there is a typo in Eq 3.10: + eta0 = stdlib_base_erfcinv( 2.0 * z ) / ( -stdlib_base_sqrt( r / 2.0 ) ); + + s = stdlib_base_sin( theta ); + c = stdlib_base_cos( theta ); + + // Now we need to perturb eta0 to get eta, which we do by evaluating the polynomial in 1/r at the bottom of page 151, to do this we first need the error terms e1, e2 e3 which we'll fill into the array "terms". Since these terms are themselves polynomials, we'll need another array "workspace" to calculate those... + terms[ 0 ] = eta0; + + // Some powers of sin(theta) cos(theta) that we'll need later: + s2 = s * s; + c2 = c * c; + sc = s * c; + sc2 = sc * sc; + sc3 = sc2 * sc; + sc4 = sc2 * sc2; + sc5 = sc2 * sc3; + sc6 = sc3 * sc3; + sc7 = sc4 * sc3; + + // Calculate e1 and put it in terms[1], see the middle of page 151: + workspace[ 0 ] = ( ( 2.0 * s2 ) - 1.0 ) / ( 3.0 * sc ); + workspace[ 1 ] = -polyval_co1( s2 ) / ( 36.0 * sc2 ); + workspace[ 2 ] = polyval_co2( s2 ) / ( 1620.0 * sc3 ); + workspace[ 3 ] = -polyval_co3( s2 ) / ( 6480.0 * sc4 ); + workspace[ 4 ] = polyval_co4( s2 ) / ( 90720.0 * sc5 ); + workspace[ 5 ] = 0.0; + terms[ 1 ] = evalpoly( workspace, 6, eta0 ); + + // Now evaluate e2 and put it in terms[2]: + workspace[ 0 ] = -polyval_co5( s2 ) / ( 405.0 * sc3 ); + workspace[ 1 ] = polyval_co6( s2 ) / ( 2592.0 * sc4 ); + workspace[ 2 ] = -polyval_co7( s2 ) / ( 204120.0 * sc5 ); + workspace[ 3 ] = -polyval_co8( s2 ) / ( 2099520.0 * sc6 ); + workspace[ 4 ] = 0.0; + workspace[ 5 ] = 0.0; + terms[ 2 ] = evalpoly( workspace, 6, eta0 ); + + // And e3, and put it in terms[3]: + workspace[ 0 ] = polyval_co9( s2 ) / ( 102060.0 * sc5 ); + workspace[ 1 ] = -polyval_co10( s2 ) / ( 20995200.0 * sc6 ); + workspace[ 2 ] = polyval_co11( s2 ) / ( 36741600.0 * sc7 ); + workspace[ 3 ] = 0.0; + workspace[ 4 ] = 0.0; + workspace[ 5 ] = 0.0; + terms[ 3 ] = evalpoly( workspace, 6, eta0 ); + + // Bring the correction terms together to evaluate eta; this is the last equation on page 151: + eta = evalpoly( terms, 4, 1.0 / r ); + + // Now that we have eta we need to back solve for x, we seek the value of x that gives eta in Eq 3.2. The two methods used are described in section 5. Begin by defining a few variables we'll need later: + alpha = c / s; + alpha *= alpha; + lu = ( -( eta * eta ) / ( 2.0 * s2 ) ) + stdlib_base_ln( s2 ) + ( c2 * stdlib_base_ln( c2 ) / s2 ); + + // Temme doesn't specify what value to switch on here, but this seems to work pretty well: + if ( stdlib_base_abs( eta ) < 0.7 ) { + // Small eta use the expansion Temme gives in the second equation of section 5, it's a polynomial in eta: + workspace[ 0 ] = s2; + workspace[ 1 ] = sc; + workspace[ 2 ] = ( 1.0 - ( 2.0 * s2 ) ) / 3.0; + workspace[ 3 ] = polyval_co12( s2 ) / ( 36.0 * sc ); + workspace[ 4 ] = polyval_co13( s2 ) / ( 270.0 * sc2 ); + workspace[ 5 ] = 0.0; + x = evalpoly( workspace, 6, eta ); + } else { + // If eta is large we need to solve Eq 3.2 more directly, begin by getting an initial approximation for x from the last equation on page 155, this is a polynomial in u: + u = stdlib_base_exp( lu ); + workspace[ 0 ] = u; + workspace[ 1 ] = alpha; + workspace[ 2 ] = 0.0; + workspace[ 3 ] = 3.0 * alpha * ( ( 3.0 * alpha ) + 1.0 ) / 6.0; + workspace[ 4 ] = 4.0 * alpha * ( ( 4.0 * alpha ) + 1.0 ) * ( ( 4.0 * alpha ) + 2.0 ) / 24.0; + workspace[ 5 ] = 5.0 * alpha * ( ( 5.0 * alpha ) + 1.0 ) * ( ( 5.0 * alpha ) + 2.0 ) * ( ( 5.0 * alpha ) + 3.0 ) / 120.0; + x = evalpoly( workspace, 6, u ); + + // At this point we may or may not have the right answer, Eq-3.2 has two solutions for x for any given eta, however the mapping in 3.2 is 1:1 with the sign of eta and x-sin^2(theta) being the same. So we can check if we have the right root of 3.2, and if not switch x for 1-x. This transformation is motivated by the fact that the distribution is *almost* symmetric so 1-x will be in the right ball park for the solution: + if ( ( x - s2 ) * eta < 0.0 ) { + x = 1.0 - x; + } + } + // The final step is a few Newton-Raphson iterations to clean up our approximation for x, this is pretty cheap in general, and very cheap compared to an incomplete beta evaluation. The limits set on x come from the observation that the sign of eta and x-sin^2(theta) are the same. + if ( eta < 0.0 ) { + lower = 0.0; + upper = s2; + } else { + lower = s2; + upper = 1.0; + } + // If our initial approximation is out of bounds then bisect: + if ( x < lower || x > upper ) { + x = ( lower + upper ) / 2.0; + } + // And iterate: + x = newtonRaphsonIterate( -lu, alpha, x, lower, upper, 32, 100 ); + return x; +} + +/** +* Carries out the third method by Temme (described in section 4). +* +* ## References +* +* - Temme, N. M. 1992. "Asymptotic Inversion of the Incomplete Beta Function." _Journal of Computational and Applied Mathematics_ 41 (1–2): 145–57. doi:[10.1016/0377-0427(92)90244-R](https://doi.org/10.1016/0377-0427(92)90244-R). +* +* @param a function parameter +* @param b function parameter +* @param p function parameter +* @param q probability equal to `1-p` +* @return function value +*/ +static double temme3( const double a, const double b, const double p, const double q ) { + double cross; + double lower; + double upper; + double eta0; + double eta; + double w10; + double w12; + double w13; + double w14; + double e1; + double e2; + double e3; + double mu; + double d2; + double d3; + double d4; + double w2; + double w3; + double w4; + double w5; + double w6; + double w7; + double w8; + double w9; + double w1; + double d; + double w; + double u; + double x; + + // Begin by getting an initial approximation for the quantity eta from the dominant part of the incomplete beta: + if ( p < q ) { + eta0 = stdlib_base_gammaincinv( p, b, true ); + } else { + eta0 = stdlib_base_gammaincinv( q, b, false ); + } + eta0 /= a; + + // Define the variables and powers we'll need later on: + mu = b / a; + w = stdlib_base_sqrt( 1.0 + mu ); + w2 = w * w; + w3 = w2 * w; + w4 = w2 * w2; + w5 = w3 * w2; + w6 = w3 * w3; + w7 = w4 * w3; + w8 = w4 * w4; + w9 = w5 * w4; + w10 = w5 * w5; + d = eta0 - mu; + d2 = d * d; + d3 = d2 * d; + d4 = d2 * d2; + w1 = w + 1.0; + w12 = w1 * w1; + w13 = w1 * w12; + w14 = w12 * w12; + + // Now we need to compute the perturbation error terms that convert eta0 to eta, these are all polynomials of polynomials. Probably these should be re-written to use tabulated data (see examples above), but it's less of a win in this case as we need to calculate the individual powers for the denominator terms anyway, so we might as well use them for the numerator-polynomials as well. Refer to p154-p155 for the details of these expansions: + e1 = ( w + 2.0 ) * ( w - 1.0 ) / ( 3.0 * w ); + e1 += ( w3 + ( 9.0 * w2 ) + ( 21.0 * w ) + 5.0 ) * d / ( 36.0 * w2 * w1 ); + e1 -= ( w4 - ( 13.0 * w3 ) + ( 69.0 * w2 ) + ( 167.0 * w ) + 46.0 ) * d2 / ( 1620.0 * w12 * w3 ); + e1 -= ( ( 7.0 * w5 ) + ( 21.0 * w4 ) + ( 70.0 * w3 ) + ( 26.0 * w2 ) - ( 93.0 * w ) - 31.0 ) * d3 / ( 6480.0 * w13 * w4 ); + e1 -= ( ( 75.0 * w6 ) + ( 202.0 * w5 ) + ( 188.0 * w4 ) - ( 888.0 * w3 ) - ( 1345.0 * w2 ) + ( 118.0 * w ) + 138.0 ) * d4 / ( 272160.0 * w14 * w5 ); + + e2 = ( ( 28.0 * w4 ) + ( 131.0 * w3 ) + ( 402.0 * w2 ) + ( 581.0 * w ) + 208.0 ) * ( w - 1.0 ) / ( 1620.0 * w1 * w3 ); + e2 -= ( ( 35.0 * w6 ) - ( 154.0 * w5 ) - ( 623.0 * w4 ) - ( 1636.0 * w3 ) - ( 3983.0 * w2 ) - ( 3514.0 * w ) - 925.0 ) * d / ( 12960.0 * w12 * w4 ); + e2 -= ( ( 2132.0 * w7 ) + ( 7915.0 * w6 ) + ( 16821.0 * w5 ) + ( 35066.0 * w4 ) + ( 87490.0 * w3 ) + ( 141183.0 * w2 ) + ( 95993.0 * w ) + 21640.0 ) * d2 / ( 816480.0 * w5 * w13 ); + e2 -= ( ( 11053.0 * w8 ) + ( 53308.0 * w7 ) + ( 117010.0 * w6 ) + ( 163924.0 * w5 ) + ( 116188.0 * w4 ) - ( 258428.0 * w3 ) - ( 677042.0 * w2 ) - ( 481940.0 * w ) - 105497.0 ) * d3 / ( 14696640.0 * w14 * w6 ); + + e3 = -( ( ( 3592.0 * w7 ) + ( 8375.0 * w6 ) - ( 1323.0 * w5 ) - ( 29198.0 * w4 ) - ( 89578.0 * w3 ) - ( 154413.0 * w2 ) - ( 116063.0 * w ) - 29632.0 ) * ( w - 1.0 ) ) / ( 816480.0 * w5 * w12 ); + e3 -= ( ( 442043.0 * w9 ) + ( 2054169.0 * w8 ) + ( 3803094.0 * w7 ) + ( 3470754.0 * w6 ) + ( 2141568.0 * w5 ) - ( 2393568.0 * w4 ) - ( 19904934.0 * w3 ) - ( 34714674.0 * w2 ) - ( 23128299.0 * w ) - 5253353.0 ) * d / ( 146966400.0 * w6 * w13 ); + e3 -= ( ( 116932.0 * w10 ) + ( 819281.0 * w9 ) + ( 2378172.0 * w8 ) + ( 4341330.0 * w7 ) + ( 6806004.0 * w6 ) + ( 10622748.0 * w5 ) + ( 18739500.0 * w4 ) + ( 30651894.0 * w3 ) + ( 30869976.0 * w2 ) + ( 15431867.0 * w ) + 2919016.0 ) * d2 / ( 146966400.0 * w14 * w7 ); + + // Combine eta0 and the error terms to compute eta (Second equation p155): + eta = eta0 + ( e1 / a ) + ( e2 / ( a * a ) ) + ( e3 / ( a * a * a ) ); + + /* + * Now we need to solve Eq 4.2 to obtain x. For any given value of eta there are two solutions to this equation, and since the distribution may be very skewed, these are not related by x ~ 1-x we used when implementing section 3 above. However we know that: + * + * cross < x <= 1 ; iff eta < mu + * x == cross ; iff eta == mu + * 0 <= x < cross ; iff eta > mu + * + * Where cross == 1 / (1 + mu). Many thanks to Prof Temme for clarifying this point. Therefore we'll just jump straight into Newton iterations to solve Eq 4.2 using these bounds, and simple bisection as the first guess, in practice this converges pretty quickly and we only need a few digits correct anyway: + */ + if ( eta <= 0.0 ) { + eta = FLOAT64_MIN_NORM; + } + u = eta - ( mu * stdlib_base_ln( eta ) ) + ( ( 1.0 + mu ) * stdlib_base_ln( 1.0 + mu ) ) - mu; + cross = 1.0 / ( 1.0 + mu ); + lower = ( eta < mu ) ? cross : 0.0; + upper = ( eta < mu ) ? 1.0 : cross; + x = ( lower + upper ) / 2.0; + + // Early exit for cases with numerical precision issues: + if ( cross == 0.0 || cross == 1.0 ) { + return cross; + } + return newtonRaphsonIterate( u, mu, x, lower, upper, 32, 100 ); +} + +/** +* Evaluates Student's t quantiles via a method due to Hill. +* +* ## References +* +* - Hill, G. W. 1970. "Algorithm 396: Student's T-Quantiles." _Communications of the ACM_ 13 (10). New York, NY, USA: ACM: 619–20. doi:[10.1145/355598.355600](https://doi.org/10.1145/355598.355600). +* +* @param ndf degrees of freedom +* @param u input probability +* @return function value +*/ +static double inverseStudentsTHill( const double ndf, const double u ) { + double a; + double b; + double c; + double d; + double q; + double x; + double y; + + if ( ndf > 1e20 ) { + return -stdlib_base_erfcinv( 2.0 * u ) * SQRT2; + } + a = 1.0 / ( ndf - 0.5 ); + b = 48.0 / ( a * a ); + c = ( ( ( ( ( 20700.0 * a / b ) - 98.0 ) * a ) - 16.0 ) * a ) + 96.36; + d = ( ( ( ( 94.5 / ( b + c ) ) - 3.0 ) / b ) + 1.0 ) * stdlib_base_sqrt( a * HALF_PI ) * ndf; + y = stdlib_base_pow( d * 2.0 * u, 2.0 / ndf ); + + if ( y > ( 0.05 + a ) ) { + // Asymptotic inverse expansion about normal: + x = -stdlib_base_erfcinv( 2.0 * u ) * SQRT2; + y = x * x; + + if ( ndf < 5.0 ) { + c += 0.3 * ( ndf - 4.5 ) * ( x + 0.6 ); + } + c += ( ( ( ( ( ( ( 0.05 * d * x ) - 5.0 ) * x ) - 7.0 ) * x ) - 2.0 ) * x ) + b; + y = ( ( ( ( ( ( ( ( ( ( 0.4 * y ) + 6.3 ) * y ) + 36.0 ) * y ) + 94.5 ) / c ) - y - 3.0 ) / b ) + 1.0 ) * x; + y = stdlib_base_expm1( a * y * y ); + } else { + y = ( ( 1.0 / ( ( ( ( ndf + 6.0 ) / ( ndf * y ) ) - ( 0.089 * d ) - 0.822 ) * ( ndf + 2.0 ) * 3.0 ) + ( 0.5 / ( ndf + 4.0 ) ) ) * y - 1.0 ) * ( ndf + 1.0 ) / ( ndf + 2.0 ) + ( 1.0 / y ); + } + q = stdlib_base_sqrt( ndf * y ); + return -q; +} + +/** +* Evaluates Student's t quantiles via a body series expansion. Tail and body series are due to Shaw. +* +* ## References +* +* - Shaw, William T. 2006. "Sampling Student's T distribution – use of the inverse cumulative distribution function." _Journal of Computational Finance_ 9 (4): 37–73. [www.mth.kcl.ac.uk/~shaww/web\_page/papers/Tdistribution06.pdf](www.mth.kcl.ac.uk/~shaww/web_page/papers/Tdistribution06.pdf). +* +* @param df degrees of freedom +* @param u input probability +* @return function value +*/ +static double inverseStudentsTBodySeries( const double df, const double u ) { + double c[ 10 ]; + double idf; + double c0; + double v; + + // Body series for small N, start with Eq 56 of Shaw: + v = stdlib_base_gamma_delta_ratio( df / 2.0, 0.5 ) * stdlib_base_sqrt( df * PI ) * ( u - 0.5 ); + + c0 = 0.0; + + // Figure out what the coefficients are. They depend only on the degrees of freedom (Eq 57 of Shaw): + idf = 1.0 / df; + c[ 0 ] = 1.0; + c[ 1 ] = polyval_co14( idf ); + c[ 2 ] = polyval_co15( idf ); + c[ 3 ] = polyval_co16( idf ); + c[ 4 ] = polyval_co17( idf ); + c[ 5 ] = polyval_co18( idf ); + c[ 6 ] = polyval_co19( idf ); + c[ 7 ] = polyval_co20( idf ); + c[ 8 ] = polyval_co21( idf ); + c[ 9 ] = polyval_co22( idf ); + + // Result is then an odd polynomial in v (see Eq 56 of Shaw)... + return c0 + ( v * evalpoly( c, 10, v * v ) ); +} + +/** +* Evaluates Student's t quantiles via a tail series expansion. Tail and body series are due to Shaw. +* +* ## References +* +* - Shaw, William T. 2006. "Sampling Student's T distribution – use of the inverse cumulative distribution function." _Journal of Computational Finance_ 9 (4): 37–73. [www.mth.kcl.ac.uk/~shaww/web\_page/papers/Tdistribution06.pdf](www.mth.kcl.ac.uk/~shaww/web_page/papers/Tdistribution06.pdf). +* +* @param df degrees of freedom +* @param v function value +* @return tail value +*/ +static double inverseStudentsTTailSeries( const double df, const double v ) { + double result; + double d[ 7 ]; + double power; + double div; + double np2; + double np4; + double np6; + double rn; + double w; + + // Tail series expansion, see section 6 of Shaw's paper. `w` is calculated using Eq 60: + w = stdlib_base_gamma_delta_ratio( df / 2.0, 0.5 ) * stdlib_base_sqrt( df * PI ) * v; + + // Define some variables: + np2 = df + 2.0; + np4 = df + 4.0; + np6 = df + 6.0; + + d[ 0 ] = 1.0; + d[ 1 ] = -( df + 1.0 ) / ( 2.0 * np2 ); + np2 *= ( df + 2.0 ); + d[ 2 ] = -df * ( df + 1.0 ) * ( df + 3.0 ) / ( 8.0 * np2 * np4 ); + np2 *= df + 2.0; + d[ 3 ] = -df * ( df + 1.0 ) * ( df + 5.0 ) * ( ( ( ( 3.0 * df ) + 7.0 ) * df ) - 2.0 ) / ( 48.0 * np2 * np4 * np6 ); + np2 *= ( df + 2.0 ); + np4 *= ( df + 4.0 ); + d[ 4 ] = -df * ( df + 1.0 ) * ( df + 7.0 ) * ( ( ( ( ( ( ( ( ( 15.0 * df ) + 154.0 ) * df ) + 465.0 ) * df + 286.0 ) * df ) - 336.0 ) * df ) + 64.0 ) / ( 384.0 * np2 * np4 * np6 * ( df + 8.0 ) ); + np2 *= ( df + 2.0 ); + d[ 5 ] = -df * ( df + 1.0 ) * ( df + 3.0 ) * ( df + 9.0 ) * ( ( ( ( ( ( ( ( ( ( ( 35.0 * df ) + 452.0 ) * df ) + 1573.0 ) * df ) + 600.0 ) * df ) - 2020.0 ) * df ) + 928.0 ) * df - 128.0 ) / ( 1280.0 * np2 * np4 * np6 * ( df + 8.0 ) * ( df + 10.0 ) ); + np2 *= ( df + 2.0 ); + np4 *= ( df + 4.0 ); + np6 *= ( df + 6.0 ); + d[ 6 ] = -df * ( df + 1.0 ) * ( df + 11.0 ) * ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 945.0 * df ) + 31506.0 ) * df ) + 425858.0 ) * df ) + 2980236.0 ) * df ) + 11266745.0 ) * df ) + 20675018.0 ) * df ) + 7747124.0 ) * df ) - 22574632.0 ) * df ) - 8565600.0 ) * df ) + 18108416.0 ) * df ) - 7099392.0 ) * df ) + 884736.0 ) ) / ( 46080.0 * np2 * np4 * np6 * ( df + 8.0 ) * ( df + 10.0 ) * ( df + 12.0 ) ); + + // Now bring everything together to provide the result this is Eq 62 of Shaw: + rn = stdlib_base_sqrt( df ); + div = stdlib_base_pow( rn * w, 1.0 / df ); + power = div * div; + result = evalpoly( d, 7, power ); + result *= rn; + result /= div; + return -result; +} + +/** +* Evaluates Student's t quantiles. +* +* @param df degrees of freedom +* @param u input probability +* @param v probability equal to `1-u` +* @return function value +*/ +static double inverseStudentsT( const double df, const double u, const double v ) { + double crossover; + double tolerance; + double rootAlpha; + double result; + int32_t uexp; + double alpha; + double frac; + bool invert; + double tmp; + double p0; + double p2; + double p4; + double p5; + double uc; + double vc; + double p; + double r; + double x; + double a; + double b; + + uc = u; + vc = v; + + result = 0.0; + if ( uc > vc ) { + // Function is symmetric, so invert it: + tmp = vc; + vc = uc; + uc = tmp; + invert = true; + } else { + invert = false; + } + if ( stdlib_base_floor( df ) == df && df < 20.0 ) { + // We have integer degrees of freedom, try for the special cases first... + + // NOTE: the original JavaScript implementation computes `ldexp( 1.0, (2.0*53.0)/3.0 )`, in which the fractional exponent is truncated toward zero (i.e., `2^35`). We faithfully replicate that behavior: + tolerance = stdlib_base_ldexp( 1.0, 35 ); + + switch ( (int32_t)stdlib_base_floor( df ) ) { + case 1: + // `df = 1` is the same as the Cauchy distribution, see Shaw Eq 35: + if ( uc == 0.5 ) { + result = 0.0; + } else { + result = -stdlib_base_cos( PI * uc ) / stdlib_base_sin( PI * uc ); + } + break; + case 2: + // `df = 2` has an exact result, see Shaw Eq 36: + result = ( ( 2.0 * uc ) - 1.0 ) / stdlib_base_sqrt( 2.0 * uc * vc ); + break; + case 4: + // `df = 4` has an exact result, see Shaw Eq 38 & 39: + alpha = 4.0 * uc * vc; + rootAlpha = stdlib_base_sqrt( alpha ); + r = 4.0 * stdlib_base_cos( stdlib_base_acos( rootAlpha ) / 3.0 ) / rootAlpha; + x = stdlib_base_sqrt( r - 4.0 ); + result = ( uc - 0.5 < 0.0 ) ? -x : x; + break; + case 6: + // We get numeric overflow in this area: + if ( uc < 1.0e-150 ) { + return ( ( invert ) ? -1.0 : 1.0 ) * inverseStudentsTHill( df, uc ); + } + // Newton-Raphson iteration of a polynomial case, choice of seed value is taken from Shaw's online supplement: + a = 4.0 * ( uc - ( uc * uc ) ); // 1 - 4 * (u - 0.5f) * (u - 0.5f); + b = stdlib_base_cbrt( a ); + p = 6.0 * ( 1.0 + ( CONST_C * ( ( 1.0 / b ) - 1.0 ) ) ); + do { + p2 = p * p; + p4 = p2 * p2; + p5 = p * p4; + p0 = p; + + // Next term is given by Eq 41: + p = 2.0 * ( ( 8.0 * a * p5 ) - ( 270.0 * p2 ) + 2187.0 ) / ( 5.0 * ( ( 4.0 * a * p4 ) - ( 216.0 * p ) - 243.0 ) ); + } while ( stdlib_base_abs( ( p - p0 ) / p ) > tolerance ); + + // Use Eq 45 to extract the result: + p = stdlib_base_sqrt( p - df ); + result = ( uc - 0.5 < 0.0 ) ? -p : p; + break; + default: + if ( df > DF_THRESHOLD ) { // 2^28 + result = -stdlib_base_erfcinv( 2.0 * uc ) * SQRT2; + } else if ( df < 3.0 ) { + // Use a roughly linear scheme to choose between Shaw's tail series and body series: + crossover = 0.2742 - ( df * 0.0242143 ); + if ( uc > crossover ) { + result = inverseStudentsTBodySeries( df, uc ); + } else { + result = inverseStudentsTTailSeries( df, uc ); + } + } else { + // Use Hill's method except in the extreme tails where we use Shaw's tail series. The crossover point is roughly exponential in -df (i.e., use Hill's method when `u > 2^(-df/0.654)`), which we evaluate via the binary exponent of `u` in order to avoid underflow for large `df`. + // NOTE: the Boost implementation tests `u_exp < df / 0.654`, which contradicts the stated intent (the tail series would never be selected); we implement the stated intent, which reproduces the behavior of earlier Boost versions: + stdlib_base_frexp( uc, &frac, &uexp ); + if ( frac > 0.0 && (double)uexp > df / -0.654 ) { + result = inverseStudentsTHill( df, uc ); + } else { + result = inverseStudentsTTailSeries( df, uc ); + } + } + } + } else if ( df > DF_THRESHOLD ) { + result = -stdlib_base_erfcinv( 2.0 * uc ) * SQRT2; + } else if ( df < 3.0 ) { + // Use a roughly linear scheme to choose between Shaw's tail series and body series: + crossover = 0.2742 - ( df * 0.0242143 ); + if ( uc > crossover ) { + result = inverseStudentsTBodySeries( df, uc ); + } else { + result = inverseStudentsTTailSeries( df, uc ); + } + } else { + // Use Hill's method except in the extreme tails where we use Shaw's tail series. The crossover point is roughly exponential in -df (i.e., use Hill's method when `u > 2^(-df/0.654)`), which we evaluate via the binary exponent of `u` in order to avoid underflow for large `df`. + // NOTE: the Boost implementation tests `u_exp < df / 0.654`, which contradicts the stated intent (the tail series would never be selected); we implement the stated intent, which reproduces the behavior of earlier Boost versions: + stdlib_base_frexp( uc, &frac, &uexp ); + if ( frac > 0.0 && (double)uexp > df / -0.654 ) { + result = inverseStudentsTHill( df, uc ); + } else { + result = inverseStudentsTTailSeries( df, uc ); + } + } + return ( invert ) ? -result : result; +} + +/** +* Returns the inverse of the incomplete beta function via the Student t distribution. +* +* ## Notes +* +* - The function writes one minus the returned value to `py`. +* +* @param a function parameter +* @param p probability value +* @param py destination for one minus the returned value +* @return function value +*/ +static double findIBetaInvFromTDist( const double a, const double p, double *py ) { + double df; + double u; + double v; + double t; + + u = p / 2.0; + v = 1.0 - u; + df = a * 2.0; + t = inverseStudentsT( df, u, v ); + *py = t * t / ( df + ( t * t ) ); + return df / ( df + ( t * t ) ); +} + +/** +* Computes the inverse of the lower incomplete beta function. +* +* ## Notes +* +* - The function writes the function value `y` to `out1` and `1-y` to `out2`. +* +* @param a function parameter +* @param b function parameter +* @param p function parameter +* @param q probability equal to `1-p` +* @param out1 destination for the function value +* @param out2 destination for one minus the function value +* +* @example +* double out1; +* double out2; +* +* stdlib_base_kernel_betaincinv( 3.0, 3.0, 0.2, 0.8, &out1, &out2 ); +*/ +void stdlib_base_kernel_betaincinv( const double a, const double b, const double p, const double q, double *out1, double *out2 ) { + double terms[ 5 ]; + int32_t digits; + double lambda; + double deriv; + double lower; + double theta; + double upper; + bool invert; + double maxv; + double minv; + double bet; + double ppa; + double tmp; + double xs2; + double ap1; + double bm1; + double ac; + double bc; + double pc; + double qc; + double fs; + double fv; + double lx; + double ps; + double xg; + double xs; + double yp; + double a2; + double a3; + double b2; + double r; + double l; + double u; + double x; + double y; + + ac = a; + bc = b; + pc = p; + qc = q; + + // The flag invert is set to true if we swap a for b and p for q, in which case the result has to be subtracted from 1: + invert = false; + + // Handle trivial cases first... + if ( qc == 0.0 ) { + *out1 = 1.0; + *out2 = 0.0; + return; + } + if ( pc == 0.0 ) { + *out1 = 0.0; + *out2 = 1.0; + return; + } + if ( ac == 1.0 ) { + if ( bc == 1.0 ) { + *out1 = pc; + *out2 = 1.0 - pc; + return; + } + // Change things around so we can handle as b == 1 special case below: + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + + invert = true; + } + // Depending upon which approximation method we use, we may end up calculating either x or y initially (where y = 1-x): + x = 0.0; + y = 0.0; + + // For some of the methods we can put tighter bounds on the result than simply [0,1]: + lower = 0.0; + upper = 1.0; + + // Student's T with b = 0.5 gets handled as a special case, swap around if the arguments are in the "wrong" order: + if ( ac == 0.5 ) { + if ( bc == 0.5 ) { + x = stdlib_base_sin( pc * HALF_PI ); + x *= x; + y = stdlib_base_sin( qc * HALF_PI ); + y *= y; + *out1 = x; + *out2 = y; + return; + } + if ( bc > 0.5 ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + + invert = !invert; + } + } + // Select calculation method for the initial estimate: + if ( bc == 0.5 && ac >= 0.5 && pc != 1.0 ) { + // We have a Student's T distribution: + yp = 0.0; + x = findIBetaInvFromTDist( ac, pc, &yp ); + y = yp; + } + else if ( bc == 1.0 ) { + if ( pc < qc ) { + if ( ac > 1.0 ) { + x = stdlib_base_pow( pc, 1.0 / ac ); + y = -stdlib_base_expm1( stdlib_base_ln( pc ) / ac ); + } else { + x = stdlib_base_pow( pc, 1.0 / ac ); + y = 1.0 - x; + } + } else { + x = stdlib_base_exp( stdlib_base_log1p( -qc ) / ac ); + y = -stdlib_base_expm1( stdlib_base_log1p( -qc ) / ac ); + } + if ( invert ) { + tmp = y; + y = x; + x = tmp; + } + *out1 = x; + *out2 = y; + return; + } + else if ( ac + bc > 5.0 ) { + // When a+b is large then we can use one of Prof Temme's asymptotic expansions, begin by swapping things around so that p < 0.5, we do this to avoid cancellations errors when p is large. + if ( pc > 0.5 ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + + invert = !invert; + } + minv = stdlib_base_min( ac, bc ); + maxv = stdlib_base_max( ac, bc ); + if ( ( stdlib_base_sqrt( minv ) > ( maxv - minv ) ) && minv > 5.0 ) { + // When a and b differ by a small amount the curve is quite symmetrical and we can use an error function to approximate the inverse. This is the cheapest of the three Temme expansions, and the calculated value for x will never be much larger than p, so we don't have to worry about cancellation as long as p is small. + x = temme1( ac, bc, pc ); + y = 1.0 - x; + } else { + r = ac + bc; + theta = stdlib_base_asin( stdlib_base_sqrt( ac / r ) ); + lambda = minv / r; + if ( + lambda >= 0.2 && + lambda <= 0.8 && + r >= 10.0 + ) { + // The second error function case is the next cheapest to use, it breaks down when the result is likely to be very small, if `a+b` is also small, but we can use a cheaper expansion there in any case. As before `x` won't be much larger than `p`, so as long as `p` is small we should be free of cancellation error. + ppa = stdlib_base_pow( pc, 1.0 / ac ); + if ( ppa < 0.0025 && ( ac + bc ) < 200.0 ) { + x = ppa * stdlib_base_pow( ac * stdlib_base_beta( ac, bc ), 1.0 / ac ); + } else { + x = temme2( pc, r, theta ); + } + y = 1.0 - x; + } else { + // If we get here then a and b are very different in magnitude and we need to use the third of Temme's methods which involves inverting the incomplete gamma. This is much more expensive than the other methods. We also can only use this method when a > b, which can lead to cancellation errors if we really want y (as we will when x is close to 1), so a different expansion is used in that case. + if ( ac < bc ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + invert = !invert; + } + // Try to compute the easy way first: + bet = 0.0; + if ( bc < 2.0 ) { + bet = stdlib_base_beta( ac, bc ); + if ( bet == PINF ) { + bet = FLOAT64_MAX; + } + } + if ( bet == 0.0 ) { + y = 1.0; + } else { + y = stdlib_base_pow( bc * qc * bet, 1.0 / bc ); + x = 1.0 - y; + } + if ( y > 1.0e-5 && stdlib_base_min( ac, bc ) < 1000.0 ) { + x = temme3( ac, bc, pc, qc ); + y = 1.0 - x; + } else if ( y > 1.0e-5 && stdlib_base_min( ac, bc ) > 1000.0 ) { + // All options have failed, so use the saddle point as a starting location: + x = stdlib_base_max( ac, bc ) / ( ac + bc ); + y = stdlib_base_min( ac, bc ) / ( ac + bc ); + } + } + } + } + else if ( ac < 1.0 && bc < 1.0 ) { + // Both a and b less than 1, there is a point of inflection at xs: + xs = ( 1.0 - ac ) / ( 2.0 - ac - bc ); + + // Now we need to ensure that we start our iteration from the right side of the inflection point: + stdlib_base_kernel_betainc( xs, ac, bc, true, false, &fv, &deriv ); + fs = fv - pc; + if ( stdlib_base_abs( fs ) / pc < EPSILON * 3.0 ) { + // The result is at the point of inflection, best just return it: + if ( invert ) { + *out1 = 1.0 - xs; + *out2 = xs; + return; + } + *out1 = xs; + *out2 = 1.0 - xs; + return; + } + if ( fs < 0.0 ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + + invert = !invert; + xs = 1.0 - xs; + } + if ( ac < FLOAT64_MIN_NORM && bc > FLOAT64_MIN_NORM ) { + // Nothing interesting is going on here: + if ( invert ) { + *out1 = 1.0; + *out2 = 0.0; + return; + } + *out1 = 0.0; + *out2 = 1.0; + return; + } + // The computation of `beta` may overflow to infinity, in which case we compute the estimate via logarithms: + bet = stdlib_base_beta( ac, bc ); + if ( bet == PINF ) { + xg = stdlib_base_exp( ( stdlib_base_gammaln( ac + 1.0 ) + stdlib_base_gammaln( bc ) - stdlib_base_gammaln( ac + bc ) + stdlib_base_ln( pc ) ) / ac ); + if ( xg > 2.0 / EPSILON ) { + xg = 2.0 / EPSILON; + } + } else { + xg = stdlib_base_pow( ac * pc * bet, 1.0 / ac ); + } + x = xg / ( 1.0 + xg ); + y = 1.0 / ( 1.0 + xg ); + + // And finally we know that our result is below the inflection point, so set an upper limit on our search: + if ( x > xs ) { + x = xs; + } + upper = xs; + } + else if ( ac > 1.0 && bc > 1.0 ) { + // Small a and b, both greater than 1, there is a point of inflection at xs, and its complement is xs2, we must always start our iteration from the right side of the point of inflection. + xs = ( ac - 1.0 ) / ( ac + bc - 2.0 ); + xs2 = ( bc - 1.0 ) / ( ac + bc - 2.0 ); + stdlib_base_kernel_betainc( xs, ac, bc, true, false, &fv, &deriv ); + ps = fv - pc; + + if ( ps < 0.0 ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + + tmp = xs2; + xs2 = xs; // cppcheck-suppress unreadVariable + xs = tmp; + + invert = !invert; + } + // Estimate x and y, using expm1 to get a good estimate for y when it's very small: + lx = stdlib_base_ln( pc * ac * stdlib_base_beta( ac, bc ) ) / ac; + x = stdlib_base_exp( lx ); + y = ( x < 0.9 ) ? 1.0 - x : -stdlib_base_expm1( lx ); + + if ( bc < ac && x < 0.2 ) { + // Under a limited range of circumstances we can improve our estimate for x... + ap1 = ac - 1.0; + bm1 = bc - 1.0; + a2 = ac * ac; + a3 = ac * a2; + b2 = bc * bc; + terms[ 0 ] = 0.0; + terms[ 1 ] = 1.0; + terms[ 2 ] = bm1 / ap1; + ap1 *= ap1; + terms[ 3 ] = bm1 * ( ( 3.0 * ac * bc ) + ( 5.0 * bc ) + a2 - ac - 4.0 ) / ( 2.0 * ( ac + 2.0 ) * ap1 ); + ap1 *= ( ac + 1.0 ); + terms[ 4 ] = bm1 * ( ( 33.0 * ac * b2 ) + ( 31.0 * b2 ) + ( 8.0 * a2 * b2 ) - ( 30.0 * ac * bc ) - ( 47.0 * bc ) + ( 11.0 * a2 * bc ) + ( 6.0 * a3 * bc ) + 18.0 + ( 4.0 * ac ) - a3 + ( a2 * a2 ) - ( 10.0 * a2 ) ); + terms[ 4 ] /= ( 3.0 * ( ac + 3.0 ) * ( ac + 2.0 ) * ap1 ); + x = evalpoly( terms, 5, x ); + } + // Know that result is below the inflection point, so set an upper limit on search... + if ( x > xs ) { + x = xs; + } + upper = xs; + } else { + // Case: ( a <= 1 ) != ( b <= 1 ). If all else fails we get here, only one of a and b is above 1, and a+b is small. Start by swapping things around so that we have a concave curve with b > a and no points of inflection in [0,1]. As long as we expect x to be small then we can use the simple (and cheap) power term to estimate x, but when we expect x to be large then this greatly underestimates x and leaves us trying to iterate "round the corner" which may take almost forever. We could use Temme's inverse gamma function case in that case, this works really rather well (albeit expensively) even though strictly speaking we're outside it's defined range. However it's expensive to compute, and an alternative approach which models the curve as a distorted quarter circle is much cheaper to compute, and still keeps the number of iterations required down to a reasonable level. With thanks to Prof. Temme for this suggestion. + if ( bc < ac ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + invert = !invert; + } + if ( ac < FLOAT64_MIN_NORM ) { + // Avoid spurious overflows for denormalized `a`: + if ( pc < 1.0 ) { + x = 1.0; + y = 0.0; + } else { + x = 0.0; + y = 1.0; + } + } else if ( stdlib_base_pow( pc, 1.0 / ac ) < 0.5 ) { + x = stdlib_base_pow( pc * ac * stdlib_base_beta( ac, bc ), 1.0 / ac ); + if ( x > 1.0 || x == PINF ) { + x = 1.0; + } + if ( x == 0.0 ) { + x = FLOAT64_MIN_NORM; + } + y = 1.0 - x; + } + // Case: pow(q, 1/b) < 0.1 + else { + // Model a distorted quarter circle: + y = stdlib_base_pow( 1.0 - stdlib_base_pow( pc, bc * stdlib_base_beta( ac, bc ) ), 1.0 / bc ); + if ( y > 1.0 || y == PINF ) { + y = 1.0; + } + if ( y == 0.0 ) { + y = FLOAT64_MIN_NORM; + } + x = 1.0 - y; + } + } + // Now we have a guess for x (and for y) we can set things up for iteration. If x > 0.5 it pays to swap things round: + if ( x > 0.5 ) { + tmp = bc; + bc = ac; + ac = tmp; + + tmp = qc; + qc = pc; + pc = tmp; + + tmp = y; + y = x; // cppcheck-suppress unreadVariable + x = tmp; + + invert = !invert; + l = 1.0 - upper; + u = 1.0 - lower; + lower = l; + upper = u; + } + // Lower bound for our search: We're not interested in denormalized answers as these tend to take up lots of iterations, given that we can't get accurate derivatives in this area (they tend to be infinite). + if ( lower == 0.0 ) { + lower = FLOAT64_MIN_NORM; + if ( x < lower ) { + x = lower; + } + } + // Figure out how many digits to iterate towards: + digits = DIGITS; + if ( x < 1.0e-50 && ( ac < 1.0 || bc < 1.0 ) ) { + // If we're in a region where the first derivative is very large, then we have to take care that the root-finder doesn't terminate prematurely. We'll bump the precision up to avoid this, but we have to take care not to set the precision too high or the last few iterations will just thrash around and convergence may be slow in this case. Try 3/4 of machine epsilon: + digits *= 3; + digits /= 2; + } + // Now iterate, we can use either p or q as the target here depending on which is smaller: + x = halleyIterate( ac, bc, ( ( pc < qc ) ? pc : qc ), pc >= qc, x, lower, upper, digits, MAX_ITERATIONS ); + + // Tidy up, if we "lower" was too high then zero is the best answer we have: + if ( x == lower ) { + x = 0.0; + } + if ( invert ) { + *out1 = 1.0 - x; + *out2 = x; + return; + } + *out1 = x; + *out2 = 1.0 - x; + return; +} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/Makefile b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/Makefile deleted file mode 100644 index 7b6175aa69db..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/Makefile +++ /dev/null @@ -1,120 +0,0 @@ -#/ -# @license Apache-2.0 -# -# Copyright (c) 2018 The Stdlib Authors. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -#/ - - -# VARIABLES # - -ifndef VERBOSE - QUIET := @ -endif - -# Specify the path to Boost: -BOOST ?= - -# Determine the OS: -# -# [1]: https://en.wikipedia.org/wiki/Uname#Examples -# [2]: http://stackoverflow.com/a/27776822/2225624 -OS ?= $(shell uname) -ifneq (, $(findstring MINGW,$(OS))) - OS := WINNT -else -ifneq (, $(findstring MSYS,$(OS))) - OS := WINNT -else -ifneq (, $(findstring CYGWIN,$(OS))) - OS := WINNT -endif -endif -endif - -# Define the program used for compiling C++ source files: -ifdef CXX_COMPILER - CXX := $(CXX_COMPILER) -else - CXX := g++ -endif - -# Define the command-line options when compiling C++ files: -CXXFLAGS ?= \ - -std=c++11 \ - -O3 \ - -Wall \ - -pedantic - -# Determine whether to generate [position independent code][1]: -# -# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options -# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option -ifeq ($(OS), WINNT) - fPIC ?= -else - fPIC ?= -fPIC -endif - -# List of C++ targets: -cxx_targets := runner.out - - -# TARGETS # - -# Default target. -# -# This target is the default target. - -all: $(cxx_targets) - -.PHONY: all - - -# Compile C++ source. -# -# This target compiles C++ source files. - -$(cxx_targets): %.out: %.cpp $(BOOST) - $(QUIET) $(CXX) $(CXXFLAGS) $(fPIC) -I $(BOOST) -o $@ $< -lm - - -# Generate test fixtures. -# -# This target generates test fixtures. - -run: $(cxx_targets) - $(QUIET) ./$< - -.PHONY: run - - -# Perform clean-up. -# -# This target removes generated files. - -clean: - $(QUIET) -rm -f *.o *.out - -.PHONY: clean - - -# Remove fixtures. -# -# This target removes fixture data. - -clean-fixtures: - $(QUIET) -rm -f *.json - -.PHONY: clean-fixtures diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/output.json b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/output.json deleted file mode 100644 index 41c912cd4acf..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/output.json +++ /dev/null @@ -1 +0,0 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/runner.cpp b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/runner.cpp deleted file mode 100644 index 1fa7a30b4bc9..000000000000 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/cpp/runner.cpp +++ /dev/null @@ -1,334 +0,0 @@ -/** -* @license Apache-2.0 -* -* Copyright (c) 2018 The Stdlib Authors. -* -* Licensed under the Apache License, Version 2.0 (the "License"); -* you may not use this file except in compliance with the License. -* You may obtain a copy of the License at -* -* http://www.apache.org/licenses/LICENSE-2.0 -* -* Unless required by applicable law or agreed to in writing, software -* distributed under the License is distributed on an "AS IS" BASIS, -* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -* See the License for the specific language governing permissions and -* limitations under the License. -*/ - -/** -* Generate Boost test fixtures. -* -* ## Notes -* -* - Run this script from the directory in which fixtures should be written. -* -*/ -#include -#include -#include -#include -#include -#include - -using boost::random::uniform_real_distribution; -using boost::random::uniform_int_distribution; -using boost::random::mt19937; - -// Define a new pseudorandom number generator: -mt19937 rng; - -/** -* Generates a linearly spaced numeric array of doubles. -* -* ## Notes -* -* - Assumes that the output array has at least 2 elements. -* - Output array is guaranteed to include both the start and end values. -* -* -* @param out output array -* @param len array length -* @param start first value -* @param end last value -*/ -void linspace_f64( double *out, const unsigned int len, const double start, const double end ) { - unsigned int i; - double incr; - - incr = (end-start) / (len-1); - for ( i = 0; i < len-1; i++ ) { - out[ i ] = start + (incr*i); - } - out[ i ] = end; -} - -/** -* Generates a linearly spaced numeric array of integers. -* -* ## Notes -* -* - Assumes that the output array has at least 2 elements. -* - Output array is guaranteed to include both the start and end values. -* -* -* @param out output array -* @param len array length -* @param start first value -* @param end last value -*/ -void linspace_i32( int *out, const unsigned int len, const int start, const int end ) { - unsigned int i; - int incr; - - incr = (end-start) / (len-1); - for ( i = 0; i < len-1; i++ ) { - out[ i ] = start + (incr*i); - } - out[ i ] = end; -} - -/** -* Generates an array of pseudorandom doubles drawn from a uniform distribution. -* -* @param out output array -* @param len array length -* @param a lower bound (inclusive) -* @param b upper bound (exclusive) -*/ -void rand_array_f64( double *out, const unsigned int len, const double a, const double b ) { - unsigned int i; - - // Define a uniform distribution for generating pseudorandom numbers: - uniform_real_distribution<> randu( a, b ); - - for ( i = 0; i < len; i++ ) { - out[ i ] = randu( rng ); - } -} - -/** -* Generates an array of pseudorandom integers drawn from a uniform distribution. -* -* @param out output array -* @param len array length -* @param a lower bound (inclusive) -* @param b upper bound (exclusive) -*/ -void rand_array_i32( int *out, const unsigned int len, const int a, const int b ) { - unsigned int i; - - // Define a uniform distribution for generating pseudorandom numbers: - uniform_int_distribution<> randi( a, b ); - - for ( i = 0; i < len; i++ ) { - out[ i ] = randi( rng ); - } -} - -/** -* Casts an array of integers to an array of doubles. -* -* @param out output array -* @param x input array -* @param len array length -*/ -void i32_to_f64( double *out, int *x, unsigned int len ) { - unsigned int i; - - for ( i = 0; i < len; i++ ) { - out[ i ] = (double) x[ i ]; - } -} - -/** -* Casts an array of doubles to an array of integers. -* -* @param out output array -* @param x input array -* @param len array length -*/ -void f64_to_i32( int *out, double *x, unsigned int len ) { - unsigned int i; - - for ( i = 0; i < len; i++ ) { - out[ i ] = (int) x[ i ]; - } -} - -/** -* Writes an array of doubles to a file as a series of comma-separated values. -* -* @param f file to write to -* @param x array of doubles -* @param len array length -*/ -void write_array_f64( FILE *f, const double *x, const unsigned int len ) { - unsigned int i; - for ( i = 0; i < len; i++ ) { - fprintf( f, "%.17g", x[ i ] ); - if ( i < len-1 ) { - fprintf( f, "," ); - } - } -} - -/** -* Writes an array of integers to a file as a series of comma-separated values. -* -* @param f file to write to -* @param x array of integers -* @param len array length -*/ -void write_array_i32( FILE *f, const int *x, const unsigned int len ) { - unsigned int i; - - for ( i = 0; i < len; i++ ) { - fprintf( f, "%d", x[ i ] ); - if ( i < len-1 ) { - fprintf( f, "," ); - } - } -} - -/** -* Writes a named array of doubles to a file as JSON. -* -* @param f file to write to -* @param name array name -* @param x data -* @param len array length -*/ -void write_named_array_f64( FILE *f, const char *name, const double *x, const unsigned int len ) { - fprintf( f, "\"%s\":[", name ); - write_array_f64( f, x, len ); - fprintf( f, "]" ); -} - -/** -* Writes a named array of integers to a file as JSON. -* -* @param f file to write to -* @param name array name -* @param x data -* @param len array length -*/ -void write_named_array_i32( FILE *f, const char *name, const int *x, const unsigned int len ) { - fprintf( f, "\"%s\":[", name ); - write_array_i32( f, x, len ); - fprintf( f, "]" ); -} - -/** -* Writes data to a file as JSON. -* -* ## Notes -* -* - This function SHOULD be tailored to the input data (e.g., input types, output types, number of arguments, etc) and may vary from use case to use case. -* -* -* @param f file to write to -* @param p first parameter -* @param a second parameter -* @param b third parameter -* @param y inverse of lower regularized incomplete beta function -* @param len array length -*/ -void write_data_as_json( FILE *f, const double *p, const double *a, const double *b, const double *y, const unsigned int len ) { - fprintf( f, "{" ); - write_named_array_f64( f, "p", p, len ); - fprintf( f, "," ); - write_named_array_f64( f, "a", a, len ); - fprintf( f, "," ); - write_named_array_f64( f, "b", b, len ); - fprintf( f, "," ); - write_named_array_f64( f, "y", y, len ); - fprintf( f, "}" ); -} - -/** -* Generates test fixtures. -* -* @param p first parameter -* @param a second parameter -* @param b third parameter -* @param len number of values in the domain -* @param name output filename -*/ -void generate( double *p, double *a, double *b, const unsigned int len, const char *name ) { - double *y; - unsigned int i; - FILE *f; - - // Allocate an output array: - y = (double*) malloc( len * sizeof(double) ); - if ( y == NULL ) { - printf( "Error allocating memory.\n" ); - exit( 1 ); - } - - // Generate fixture data: - for ( i = 0; i < len; i++ ) { - double arg1 = a[ i ]; - double arg2 = b[ i ]; - double arg3 = p[ i ]; - y[ i ] = boost::math::ibeta_inv( arg1, arg2, arg3 ); - } - // Open a new file: - f = fopen( name, "w" ); - if ( f == NULL ) { - printf( "Error opening file.\n" ); - exit( 1 ); - } - // Write data as JSON: - write_data_as_json( f, p, a, b, y, len ); - - // Close the file: - fclose( f ); - - // Free allocated memory: - free( y ); -} - -/** -* Main execution sequence. -*/ -int main( void ) { - unsigned int len; - double *p; - double *a; - double *b; - - // Define the array length: - len = 2000; - - // Allocate arrays: - p = (double*) malloc( len * sizeof(double) ); - if ( p == NULL ) { - printf( "Error allocating memory.\n" ); - exit( 1 ); - } - a = (double*) malloc( len * sizeof(double) ); - if ( a == NULL ) { - printf( "Error allocating memory.\n" ); - exit( 1 ); - } - b = (double*) malloc( len * sizeof(double) ); - if ( b == NULL ) { - printf( "Error allocating memory.\n" ); - exit( 1 ); - } - - // Generate fixture data: - rand_array_f64( p, len, 0.001, 0.999 ); - rand_array_f64( a, len, 1.0, 40.0 ); - rand_array_f64( b, len, 1.0, 40.0 ); - generate( p, a, b, len, "output.json" ); - - // Free allocated memory: - free( p ); - free( a ); - free( b ); - - return 0; -} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/python/huge.json b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/python/huge.json new file mode 100644 index 000000000000..574fa1cc4d5b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/python/huge.json @@ -0,0 +1 @@ +{"a": [16770118.892992446, 21056.400478625335, 9178.32871738389, 512213.36651567207, 55823557.48773234, 1091.2586983272822, 1632.497964918463, 104195.66177855399, 32460.17785126978, 36209.56358643722, 132027.73893279748, 44816801.079973705, 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2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +"""Generate fixtures.""" + +import os +import json +import numpy as np +from scipy.special import betaincinv, betainccinv + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + +# Seeded random number generator to ensure reproducible fixtures: +RNG = np.random.default_rng(1234) + + +def gen(a, b, p, name): + """Generate fixture data and write to file. + + # Arguments + + * `a`: first function parameter + * `b`: second function parameter + * `p`: probability values + * `name::str`: output filename + + # Notes + + * Reference values are computed via SciPy, whose `betaincinv` and + `betainccinv` routines wrap the `ibeta_inv` and `ibetac_inv` + routines, respectively, from the Boost Math C++ library. + * The reference for each output is computed from whichever of `p` + and `q` is smaller, matching the target selection performed by + the implementation under test and avoiding loss of precision + when the complement `q = 1 - p` rounds to unity. + + # Examples + + ``` python + python> a = np.linspace(1.0, 40.0, 500) + python> b = np.linspace(1.0, 40.0, 500) + python> p = np.linspace(0.001, 0.999, 500) + python> gen(a, b, p, './data.json') + ``` + """ + a = np.asarray(a, dtype=np.float64) + b = np.asarray(b, dtype=np.float64) + p = np.asarray(p, dtype=np.float64) + q = 1.0 - p + + expected1 = np.where( + p <= q, betaincinv(a, b, p), betainccinv(a, b, q) + ) + expected2 = np.where( + p <= q, betainccinv(b, a, p), betaincinv(b, a, q) + ) + + # Exclude any values for which the reference implementation failed + # to return a finite reference value: + keep = np.isfinite(expected1) & np.isfinite(expected2) + + data = { + "a": a[keep].tolist(), + "b": b[keep].tolist(), + "p": p[keep].tolist(), + "q": q[keep].tolist(), + "expected1": expected1[keep].tolist(), + "expected2": expected2[keep].tolist() + } + + # Based on the script directory, create an output filepath: + filepath = os.path.join(DIR, name) + + # Write the data to the output filepath as JSON (terminated by a newline): + with open(filepath, "w", encoding="utf-8") as outfile: + json.dump(data, outfile) + outfile.write("\n") + + +def log_uniform(low, high, size): + """Draw log-uniformly distributed values over an interval. + + # Arguments + + * `low`: lower bound (inclusive) + * `high`: upper bound (exclusive) + * `size`: number of values to draw + + # Examples + + ``` python + python> x = log_uniform(10.0, 1.0e6, 500) + ``` + """ + return np.exp(RNG.uniform(np.log(low), np.log(high), size)) + + +def main(): + """Generate fixture data.""" + n = 500 + + # Medium parameters: + a = RNG.uniform(1.0, 40.0, n) + b = RNG.uniform(1.0, 40.0, n) + p = RNG.uniform(0.001, 0.999, n) + gen(a, b, p, "medium.json") + + # Small parameters (`a` and `b` both less than one): + a = RNG.uniform(0.01, 1.0, n) + b = RNG.uniform(0.01, 1.0, n) + p = RNG.uniform(1.0e-4, 0.9999, n) + gen(a, b, p, "small.json") + + # Mixed parameters (exactly one of `a` and `b` less than one): + half = n // 2 + a = np.concatenate([ + RNG.uniform(0.05, 0.95, half), + RNG.uniform(1.05, 4.0, half) + ]) + b = np.concatenate([ + RNG.uniform(1.05, 4.0, half), + RNG.uniform(0.05, 0.95, half) + ]) + p = RNG.uniform(1.0e-6, 0.999999, n) + gen(a, b, p, "mixed.json") + + # Large nearly-equal parameters: + a = log_uniform(10.0, 1.0e6, n) + b = a * RNG.uniform(0.96, 1.04, n) + p = RNG.uniform(0.001, 0.999, n) + gen(a, b, p, "large_symmetric.json") + + # Large asymmetric parameters: + a = log_uniform(1.0e2, 1.0e5, n) + b = RNG.uniform(0.55, 5.0, n) + swap = RNG.integers(0, 2, n).astype(bool) + p = RNG.uniform(0.001, 0.999, n) + gen(np.where(swap, b, a), np.where(swap, a, b), p, "large_asymmetric.json") + + # Very large parameters: + a = log_uniform(1.0e3, 1.0e8, 300) + b = log_uniform(1.0e3, 1.0e8, 300) + p = RNG.uniform(0.01, 0.99, 300) + gen(a, b, p, "huge.json") + + # Student's t special path (`b = 0.5`), including integer degrees + # of freedom and the deep tail: + a = np.concatenate([ + np.array([0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 5.0, 7.0, 10.0]), + log_uniform(0.5, 1.0e5, 440), + np.array([1.0e9, 1.0e10, 1.0e12]) + ]) + p = np.concatenate([ + RNG.uniform(1.0e-3, 0.999, 353), + 10.0 ** RNG.uniform(-30.0, -3.0, 100) + ]) + gen(a, np.full(len(a), 0.5), np.resize(p, len(a)), "students_t.json") + + # Closed-form path (`a = 1` or `b = 1`): + a = log_uniform(0.05, 100.0, 400) + swap = RNG.integers(0, 2, 400).astype(bool) + p = RNG.uniform(1.0e-6, 0.999999, 400) + gen(np.where(swap, 1.0, a), np.where(swap, a, 1.0), p, "linear.json") + + # Very small probabilities: + a = log_uniform(1.0, 30.0, 400) + b = log_uniform(1.0, 30.0, 400) + p = 10.0 ** RNG.uniform(-280.0, -10.0, 400) + gen(a, b, p, "tiny_p.json") + + # Probabilities near unity: + a = log_uniform(0.5, 50.0, 400) + b = log_uniform(0.5, 50.0, 400) + q = 10.0 ** RNG.uniform(-14.0, -3.0, 400) + gen(a, b, 1.0 - q, "p_near_one.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/python/small.json b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/python/small.json new file mode 100644 index 000000000000..a121bade5ce0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/fixtures/python/small.json @@ -0,0 +1 @@ +{"a": [0.6787438939503079, 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1.0, 1.0, 0.9999226656276274, 1.0, 1.0, 0.9999544119676681, 0.7237855640140034, 0.9988584512128464, 1.0, 1.0, 1.0, 0.9999999243351015, 1.0, 1.0, 1.0, 0.9999990625861108, 1.0, 1.0, 0.9989863037593358, 1.0, 1.0, 0.9999999803580626, 1.0, 0.9999997479826603, 0.9999999999985364, 0.99999982909929, 0.9999990917800036, 0.9999999999997315, 0.9999996126404622, 0.9999999980808941, 1.0, 0.9999999833023889, 1.0, 1.0, 1.0, 0.9994746049580152, 1.0, 0.999024829831516, 1.0, 1.0, 0.9999955924770142, 1.0, 1.0, 1.0, 1.0, 0.9999999756124959, 1.0, 1.0, 1.0, 0.9999999993921582, 0.9992662489496373, 1.0, 1.0, 1.0, 0.9999982761554967, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9998953906919831, 0.9999666505899961, 1.0, 0.9715997107665603, 1.0, 0.9999999999849476, 1.0, 1.0, 0.9999991582838884, 1.0, 1.0, 1.0, 0.9999997002917056, 1.0, 1.0, 1.0, 0.9999999999999893, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999964732632, 1.0, 1.0, 0.9999999990249869, 1.0, 1.0, 1.0, 0.9989135818958493, 0.999624143830673, 1.0, 1.0, 0.9999999998457043, 0.9999965279688595, 0.9960929591439648, 0.9999999924584537, 1.0, 1.0, 0.9999999999895584, 1.0, 0.9999999480768932, 0.9999999595862926, 0.999999999987974, 1.0, 0.9999999967272697, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999998432286342, 1.0, 0.9999999989336065, 0.9999999999920591, 0.9999998724462678, 1.0, 0.9999999999999999, 0.9999999999921904, 0.9999997608061011, 0.9999999999999816, 1.0, 1.0, 1.0, 0.9999999832725693, 0.9266494274476176, 1.0, 1.0, 1.0, 0.9999999992652684, 0.9999999999999861, 1.0, 0.9999996726474627, 1.0, 1.0, 1.0, 0.9999999999976331, 0.9999999999770344, 0.9999101602031123, 1.0, 0.9999999436316941, 0.9999999999989245, 0.9999979066694341, 0.9999999999994756, 1.0, 0.9999997362284515, 0.996084280067213, 1.0, 0.9999999999166352, 0.9999399307325543, 1.0, 0.9951854061974483, 0.9995012961536469, 0.9999999999999664, 0.9999720439923204, 1.0, 1.0, 1.0, 0.9998340172171647, 1.0, 0.9999999992628629, 1.0, 0.9268379249227724, 1.0, 1.0, 1.0, 0.999999661517225, 1.0, 1.0, 1.0, 0.9999999969612007, 0.9999999846702596, 0.9999998264308032, 0.9250744632308696, 1.0, 1.0, 1.0, 0.9999999651740116, 0.9999999996847042, 1.0, 1.0, 1.0, 1.0, 0.9463491505251632, 0.9999998967076916, 1.0, 0.8771304966646001, 0.9999978907276144, 0.9999999400585949, 0.9995711415172994, 0.9999999988449226, 1.0, 0.9999999999683938, 0.9999999996601063, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999988325595, 0.9999960068995047, 1.0, 1.0, 0.9999999999999998, 0.9999999733454417, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999999999799, 1.0, 0.9999881965636964, 0.9999999938055417, 1.0, 1.0, 0.9999999999999621, 0.999999999999994, 1.0, 0.9999999999999989, 1.0, 1.0, 0.9999999999976457, 0.9999998827579545, 1.0, 1.0, 0.9999999498429188, 1.0, 1.0, 1.0, 0.9999999999999534, 1.0, 1.0, 0.9999999990586229, 0.9999999985177122, 1.0, 1.0]} diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.js index 2cb34d554bcf..8b468ead072c 100644 --- a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.js @@ -22,12 +22,59 @@ var tape = require( 'tape' ); var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); +var isNaNArray = require( '@stdlib/assert/is-nan-array' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); var kernelBetaincinv = require( './../lib' ); // FIXTURES // -var data = require( './fixtures/cpp/output.json' ); +var largeAsymmetric = require( './fixtures/python/large_asymmetric.json' ); +var largeSymmetric = require( './fixtures/python/large_symmetric.json' ); +var studentsT = require( './fixtures/python/students_t.json' ); +var pNearOne = require( './fixtures/python/p_near_one.json' ); +var medium = require( './fixtures/python/medium.json' ); +var linear = require( './fixtures/python/linear.json' ); +var tinyP = require( './fixtures/python/tiny_p.json' ); +var mixed = require( './fixtures/python/mixed.json' ); +var small = require( './fixtures/python/small.json' ); +var huge = require( './fixtures/python/huge.json' ); + + +// FUNCTIONS // + +/** +* Tests the function against a fixture set. +* +* @private +* @param {Object} t - test object +* @param {Object} fixtures - fixture data +* @param {NonNegativeInteger} tol1 - ULP tolerance for the first output value +* @param {NonNegativeInteger} tol2 - ULP tolerance for the second output value +*/ +function testFixtures( t, fixtures, tol1, tol2 ) { + var expected1; + var expected2; + var out; + var a; + var b; + var p; + var q; + var i; + + a = fixtures.a; + b = fixtures.b; + p = fixtures.p; + q = fixtures.q; + expected1 = fixtures.expected1; + expected2 = fixtures.expected2; + for ( i = 0; i < p.length; i++ ) { + out = kernelBetaincinv( a[ i ], b[ i ], p[ i ], q[ i ] ); + t.strictEqual( isAlmostSameValue( out[ 0 ], expected1[ i ], tol1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( out[ 1 ], expected2[ i ], tol2 ), true, 'returns expected value' ); + } +} // TESTS // @@ -38,21 +85,161 @@ tape( 'main export is a function', function test( t ) { t.end(); }); -tape( 'the function evaluates the inverse of the lower regularized incomplete beta function', function test( t ) { - var expected; - var y; - var i; - var a; - var b; - var p; +tape( 'the function returns `[ NaN, NaN ]` if provided `NaN` for any parameter', function test( t ) { + var out; - p = data.p; - a = data.a; - b = data.b; - expected = data.y; - for ( i = 0; i < p.length; i++ ) { - y = kernelBetaincinv( a[i], b[i], p[i], 1.0-p[i] )[ 0 ]; - t.strictEqual( isAlmostSameValue( y, expected[ i ], 20 ), true, 'returns expected value' ); - } + out = kernelBetaincinv( NaN, 3.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, NaN, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, NaN, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, 0.5, NaN ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ NaN, NaN ]` if provided a negative `a` or `b`', function test( t ) { + var out; + + out = kernelBetaincinv( -1.0, 3.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, -1.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( NINF, 3.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ NaN, NaN ]` if provided `p` outside the interval `[0,1]`', function test( t ) { + var out; + + out = kernelBetaincinv( 2.0, 3.0, 1.5, -0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, -0.5, 1.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, PINF, NINF ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ 0.0, 1.0 ]` if provided `p = 0`', function test( t ) { + var out; + + out = kernelBetaincinv( 2.0, 3.0, 0.0, 1.0 ); + t.strictEqual( out[ 0 ], 0.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 1.0, 'returns expected value' ); + + out = kernelBetaincinv( 0.3, 0.7, 0.0, 1.0 ); + t.strictEqual( out[ 0 ], 0.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 1.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ 1.0, 0.0 ]` if provided `q = 0`', function test( t ) { + var out; + + out = kernelBetaincinv( 2.0, 3.0, 1.0, 0.0 ); + t.strictEqual( out[ 0 ], 1.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.0, 'returns expected value' ); + + out = kernelBetaincinv( 0.3, 0.7, 1.0, 0.0 ); + t.strictEqual( out[ 0 ], 1.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ p, 1 - p ]` if provided `a = 1` and `b = 1`', function test( t ) { + var out; + + out = kernelBetaincinv( 1.0, 1.0, 0.3, 0.7 ); + t.strictEqual( out[ 0 ], 0.3, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.7, 'returns expected value' ); + + out = kernelBetaincinv( 1.0, 1.0, 0.925, 0.075 ); + t.strictEqual( out[ 0 ], 0.925, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.07499999999999996, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function uses a closed-form expression if provided `a = 0.5` and `b = 0.5`', function test( t ) { + var out; + + out = kernelBetaincinv( 0.5, 0.5, 0.25, 0.75 ); + t.strictEqual( out[ 0 ], 0.14644660940672624, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.8535533905932737, 'returns expected value' ); + + out = kernelBetaincinv( 0.5, 0.5, 0.5, 0.5 ); + t.strictEqual( out[ 0 ], 0.4999999999999999, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.4999999999999999, 'returns expected value' ); + + out = kernelBetaincinv( 0.5, 0.5, 0.75, 0.25 ); + t.strictEqual( out[ 0 ], 0.8535533905932737, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.14644660940672624, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (medium `a` and `b`)', function test( t ) { + testFixtures( t, medium, 100, 100 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (small `a` and `b`)', function test( t ) { + testFixtures( t, small, 700, 700 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (mixed small and large parameters)', function test( t ) { + testFixtures( t, mixed, 200, 200 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (large nearly equal `a` and `b`)', function test( t ) { + testFixtures( t, largeSymmetric, 2000, 2000 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (large asymmetric `a` and `b`)', function test( t ) { + testFixtures( t, largeAsymmetric, 50, 50 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (very large `a` and `b`)', function test( t ) { + // NOTE: for very large parameters, the reference values themselves are only accurate to a relative error on the order of `1e-11`; the wide tolerances reflect reference-value accuracy, not implementation error. + testFixtures( t, huge, 75000, 150000 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (Student\'s t case, `b = 0.5`)', function test( t ) { + testFixtures( t, studentsT, 50, 50 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (`a = 1` or `b = 1`)', function test( t ) { + testFixtures( t, linear, 100, 100 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (very small `p`)', function test( t ) { + testFixtures( t, tinyP, 200, 50 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (`p` near unity)', function test( t ) { + testFixtures( t, pNearOne, 100, 300 ); t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.native.js new file mode 100644 index 000000000000..472581371eaa --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/kernel-betaincinv/test/test.native.js @@ -0,0 +1,254 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); +var isNaNArray = require( '@stdlib/assert/is-nan-array' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); + + +// VARIABLES // + +var kernelBetaincinv = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( kernelBetaincinv instanceof Error ) +}; + + +// FIXTURES // + +var largeAsymmetric = require( './fixtures/python/large_asymmetric.json' ); +var largeSymmetric = require( './fixtures/python/large_symmetric.json' ); +var studentsT = require( './fixtures/python/students_t.json' ); +var pNearOne = require( './fixtures/python/p_near_one.json' ); +var medium = require( './fixtures/python/medium.json' ); +var linear = require( './fixtures/python/linear.json' ); +var tinyP = require( './fixtures/python/tiny_p.json' ); +var mixed = require( './fixtures/python/mixed.json' ); +var small = require( './fixtures/python/small.json' ); +var huge = require( './fixtures/python/huge.json' ); + + +// FUNCTIONS // + +/** +* Tests the function against a fixture set. +* +* @private +* @param {Object} t - test object +* @param {Object} fixtures - fixture data +* @param {NonNegativeInteger} tol1 - ULP tolerance for the first output value +* @param {NonNegativeInteger} tol2 - ULP tolerance for the second output value +*/ +function testFixtures( t, fixtures, tol1, tol2 ) { + var expected1; + var expected2; + var out; + var a; + var b; + var p; + var q; + var i; + + a = fixtures.a; + b = fixtures.b; + p = fixtures.p; + q = fixtures.q; + expected1 = fixtures.expected1; + expected2 = fixtures.expected2; + for ( i = 0; i < p.length; i++ ) { + out = kernelBetaincinv( a[ i ], b[ i ], p[ i ], q[ i ] ); + t.strictEqual( isAlmostSameValue( out[ 0 ], expected1[ i ], tol1 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( out[ 1 ], expected2[ i ], tol2 ), true, 'returns expected value' ); + } +} + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof kernelBetaincinv, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `[ NaN, NaN ]` if provided `NaN` for any parameter', opts, function test( t ) { + var out; + + out = kernelBetaincinv( NaN, 3.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, NaN, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, NaN, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, 0.5, NaN ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ NaN, NaN ]` if provided a negative `a` or `b`', opts, function test( t ) { + var out; + + out = kernelBetaincinv( -1.0, 3.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, -1.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( NINF, 3.0, 0.5, 0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ NaN, NaN ]` if provided `p` outside the interval `[0,1]`', opts, function test( t ) { + var out; + + out = kernelBetaincinv( 2.0, 3.0, 1.5, -0.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, -0.5, 1.5 ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + out = kernelBetaincinv( 2.0, 3.0, PINF, NINF ); + t.strictEqual( isNaNArray( out ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ 0.0, 1.0 ]` if provided `p = 0`', opts, function test( t ) { + var out; + + out = kernelBetaincinv( 2.0, 3.0, 0.0, 1.0 ); + t.strictEqual( out[ 0 ], 0.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 1.0, 'returns expected value' ); + + out = kernelBetaincinv( 0.3, 0.7, 0.0, 1.0 ); + t.strictEqual( out[ 0 ], 0.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 1.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ 1.0, 0.0 ]` if provided `q = 0`', opts, function test( t ) { + var out; + + out = kernelBetaincinv( 2.0, 3.0, 1.0, 0.0 ); + t.strictEqual( out[ 0 ], 1.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.0, 'returns expected value' ); + + out = kernelBetaincinv( 0.3, 0.7, 1.0, 0.0 ); + t.strictEqual( out[ 0 ], 1.0, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `[ p, 1 - p ]` if provided `a = 1` and `b = 1`', opts, function test( t ) { + var out; + + out = kernelBetaincinv( 1.0, 1.0, 0.3, 0.7 ); + t.strictEqual( out[ 0 ], 0.3, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.7, 'returns expected value' ); + + out = kernelBetaincinv( 1.0, 1.0, 0.925, 0.075 ); + t.strictEqual( out[ 0 ], 0.925, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.07499999999999996, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function uses a closed-form expression if provided `a = 0.5` and `b = 0.5`', opts, function test( t ) { + var out; + + out = kernelBetaincinv( 0.5, 0.5, 0.25, 0.75 ); + t.strictEqual( out[ 0 ], 0.14644660940672624, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.8535533905932737, 'returns expected value' ); + + out = kernelBetaincinv( 0.5, 0.5, 0.5, 0.5 ); + t.strictEqual( out[ 0 ], 0.4999999999999999, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.4999999999999999, 'returns expected value' ); + + out = kernelBetaincinv( 0.5, 0.5, 0.75, 0.25 ); + t.strictEqual( out[ 0 ], 0.8535533905932737, 'returns expected value' ); + t.strictEqual( out[ 1 ], 0.14644660940672624, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (medium `a` and `b`)', opts, function test( t ) { + testFixtures( t, medium, 100, 100 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (small `a` and `b`)', opts, function test( t ) { + testFixtures( t, small, 700, 700 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (mixed small and large parameters)', opts, function test( t ) { + testFixtures( t, mixed, 200, 200 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (large nearly equal `a` and `b`)', opts, function test( t ) { + testFixtures( t, largeSymmetric, 2000, 2000 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (large asymmetric `a` and `b`)', opts, function test( t ) { + testFixtures( t, largeAsymmetric, 50, 50 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (very large `a` and `b`)', opts, function test( t ) { + // NOTE: for very large parameters, the reference values themselves are only accurate to a relative error on the order of `1e-11`; the wide tolerances reflect reference-value accuracy, not implementation error. + testFixtures( t, huge, 75000, 150000 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (Student\'s t case, `b = 0.5`)', opts, function test( t ) { + testFixtures( t, studentsT, 50, 50 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (`a = 1` or `b = 1`)', opts, function test( t ) { + testFixtures( t, linear, 100, 100 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (very small `p`)', opts, function test( t ) { + testFixtures( t, tinyP, 200, 50 ); + t.end(); +}); + +tape( 'the function evaluates the inverse of the lower regularized incomplete beta function (`p` near unity)', opts, function test( t ) { + testFixtures( t, pNearOne, 100, 300 ); + t.end(); +});