From c473878b290958a4f4e5399f75751ce7f98b3ad2 Mon Sep 17 00:00:00 2001 From: headlessNode Date: Sat, 13 Jun 2026 01:40:16 +0500 Subject: [PATCH 1/5] feat: add integrate/strided/dtrapezoid --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: passed - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: passed - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: missing_dependencies - task: lint_c_examples status: missing_dependencies - task: 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+ +The [trapezoidal rule][trapezoidal-rule] approximates the definite integral of a function sampled at discrete points as a sum of trapezoids: + + + +```math +\int_a^b f(x)\,dx \approx \frac{1}{2} \sum_{i=0}^{n-1} (x_{i+1} - x_i)(f(x_i) + f(x_{i+1})) +``` + + + + + +where `x` is an array of sample points and `f(x)` is an array of function values (dependent variable) at those points. + +
+ + + +
+ +## Usage + +```javascript +var dtrapezoid = require( '@stdlib/integrate/strided/dtrapezoid' ); +``` + +#### dtrapezoid( N, x, strideX, y, strideY ) + +Computes the integral of a double-precision floating-point strided array using the trapezoidal rule. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); +var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + +var out = dtrapezoid( x.length, x, 1, y, 1 ); +// returns 9.5 +``` + +The function has the following parameters: + +- **N**: number of indexed elements. +- **x**: first input [`Float64Array`][@stdlib/array/float64]. +- **strideX**: stride length for `x`. +- **y**: second input [`Float64Array`][@stdlib/array/float64]. +- **strideY**: stride length for `y`. + +The `N` and strides parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the integral using every other value: + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] ); +var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0, 16.0, 25.0 ] ); + +var out = dtrapezoid( 3, x, 2, y, 2 ); +// returns 24.0 +``` + +Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +// Initial arrays... +var x0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] ); +var y0 = new Float64Array( [ 0.0, 1.0, 4.0, 9.0, 16.0 ] ); + +// Create offset views... +var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element +var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element + +var out = dtrapezoid( 3, x1, 1, y1, 1 ); +// returns 9.0 +``` + +#### dtrapezoid.ndarray( N, x, strideX, offsetX, y, strideY, offsetY ) + +Computes the integral of a double-precision floating-point strided array using the trapezoidal rule and alternative indexing semantics. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); +var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + +var out = dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, 0 ); +// returns 9.5 +``` + +The function has the following additional parameters: + +- **offsetX**: starting index for `x`. +- **offsetY**: starting index for `y`. + +While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to compute the integral using the last 3 elements: + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); + +var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] ); +var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0, 16.0, 25.0 ] ); + +var v = dtrapezoid.ndarray( 3, x, 1, 3, y, 1, 3 ); +// returns 33.0 +``` + +
+ + + +
+ +## Notes + +- If `N <= 1`, the function returns `0.0`. +- The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function. + +
+ + + +
+ +## Examples + + + +```javascript +var uniform = require( '@stdlib/random/array/uniform' ); +var dtrapezoid = require( '@stdlib/integrate/strided/dtrapezoid' ); + +var opts = { + 'dtype': 'float64' +}; +var x = uniform( 10, 0.0, 10.0, opts ); +console.log( x ); + +var y = uniform( x.length, 0.0, 10.0, opts ); +console.log( y ); + +var v = dtrapezoid( x.length, x, 1, y, 1 ); +console.log( v ); +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/integrate/strided/dtrapezoid.h" +``` + +#### stdlib_strided_dtrapezoid( N, \*X, strideX, \*Y, strideY ) + +Computes the integral of a double-precision floating-point strided array using the trapezoidal rule. + +```c +const double x[] = { 0.0, 1.0, 2.0, 3.0 }; +const double y[] = { 0.0, 1.0, 4.0, 9.0 }; + +double out = stdlib_strided_dtrapezoid( 4, x, 1, y, 1 ); +// returns 9.5 +``` + +The function accepts the following arguments: + +- **N**: `[in] CBLAS_INT` number of indexed elements. +- **X**: `[in] double*` first input array. +- **strideX**: `[in] CBLAS_INT` stride length for `X`. +- **Y**: `[in] double*` second input array. +- **strideY**: `[in] CBLAS_INT` stride length for `Y`. + +```c +double stdlib_strided_dtrapezoid( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY ); +``` + + + +#### stdlib_strided_dtrapezoid_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY ) + + + +Computes the integral of a double-precision floating-point strided array using the trapezoidal rule and alternative indexing semantics. + +```c +const double x[] = { 0.0, 1.0, 2.0, 3.0 }; +const double y[] = { 0.0, 1.0, 4.0, 9.0 }; + +double out = stdlib_strided_dtrapezoid_ndarray( 4, x, 1, 0, y, 1, 0 ); +// returns 9.5 +``` + +The function accepts the following arguments: + +- **N**: `[in] CBLAS_INT` number of indexed elements. +- **X**: `[in] double*` first input array. +- **strideX**: `[in] CBLAS_INT` stride length for `X`. +- **offsetX**: `[in] CBLAS_INT` starting index for `X`. +- **Y**: `[in] double*` second input array. +- **strideY**: `[in] CBLAS_INT` stride length for `Y`. +- **offsetY**: `[in] CBLAS_INT` starting index for `Y`. + +```c +double stdlib_strided_dtrapezoid_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/integrate/strided/dtrapezoid.h" +#include + +int main( void ) { + // Create strided arrays: + const double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 }; + const double y[] = { 0.0, 1.0, 4.0, 9.0, 16.0, 25.0 }; + + // Specify the number of elements: + const int N = 6; + + // Specify strides: + const int strideX = 1; + const int strideY = 1; + + // Compute the integral: + double out = stdlib_strided_dtrapezoid( N, x, strideX, y, strideY ); + + // Print the result: + printf( "integral: %lf\n", out ); +} +``` + +
+ + + +
+ + + + + + + + + + + + + + diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.js new file mode 100644 index 000000000000..f17c0be5f744 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.js @@ -0,0 +1,104 @@ +/** +* @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 bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var dtrapezoid = require( './../lib/dtrapezoid.js' ); + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var x = uniform( len, 0.0, 10.0, options ); + var y = uniform( len, 0.0, 10.0, options ); + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var out; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + out = dtrapezoid( x.length, x, 1, y, 1 ); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var len; + var min; + var max; + var f; + var i; + + min = 1; // 10^min + max = 6; // 10^max + + for ( i = min; i <= max; i++ ) { + len = pow( 10, i ); + f = createBenchmark( len ); + bench( format( '%s:len=%d', pkg, len ), f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.native.js new file mode 100644 index 000000000000..b5e304599faa --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.native.js @@ -0,0 +1,109 @@ +/** +* @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 pow = require( '@stdlib/math/base/special/pow' ); +var format = require( '@stdlib/string/format' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; +var dtrapezoid = tryRequire( resolve( __dirname, './../lib/dtrapezoid.native.js' ) ); +var opts = { + 'skip': ( dtrapezoid instanceof Error ) +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var x = uniform( len, 0.0, 10.0, options ); + var y = uniform( len, 0.0, 10.0, options ); + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var out; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + out = dtrapezoid( x.length, x, 1, y, 1 ); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var len; + var min; + var max; + var f; + var i; + + min = 1; // 10^min + max = 6; // 10^max + + for ( i = min; i <= max; i++ ) { + len = pow( 10, i ); + f = createBenchmark( len ); + bench( format( '%s::native:len=%d', pkg, len ), opts, f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.ndarray.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.ndarray.js new file mode 100644 index 000000000000..bf0f659a7a00 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.ndarray.js @@ -0,0 +1,104 @@ +/** +* @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 bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var dtrapezoid = require( './../lib/ndarray.js' ); + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var x = uniform( len, 0.0, 10.0, options ); + var y = uniform( len, 0.0, 10.0, options ); + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var out; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var len; + var min; + var max; + var f; + var i; + + min = 1; // 10^min + max = 6; // 10^max + + for ( i = min; i <= max; i++ ) { + len = pow( 10, i ); + f = createBenchmark( len ); + bench( format( '%s:ndarray:len=%d', pkg, len ), f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.ndarray.native.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.ndarray.native.js new file mode 100644 index 000000000000..0f551c62beb7 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/benchmark.ndarray.native.js @@ -0,0 +1,109 @@ +/** +* @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 pow = require( '@stdlib/math/base/special/pow' ); +var format = require( '@stdlib/string/format' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; +var dtrapezoid = tryRequire( resolve( __dirname, './../lib/ndarray.native.js' ) ); +var opts = { + 'skip': ( dtrapezoid instanceof Error ) +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} len - array length +* @returns {Function} benchmark function +*/ +function createBenchmark( len ) { + var x = uniform( len, 0.0, 10.0, options ); + var y = uniform( len, 0.0, 10.0, options ); + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var out; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( out ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var len; + var min; + var max; + var f; + var i; + + min = 1; // 10^min + max = 6; // 10^max + + for ( i = min; i <= max; i++ ) { + len = pow( 10, i ); + f = createBenchmark( len ); + bench( format( '%s::ndarray:native:len=%d', pkg, len ), opts, f ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/c/Makefile b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/c/Makefile new file mode 100644 index 000000000000..0756dc7da20a --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/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 := benchmark.length.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/integrate/strided/dtrapezoid/benchmark/c/benchmark.length.c b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/c/benchmark.length.c new file mode 100644 index 000000000000..ff891bbca71e --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/benchmark/c/benchmark.length.c @@ -0,0 +1,203 @@ +/** +* @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/integrate/strided/dtrapezoid.h" +#include +#include +#include +#include +#include + +#define NAME "dtrapezoid" +#define ITERATIONS 10000000 +#define REPEATS 3 +#define MIN 1 +#define MAX 6 + +/** +* 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 iterations number of iterations +* @param elapsed elapsed time in seconds +*/ +static void print_results( int iterations, 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 [0,1). +* +* @return random number +*/ +static double rand_double( void ) { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @param iterations number of iterations +* @param len array length +* @return elapsed time in seconds +*/ +static double benchmark1( int iterations, int len ) { + double elapsed; + double *x; + double *y; + double z; + double t; + int i; + + x = (double *) malloc( len * sizeof( double ) ); + y = (double *) malloc( len * sizeof( double ) ); + for ( i = 0; i < len; i++ ) { + x[ i ] = ( rand_double()*20.0 ) - 10.0; + y[ i ] = ( rand_double()*20.0 ) - 10.0; + } + z = 0.0; + t = tic(); + for ( i = 0; i < iterations; i++ ) { + z = stdlib_strided_dtrapezoid( len, x, 1, y, 1 ); + if ( z != z ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( z != z ) { + printf( "should not return NaN\n" ); + } + free( x ); + free( y ); + return elapsed; +} + +/** +* Runs a benchmark. +* +* @param iterations number of iterations +* @param len array length +* @return elapsed time in seconds +*/ +static double benchmark2( int iterations, int len ) { + double elapsed; + double *x; + double *y; + double z; + double t; + int i; + + x = (double *) malloc( len * sizeof( double ) ); + y = (double *) malloc( len * sizeof( double ) ); + for ( i = 0; i < len; i++ ) { + x[ i ] = ( rand_double()*20.0 ) - 10.0; + y[ i ] = ( rand_double()*20.0 ) - 10.0; + } + z = 0.0; + t = tic(); + for ( i = 0; i < iterations; i++ ) { + z = stdlib_strided_dtrapezoid_ndarray( len, x, 1, 0, y, 1, 0 ); + if ( z != z ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( z != z ) { + printf( "should not return NaN\n" ); + } + free( x ); + free( y ); + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int count; + int iter; + int len; + int i; + int j; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + count = 0; + for ( i = MIN; i <= MAX; i++ ) { + len = pow( 10, i ); + iter = ITERATIONS / pow( 10, i-1 ); + for ( j = 0; j < REPEATS; j++ ) { + count += 1; + printf( "# c::%s:len=%d\n", NAME, len ); + elapsed = benchmark1( iter, len ); + print_results( iter, elapsed ); + printf( "ok %d benchmark finished\n", count ); + } + for ( j = 0; j < REPEATS; j++ ) { + count += 1; + printf( "# c::%s:ndarray:len=%d\n", NAME, len ); + elapsed = benchmark2( iter, len ); + print_results( iter, elapsed ); + printf( "ok %d benchmark finished\n", count ); + } + } + print_summary( count, count ); +} diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp new file mode 100644 index 000000000000..7d0005b2e390 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2020 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/integrate/strided/dtrapezoid/docs/repl.txt b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/repl.txt new file mode 100644 index 000000000000..6c1919ab13cd --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/repl.txt @@ -0,0 +1,113 @@ + +{{alias}}( N, x, strideX, y, strideY ) + Computes the integral of a double-precision floating-point strided array + using the trapezoidal rule. + + The `N` and stride parameters determine which elements in the strided arrays + are accessed at runtime. + + Indexing is relative to the first index. To introduce an offset, use a typed + array view. + + If `N <= 1`, the function returns `0`. + + The function computes an approximation of the integral using the trapezoidal + rule whose accuracy depends on the sample point spacing and the smoothness + of the underlying function. + + Parameters + ---------- + N: integer + Number of indexed elements. + + x: Float64Array + First input array. + + strideX: integer + Stride length for `x`. + + y: Float64Array + Second input array. + + strideY: integer + Stride length for `y`. + + Returns + ------- + out: number + Integral approximation. + + Examples + -------- + // Standard usage: + > var x = new {{alias:@stdlib/array/float64}}( [ 0.0, 1.0, 2.0, 3.0 ] ); + > var y = new {{alias:@stdlib/array/float64}}( [ 0.0, 1.0, 4.0, 9.0 ] ); + > var out = {{alias}}( x.length, x, 1, y, 1 ) + 9.5 + + // Using `N` and stride parameters: + > x = new {{alias:@stdlib/array/float64}}( [ 0.0, -1.0, 1.0, -1.0, 2.0 ] ); + > y = new {{alias:@stdlib/array/float64}}( [ 0.0, 2.0, 6.0 ] ); + > out = {{alias}}( 3, x, 2, y, 1 ) + 5.0 + + // Using view offsets: + > x = new {{alias:@stdlib/array/float64}}( [ -1.0, 0.0, 1.0, 1.0, 2.0, 2.0 ] ); + > y = new {{alias:@stdlib/array/float64}}( [ -1.0, -1.0, 0.0, 1.0, 1.0, 4.0 ] ); + > var x1 = new {{alias:@stdlib/array/float64}}( x.buffer, x.BYTES_PER_ELEMENT*1 ); + > var y1 = new {{alias:@stdlib/array/float64}}( y.buffer, y.BYTES_PER_ELEMENT*3 ); + > out = {{alias}}( 3, x1, 2, y1, 1 ) + 3.5 + + +{{alias}}.ndarray( N, x, strideX, offsetX, y, strideY, offsetY ) + Computes the integral of a double-precision floating-point strided array + using the trapezoidal rule and alternative indexing semantics. + + While typed array views mandate a view offset based on the underlying + buffer, the offset parameters support indexing based on a starting index. + + Parameters + ---------- + N: integer + Number of indexed elements. + + x: Float64Array + First input array. + + strideX: integer + Stride length for `x`. + + offsetX: integer + Starting index for `x`. + + y: Float64Array + Second input array. + + strideY: integer + Stride length for `y`. + + offsetY: integer + Starting index for `y`. + + Returns + ------- + out: number + Integral approximation. + + Examples + -------- + // Standard usage: + > var x = new {{alias:@stdlib/array/float64}}( [ 0.0, 1.0, 2.0, 3.0 ] ); + > var y = new {{alias:@stdlib/array/float64}}( [ 0.0, 1.0, 4.0, 9.0 ] ); + > var out = {{alias}}.ndarray( x.length, x, 1, 0, y, 1, 0 ) + 9.5 + + // Advanced indexing: + > x = new {{alias:@stdlib/array/float64}}( [ -1.0, 0.0, 1.0, 1.0, 2.0, 2.0 ] ); + > y = new {{alias:@stdlib/array/float64}}( [ -1.0, -1.0, 0.0, 1.0, 1.0, 4.0 ] ); + > out = {{alias}}.ndarray( 3, x, 2, 1, y, 1, 3 ) + 3.5 + + See Also + -------- diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/types/index.d.ts b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/types/index.d.ts new file mode 100644 index 000000000000..0f3974688c17 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/types/index.d.ts @@ -0,0 +1,111 @@ +/* +* @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. +*/ + +// TypeScript Version: 4.1 + +/** +* Interface describing `dtrapezoid`. +*/ +interface Routine { + /** + * Computes the integral of a double-precision floating-point strided array using the trapezoidal rule. + * + * ## Notes + * + * - The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function. + * + * @param N - number of indexed elements + * @param x - first input array + * @param strideX - stride length for `x` + * @param y - second input array + * @param strideY - stride length for `y` + * @returns integral approximation + * + * @example + * var Float64Array = require( '@stdlib/array/float64' ); + * + * var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); + * var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + * + * var out = dtrapezoid( x.length, x, 1, y, 1 ); + * // returns 9.5 + */ + ( N: number, x: Float64Array, strideX: number, y: Float64Array, strideY: number ): number; + + /** + * Computes the integral of a double-precision floating-point strided array using the trapezoidal rule and alternative indexing semantics. + * + * ## Notes + * + * - The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function. + * + * @param N - number of indexed elements + * @param x - first input array + * @param strideX - stride length for `x` + * @param offsetX - starting index for `x` + * @param y - second input array + * @param strideY - stride length for `y` + * @param offsetY - starting index for `y` + * @returns integral approximation + * + * @example + * var Float64Array = require( '@stdlib/array/float64' ); + * + * var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); + * var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + * + * var out = dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, 0 ); + * // returns 9.5 + */ + ndarray( N: number, x: Float64Array, strideX: number, offsetX: number, y: Float64Array, strideY: number, offsetY: number ): number; +} + +/** +* Computes the integral of a double-precision floating-point strided array using the trapezoidal rule. +* +* @param N - number of indexed elements +* @param x - first input array +* @param strideX - stride length for `x` +* @param y - second input array +* @param strideY - stride length for `y` +* @returns integral approximation +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); +* var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); +* +* var out = dtrapezoid( x.length, x, 1, y, 1 ); +* // returns 9.5 +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); +* var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); +* +* var out = dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, 0 ); +* // returns 9.5 +*/ +declare var dtrapezoid: Routine; + + +// EXPORTS // + +export = dtrapezoid; diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/types/test.ts b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/types/test.ts new file mode 100644 index 000000000000..b76d00951d9e --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/docs/types/test.ts @@ -0,0 +1,248 @@ +/* +* @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. +*/ + +import dtrapezoid = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid( x.length, x, 1, y, 1 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid( '10', x, 1, y, 1 ); // $ExpectError + dtrapezoid( true, x, 1, y, 1 ); // $ExpectError + dtrapezoid( false, x, 1, y, 1 ); // $ExpectError + dtrapezoid( null, x, 1, y, 1 ); // $ExpectError + dtrapezoid( undefined, x, 1, y, 1 ); // $ExpectError + dtrapezoid( [], x, 1, y, 1 ); // $ExpectError + dtrapezoid( {}, x, 1, y, 1 ); // $ExpectError + dtrapezoid( ( x: number ): number => x, x, 1, y, 1 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a Float64Array... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid( x.length, 10, 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, '10', 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, true, 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, false, 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, null, 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, undefined, 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, [], 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, {}, 1, y, 1 ); // $ExpectError + dtrapezoid( x.length, ( x: number ): number => x, 1, y, 1 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a third argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid( x.length, x, '10', y, 1 ); // $ExpectError + dtrapezoid( x.length, x, true, y, 1 ); // $ExpectError + dtrapezoid( x.length, x, false, y, 1 ); // $ExpectError + dtrapezoid( x.length, x, null, y, 1 ); // $ExpectError + dtrapezoid( x.length, x, undefined, y, 1 ); // $ExpectError + dtrapezoid( x.length, x, [], y, 1 ); // $ExpectError + dtrapezoid( x.length, x, {}, y, 1 ); // $ExpectError + dtrapezoid( x.length, x, ( x: number ): number => x, y, 1 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fourth argument which is not a Float64Array... +{ + const x = new Float64Array( 10 ); + + dtrapezoid( x.length, x, 1, 10, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, '10', 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, true, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, false, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, null, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, undefined, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, [], 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, {}, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, ( x: number ): number => x, 1 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fifth argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid( x.length, x, 1, y, '10' ); // $ExpectError + dtrapezoid( x.length, x, 1, y, true ); // $ExpectError + dtrapezoid( x.length, x, 1, y, false ); // $ExpectError + dtrapezoid( x.length, x, 1, y, null ); // $ExpectError + dtrapezoid( x.length, x, 1, y, undefined ); // $ExpectError + dtrapezoid( x.length, x, 1, y, [] ); // $ExpectError + dtrapezoid( x.length, x, 1, y, {} ); // $ExpectError + dtrapezoid( x.length, x, 1, y, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid(); // $ExpectError + dtrapezoid( x.length ); // $ExpectError + dtrapezoid( x.length, x ); // $ExpectError + dtrapezoid( x.length, x, 1 ); // $ExpectError + dtrapezoid( x.length, x, 1, y ); // $ExpectError + dtrapezoid( x.length, x, 1, y, 1, 10 ); // $ExpectError +} + +// Attached to main export is an `ndarray` method which returns a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, 0 ); // $ExpectType number +} + +// The compiler throws an error if the `ndarray` method is provided a first argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( '10', x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( true, x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( false, x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( null, x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( undefined, x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( [], x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( {}, x, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( ( x: number ): number => x, x, 1, 0, y, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided a second argument which is not a Float64Array... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, 10, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, '10', 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, true, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, false, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, null, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, undefined, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, [], 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, {}, 1, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, ( x: number ): number => x, 1, 0, y, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided a third argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, x, '10', 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, true, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, false, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, null, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, undefined, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, [], 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, {}, 0, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, ( x: number ): number => x, 0, y, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided a fourth argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, x, 1, '10', y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, true, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, false, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, null, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, undefined, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, [], y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, {}, y, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, ( x: number ): number => x, y, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided a fifth argument which is not a Float64Array... +{ + const x = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, x, 1, 0, 10, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, '10', 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, true, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, false, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, null, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, undefined, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, [], 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, {}, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, ( x: number ): number => x, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided a sixth argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, x, 1, 0, y, '10', 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, true, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, false, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, null, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, undefined, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, [], 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, {}, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, ( x: number ): number => x, 0 ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided a seventh argument which is not a number... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, '10' ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, true ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, false ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, null ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, undefined ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, [] ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, {} ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided an unsupported number of arguments... +{ + const x = new Float64Array( 10 ); + const y = new Float64Array( 10 ); + + dtrapezoid.ndarray(); // $ExpectError + dtrapezoid.ndarray( x.length ); // $ExpectError + dtrapezoid.ndarray( x.length, x ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1 ); // $ExpectError + dtrapezoid.ndarray( x.length, x, 1, 0, y, 1, 0, 10 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/c/Makefile b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/c/Makefile new file mode 100644 index 000000000000..c8f8e9a1517b --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/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/integrate/strided/dtrapezoid/examples/c/example.c b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/c/example.c new file mode 100644 index 000000000000..2af9c4547aeb --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/c/example.c @@ -0,0 +1,39 @@ +/** +* @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/integrate/strided/dtrapezoid.h" +#include + +int main( void ) { + // Create strided arrays: + const double x[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 }; + const double y[] = { 0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81.0 }; + + // Specify the number of elements: + const int N = 10; + + // Specify strides: + const int strideX = 1; + const int strideY = 1; + + // Compute the integral: + double out = stdlib_strided_dtrapezoid( N, x, strideX, y, strideY ); + + // Print the result: + printf( "integral: %lf\n", out ); +} diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/index.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/index.js new file mode 100644 index 000000000000..71bcedf8c075 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/examples/index.js @@ -0,0 +1,34 @@ +/** +* @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'; + +var uniform = require( '@stdlib/random/array/uniform' ); +var dtrapezoid = require( './../lib' ); + +var opts = { + 'dtype': 'float64' +}; +var x = uniform( 10, 0.0, 10.0, opts ); +console.log( x ); + +var y = uniform( x.length, 0.0, 10.0, opts ); +console.log( y ); + +var out = dtrapezoid( x.length, x, 1, y, 1 ); +console.log( out ); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi new file mode 100644 index 000000000000..26476a8c2655 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2020 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': [ + ' 0 ) { + for ( i = 0; i < m; i++ ) { + sum += ((x[ix+1] - x[ix]) * (y[iy] + y[iy+1])); + ix += 1; + iy += 1; + } + } + if ( N - 1 < M ) { + return sum * 0.5; + } + for ( i = m; i < N - 1; i += M ) { + sum += (((x[ix+1]-x[ix])*(y[iy]+y[iy+1])) + + ((x[ix+2]-x[ix+1])*(y[iy+1]+y[iy+2])) + + ((x[ix+3]-x[ix+2])*(y[iy+2]+y[iy+3])) + + ((x[ix+4]-x[ix+3])*(y[iy+3]+y[iy+4])) + + ((x[ix+5]-x[ix+4])*(y[iy+4]+y[iy+5]))); + ix += M; + iy += M; + } + return sum * 0.5; + } + x0 = x[ix]; + y0 = y[iy]; + for ( i = 1; i < N; i++ ) { + ix += strideX; + iy += strideY; + x1 = x[ix]; + y1 = y[iy]; + sum += ((x1 - x0) * (y1 + y0)); + x0 = x1; + y0 = y1; + } + return sum * 0.5; +} + + +// EXPORTS // + +module.exports = dtrapezoid; diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.native.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.native.js new file mode 100644 index 000000000000..56be1ede96b3 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.native.js @@ -0,0 +1,60 @@ +/** +* @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 addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the integral of a double-precision floating-point strided array using the trapezoidal rule and alternative indexing semantics. +* +* ## Notes +* +* - The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function. +* +* @param {NonNegativeInteger} N - number of indexed elements +* @param {Float64Array} x - first input array +* @param {integer} strideX - stride length for `x` +* @param {NonNegativeInteger} offsetX - starting index for `x` +* @param {Float64Array} y - second input array +* @param {integer} strideY - stride length for `y` +* @param {NonNegativeInteger} offsetY - starting index for `y` +* @returns {number} integral approximation +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); +* var y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); +* +* var out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); +* // returns 9.5 +*/ +function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) { + return addon.ndarray( N, x, strideX, offsetX, y, strideY, offsetY ); +} + + +// EXPORTS // + +module.exports = dtrapezoid; diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/manifest.json b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/manifest.json new file mode 100644 index 000000000000..db881e1b375d --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/manifest.json @@ -0,0 +1,79 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/napi/export", + "@stdlib/napi/argv", + "@stdlib/napi/argv-int64", + "@stdlib/napi/argv-strided-float64array", + "@stdlib/napi/create-double", + "@stdlib/blas/base/shared", + "@stdlib/strided/base/stride2offset" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/blas/base/shared", + "@stdlib/strided/base/stride2offset" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/blas/base/shared", + "@stdlib/strided/base/stride2offset" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/package.json b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/package.json new file mode 100644 index 000000000000..1137f0a4a508 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/package.json @@ -0,0 +1,78 @@ +{ + "name": "@stdlib/integrate/strided/dtrapezoid", + "version": "0.0.0", + "description": "Compute the integral of a double-precision floating-point strided array using the trapezoidal rule.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "browser": "./lib/main.js", + "gypfile": true, + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "include": "./include", + "lib": "./lib", + "src": "./src", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "integrate", + "integration", + "numerical", + "trapezoidal", + "trapezoid", + "trapz", + "quadrature", + "strided", + "strided array", + "typed", + "array", + "float64", + "double", + "float64array" + ], + "__stdlib__": { + "wasm": false + } +} diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile new file mode 100644 index 000000000000..dd720a3de8f2 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2020 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/integrate/strided/dtrapezoid/src/addon.c b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/addon.c new file mode 100644 index 000000000000..2759c208997a --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/addon.c @@ -0,0 +1,66 @@ +/** +* @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/integrate/strided/dtrapezoid.h" +#include "stdlib/blas/base/shared.h" +#include "stdlib/napi/export.h" +#include "stdlib/napi/argv.h" +#include "stdlib/napi/argv_int64.h" +#include "stdlib/napi/argv_strided_float64array.h" +#include "stdlib/napi/create_double.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_INT64( env, N, argv, 0 ); + STDLIB_NAPI_ARGV_INT64( env, strideX, argv, 2 ); + STDLIB_NAPI_ARGV_INT64( env, strideY, argv, 4 ); + STDLIB_NAPI_ARGV_STRIDED_FLOAT64ARRAY( env, X, N, strideX, argv, 1 ); + STDLIB_NAPI_ARGV_STRIDED_FLOAT64ARRAY( env, Y, N, strideY, argv, 3 ); + STDLIB_NAPI_CREATE_DOUBLE( env, API_SUFFIX(stdlib_strided_dtrapezoid)( N, X, strideX, Y, strideY ), v ); + return v; +} + +/** +* 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_method( napi_env env, napi_callback_info info ) { + STDLIB_NAPI_ARGV( env, info, argv, argc, 7 ); + STDLIB_NAPI_ARGV_INT64( env, N, argv, 0 ); + STDLIB_NAPI_ARGV_INT64( env, strideX, argv, 2 ); + STDLIB_NAPI_ARGV_INT64( env, offsetX, argv, 3 ); + STDLIB_NAPI_ARGV_INT64( env, strideY, argv, 5 ); + STDLIB_NAPI_ARGV_INT64( env, offsetY, argv, 6 ); + STDLIB_NAPI_ARGV_STRIDED_FLOAT64ARRAY( env, X, N, strideX, argv, 1 ); + STDLIB_NAPI_ARGV_STRIDED_FLOAT64ARRAY( env, Y, N, strideY, argv, 4 ); + STDLIB_NAPI_CREATE_DOUBLE( env, API_SUFFIX(stdlib_strided_dtrapezoid_ndarray)( N, X, strideX, offsetX, Y, strideY, offsetY ), v ); + return v; +} + +STDLIB_NAPI_MODULE_EXPORT_FCN_WITH_METHOD( addon, "ndarray", addon_method ) diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/main.c b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/main.c new file mode 100644 index 000000000000..e9482741e041 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/main.c @@ -0,0 +1,113 @@ +/** +* @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/integrate/strided/dtrapezoid.h" +#include "stdlib/blas/base/shared.h" +#include "stdlib/strided/base/stride2offset.h" + +static const CBLAS_INT M = 5; + +/** +* Computes the integral of a double-precision floating-point strided array using the trapezoidal rule. +* +* Notes: +* - The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function. +* +* @param N number of indexed elements +* @param X first array +* @param strideX stride length for X +* @param Y second array +* @param strideY stride length for Y +* @return integral approximation +*/ +double API_SUFFIX(stdlib_strided_dtrapezoid)( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY ) { + CBLAS_INT ox = stdlib_strided_stride2offset( N, strideX ); + CBLAS_INT oy = stdlib_strided_stride2offset( N, strideY ); + return API_SUFFIX(stdlib_strided_dtrapezoid_ndarray)( N, X, strideX, ox, Y, strideY, oy ); +} + +/** +* Computes the integral of a double-precision floating-point strided array using the trapezoidal rule and alternative indexing semantics. +* +* Notes: +* - The function computes an approximation of the integral using the trapezoidal rule whose accuracy depends on the sample point spacing and the smoothness of the underlying function. +* +* @param N number of indexed elements +* @param X first array +* @param strideX stride length for X +* @param offsetX starting index for X +* @param Y second array +* @param strideY stride length for Y +* @param offsetY starting index for Y +* @return integral approximation +*/ +double API_SUFFIX(stdlib_strided_dtrapezoid_ndarray)( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY ) { + CBLAS_INT ix; + CBLAS_INT iy; + CBLAS_INT m; + CBLAS_INT i; + double sum; + double x0; + double x1; + double y0; + double y1; + + sum = 0.0; + if ( N <= 1 ) { + return sum; + } + ix = offsetX; + iy = offsetY; + + // If both strides are equal to `1`, use unrolled loops... + if ( strideX == 1 && strideY == 1 ) { + m = (N - 1) % M; + if ( m > 0 ) { + for ( i = 0; i < m; i++ ) { + sum += ((X[ix+1] - X[ix]) * (Y[iy] + Y[iy+1])); + ix += 1; + iy += 1; + } + } + if ( N - 1 < M ) { + return sum * 0.5; + } + for ( i = m; i < N - 1; i += M ) { + sum += (((X[ix+1]-X[ix])*(Y[iy]+Y[iy+1])) + + ((X[ix+2]-X[ix+1])*(Y[iy+1]+Y[iy+2])) + + ((X[ix+3]-X[ix+2])*(Y[iy+2]+Y[iy+3])) + + ((X[ix+4]-X[ix+3])*(Y[iy+3]+Y[iy+4])) + + ((X[ix+5]-X[ix+4])*(Y[iy+4]+Y[iy+5]))); + ix += M; + iy += M; + } + return sum * 0.5; + } + x0 = X[ix]; + y0 = Y[iy]; + for ( i = 1; i < N; i++ ) { + ix += strideX; + iy += strideY; + x1 = X[ix]; + y1 = Y[iy]; + sum += ((x1 - x0) * (y1 + y0)); + x0 = x1; + y0 = y1; + } + return sum * 0.5; +} diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.dtrapezoid.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.dtrapezoid.js new file mode 100644 index 000000000000..ef215cfef508 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.dtrapezoid.js @@ -0,0 +1,241 @@ +/** +* @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 tape = require( 'tape' ); +var Float64Array = require( '@stdlib/array/float64' ); +var dtrapezoid = require( './../lib/dtrapezoid.js' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dtrapezoid, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 5', function test( t ) { + t.strictEqual( dtrapezoid.length, 5, 'returns expected value' ); + t.end(); +}); + +tape( 'the function calculates the integral of `x` and `y`', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 9.5, 'returns expected value' ); + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 1.0, 2.0, 3.0 ] ); + + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 4.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an `N` parameter less than or equal to `1`, the function returns `0`', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0 ] ); + + out = dtrapezoid( 0, x, 1, y, 1 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( 1, x, 1, y, 1 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( -4, x, 1, y, 1 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports an `x` stride', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 2, y, 1 ); + t.strictEqual( out, -0.5, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports a `y` stride', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, y, 2 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports negative strides', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 2.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + y = new Float64Array([ + 4.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + + out = dtrapezoid( 3, x, -2, y, -2 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports complex access patterns', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, + 1.0, // 1 + 2.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 4.0, // 2 + 3.0, // 1 + 0.0, // 0 + 1.0, + 2.0 + ]); + + out = dtrapezoid( 3, x, 2, y, -1 ); + t.strictEqual( out, 5.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports view offsets', function test( t ) { + var out; + var x0; + var y0; + var x1; + var y1; + + x0 = new Float64Array([ + -1.0, + 0.0, // 0 + 1.0, + 1.0, // 1 + 2.0, + 2.0 // 2 + ]); + y0 = new Float64Array([ + -1.0, + -1.0, + 0.0, + 1.0, // 0 + 1.0, // 1 + 4.0 // 2 + ]); + + x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); + y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); + + out = dtrapezoid( 3, x1, 2, y1, 1 ); + t.strictEqual( out, 3.5, 'returns expected value' ); + + t.end(); +}); + +tape( 'if both strides are equal to `1`, the function efficiently calculates the integral', function test( t ) { + var out; + var x; + var y; + var i; + + x = new Float64Array( 100 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 323449.5, 'returns expected value' ); + + x = new Float64Array( 240 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 4550679.5, 'returns expected value' ); + + t.end(); +}); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.dtrapezoid.native.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.dtrapezoid.native.js new file mode 100644 index 000000000000..1ddaeff5607d --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.dtrapezoid.native.js @@ -0,0 +1,250 @@ +/** +* @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 Float64Array = require( '@stdlib/array/float64' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var dtrapezoid = tryRequire( resolve( __dirname, './../lib/dtrapezoid.native.js' ) ); +var opts = { + 'skip': ( dtrapezoid instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dtrapezoid, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 5', opts, function test( t ) { + t.strictEqual( dtrapezoid.length, 5, 'returns expected value' ); + t.end(); +}); + +tape( 'the function calculates the integral of `x` and `y`', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 9.5, 'returns expected value' ); + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 1.0, 2.0, 3.0 ] ); + + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 4.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an `N` parameter less than or equal to `1`, the function returns `0`', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0 ] ); + + out = dtrapezoid( 0, x, 1, y, 1 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( 1, x, 1, y, 1 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( -4, x, 1, y, 1 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports an `x` stride', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 2, y, 1 ); + t.strictEqual( out, -0.5, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports a `y` stride', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, y, 2 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports negative strides', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 2.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + y = new Float64Array([ + 4.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + + out = dtrapezoid( 3, x, -2, y, -2 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports complex access patterns', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, + 1.0, // 1 + 2.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 4.0, // 2 + 3.0, // 1 + 0.0, // 0 + 1.0, + 2.0 + ]); + + out = dtrapezoid( 3, x, 2, y, -1 ); + t.strictEqual( out, 5.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports view offsets', opts, function test( t ) { + var out; + var x0; + var y0; + var x1; + var y1; + + x0 = new Float64Array([ + -1.0, + 0.0, // 0 + 1.0, + 1.0, // 1 + 2.0, + 2.0 // 2 + ]); + y0 = new Float64Array([ + -1.0, + -1.0, + 0.0, + 1.0, // 0 + 1.0, // 1 + 4.0 // 2 + ]); + + x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); + y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); + + out = dtrapezoid( 3, x1, 2, y1, 1 ); + t.strictEqual( out, 3.5, 'returns expected value' ); + + t.end(); +}); + +tape( 'if both strides are equal to `1`, the function efficiently calculates the integral', opts, function test( t ) { + var out; + var x; + var y; + var i; + + x = new Float64Array( 100 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 323449.5, 'returns expected value' ); + + x = new Float64Array( 240 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, y, 1 ); + t.strictEqual( out, 4550679.5, 'returns expected value' ); + + t.end(); +}); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.js new file mode 100644 index 000000000000..e4f2dd9fdc77 --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.js @@ -0,0 +1,82 @@ +/** +* @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 tape = require( 'tape' ); +var proxyquire = require( 'proxyquire' ); +var IS_BROWSER = require( '@stdlib/assert/is-browser' ); +var dtrapezoid = require( './../lib' ); + + +// VARIABLES // + +var opts = { + 'skip': IS_BROWSER +}; + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dtrapezoid, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'attached to the main export is a method providing an ndarray interface', function test( t ) { + t.strictEqual( typeof dtrapezoid.ndarray, 'function', 'method is a function' ); + t.end(); +}); + +tape( 'if a native implementation is available, the main export is the native implementation', opts, function test( t ) { + var dtrapezoid = proxyquire( './../lib', { + '@stdlib/utils/try-require': tryRequire + }); + + t.strictEqual( dtrapezoid, mock, 'returns expected value' ); + t.end(); + + function tryRequire() { + return mock; + } + + function mock() { + // Mock... + } +}); + +tape( 'if a native implementation is not available, the main export is a JavaScript implementation', opts, function test( t ) { + var dtrapezoid; + var main; + + main = require( './../lib/dtrapezoid.js' ); + + dtrapezoid = proxyquire( './../lib', { + '@stdlib/utils/try-require': tryRequire + }); + + t.strictEqual( dtrapezoid, main, 'returns expected value' ); + t.end(); + + function tryRequire() { + return new Error( 'Cannot find module' ); + } +}); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.ndarray.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.ndarray.js new file mode 100644 index 000000000000..e8e47ae2020f --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.ndarray.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 tape = require( 'tape' ); +var Float64Array = require( '@stdlib/array/float64' ); +var dtrapezoid = require( './../lib/ndarray.js' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dtrapezoid, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 7', function test( t ) { + t.strictEqual( dtrapezoid.length, 7, 'returns expected value' ); + t.end(); +}); + +tape( 'the function calculates the integral of `x` and `y`', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 9.5, 'returns expected value' ); + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 1.0, 2.0, 3.0 ] ); + + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 4.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an `N` parameter less than or equal to `1`, the function returns `0`', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0 ] ); + + out = dtrapezoid( 0, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( 1, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( -4, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports an `x` stride', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 2, 0, y, 1, 0 ); + t.strictEqual( out, -0.5, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports a `y` stride', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, 0, y, 2, 0 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports an `x` offset', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + -1.0, + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, 1, y, 1, 0 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports a `y` offset', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + -1.0, + 0.0, // 0 + 1.0, // 1 + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, 0, y, 1, 1 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports negative strides', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 2.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + y = new Float64Array([ + 4.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + + out = dtrapezoid( 3, x, -2, 4, y, -2, 4 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports complex access patterns', function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, + 1.0, // 1 + 2.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 4.0, // 2 + 3.0, // 1 + 0.0, // 0 + 1.0, + 2.0 + ]); + + out = dtrapezoid( 3, x, 2, 0, y, -1, 2 ); + t.strictEqual( out, 5.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if both strides are equal to `1`, the function efficiently calculates the integral', function test( t ) { + var out; + var x; + var y; + var i; + + x = new Float64Array( 100 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 323449.5, 'returns expected value' ); + + x = new Float64Array( 240 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 4550679.5, 'returns expected value' ); + + t.end(); +}); diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.ndarray.native.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.ndarray.native.js new file mode 100644 index 000000000000..f5eb3f765f4b --- /dev/null +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/test/test.ndarray.native.js @@ -0,0 +1,263 @@ +/** +* @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 Float64Array = require( '@stdlib/array/float64' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var dtrapezoid = tryRequire( resolve( __dirname, './../lib/ndarray.native.js' ) ); +var opts = { + 'skip': ( dtrapezoid instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dtrapezoid, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 7', opts, function test( t ) { + t.strictEqual( dtrapezoid.length, 7, 'returns expected value' ); + t.end(); +}); + +tape( 'the function calculates the integral of `x` and `y`', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0, 9.0 ] ); + + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 9.5, 'returns expected value' ); + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 1.0, 2.0, 3.0 ] ); + + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 4.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided an `N` parameter less than or equal to `1`, the function returns `0`', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array( [ 0.0, 1.0, 2.0 ] ); + y = new Float64Array( [ 0.0, 1.0, 4.0 ] ); + + out = dtrapezoid( 0, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( 1, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + out = dtrapezoid( -4, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports an `x` stride', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 2, 0, y, 1, 0 ); + t.strictEqual( out, -0.5, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports a `y` stride', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + -1.0, + 1.0, // 1 + -1.0, + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, 0, y, 2, 0 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports an `x` offset', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + -1.0, + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, 1, y, 1, 0 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports a `y` offset', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, // 1 + 2.0 // 2 + ]); + y = new Float64Array([ + -1.0, + 0.0, // 0 + 1.0, // 1 + 4.0 // 2 + ]); + + out = dtrapezoid( 3, x, 1, 0, y, 1, 1 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports negative strides', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 2.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + y = new Float64Array([ + 4.0, // 2 + -1.0, + 1.0, // 1 + -1.0, + 0.0 // 0 + ]); + + out = dtrapezoid( 3, x, -2, 4, y, -2, 4 ); + t.strictEqual( out, 3.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function supports complex access patterns', opts, function test( t ) { + var out; + var x; + var y; + + x = new Float64Array([ + 0.0, // 0 + 1.0, + 1.0, // 1 + 2.0, + 2.0 // 2 + ]); + y = new Float64Array([ + 4.0, // 2 + 3.0, // 1 + 0.0, // 0 + 1.0, + 2.0 + ]); + + out = dtrapezoid( 3, x, 2, 0, y, -1, 2 ); + t.strictEqual( out, 5.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if both strides are equal to `1`, the function efficiently calculates the integral', opts, function test( t ) { + var out; + var x; + var y; + var i; + + x = new Float64Array( 100 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 323449.5, 'returns expected value' ); + + x = new Float64Array( 240 ); + y = new Float64Array( x.length ); + for ( i = 0; i < x.length; i++ ) { + x[ i ] = i; + y[ i ] = i * i; + } + out = dtrapezoid( x.length, x, 1, 0, y, 1, 0 ); + t.strictEqual( out, 4550679.5, 'returns expected value' ); + + t.end(); +}); From e0b93258d7f602bed88475cdf0f47ae9de14f230 Mon Sep 17 00:00:00 2001 From: headlessNode Date: Sat, 13 Jun 2026 01:50:41 +0500 Subject: [PATCH 2/5] fix: lint err --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/integrate/strided/dtrapezoid/binding.gyp | 2 +- .../@stdlib/integrate/strided/dtrapezoid/include.gypi | 2 +- .../@stdlib/integrate/strided/dtrapezoid/src/Makefile | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp index 7d0005b2e390..0d6508a12e99 100644 --- a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/binding.gyp @@ -1,6 +1,6 @@ # @license Apache-2.0 # -# Copyright (c) 2020 The Stdlib Authors. +# 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. diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi index 26476a8c2655..bee8d41a2caf 100644 --- a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/include.gypi @@ -1,6 +1,6 @@ # @license Apache-2.0 # -# Copyright (c) 2020 The Stdlib Authors. +# 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. diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile index dd720a3de8f2..2caf905cedbe 100644 --- a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/src/Makefile @@ -1,7 +1,7 @@ #/ # @license Apache-2.0 # -# Copyright (c) 2020 The Stdlib Authors. +# 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. From 6f0bb6db52a8af10f11931aa642c534fc7d2c1e5 Mon Sep 17 00:00:00 2001 From: Athan Date: Fri, 12 Jun 2026 21:47:11 -0700 Subject: [PATCH 3/5] Apply suggestions from code review Co-authored-by: Athan Signed-off-by: Athan --- .../strided/dtrapezoid/lib/ndarray.js | 22 +++++++++---------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js index 5ec33fcffca6..15f355537b95 100644 --- a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js @@ -75,7 +75,7 @@ function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) { // If we have a remainder, run a clean-up loop... if ( m > 0 ) { for ( i = 0; i < m; i++ ) { - sum += ((x[ix+1] - x[ix]) * (y[iy] + y[iy+1])); + sum += ( x[ ix+1 ] - x[ ix ] ) * ( y[ iy ] + y[ iy+1 ] ); ix += 1; iy += 1; } @@ -84,24 +84,24 @@ function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) { return sum * 0.5; } for ( i = m; i < N - 1; i += M ) { - sum += (((x[ix+1]-x[ix])*(y[iy]+y[iy+1])) + - ((x[ix+2]-x[ix+1])*(y[iy+1]+y[iy+2])) + - ((x[ix+3]-x[ix+2])*(y[iy+2]+y[iy+3])) + - ((x[ix+4]-x[ix+3])*(y[iy+3]+y[iy+4])) + - ((x[ix+5]-x[ix+4])*(y[iy+4]+y[iy+5]))); + sum += ( ( x[ix+1]-x[ix] ) * ( y[iy]+y[iy+1] ) ) + + ( ( x[ix+2]-x[ix+1] ) * ( y[iy+1]+y[iy+2] ) ) + + ( ( x[ix+3]-x[ix+2] ) * ( y[iy+2]+y[iy+3] ) ) + + ( ( x[ix+4]-x[ix+3] ) * ( y[iy+3]+y[iy+4] ) ) + + ( ( x[ix+5]-x[ix+4] ) * ( y[iy+4]+y[iy+5] ) ); ix += M; iy += M; } return sum * 0.5; } - x0 = x[ix]; - y0 = y[iy]; + x0 = x[ ix ]; + y0 = y[ iy ]; for ( i = 1; i < N; i++ ) { ix += strideX; iy += strideY; - x1 = x[ix]; - y1 = y[iy]; - sum += ((x1 - x0) * (y1 + y0)); + x1 = x[ ix ]; + y1 = y[ iy ]; + sum += ( x1-x0 ) * ( y1+y0 ); x0 = x1; y0 = y1; } From f6d3bf2a47246c86be411fd122dc1f53a39ff66f Mon Sep 17 00:00:00 2001 From: Athan Date: Fri, 12 Jun 2026 21:49:39 -0700 Subject: [PATCH 4/5] Apply suggestions from code review Co-authored-by: Athan Signed-off-by: Athan --- .../@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js index 15f355537b95..b5108ecf6eb7 100644 --- a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js @@ -70,7 +70,7 @@ function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) { // Use unrolled loops if both strides are equal to `1`... if ( strideX === 1 && strideY === 1 ) { - m = (N - 1) % M; + m = ( N - 1 ) % M; // If we have a remainder, run a clean-up loop... if ( m > 0 ) { From defa190dfb648c90ac593825f7eef9a389319420 Mon Sep 17 00:00:00 2001 From: Athan Date: Fri, 12 Jun 2026 21:52:02 -0700 Subject: [PATCH 5/5] Apply suggestions from code review Co-authored-by: Athan Signed-off-by: Athan --- .../@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js index b5108ecf6eb7..2e36ca94951a 100644 --- a/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js +++ b/lib/node_modules/@stdlib/integrate/strided/dtrapezoid/lib/ndarray.js @@ -70,7 +70,7 @@ function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) { // Use unrolled loops if both strides are equal to `1`... if ( strideX === 1 && strideY === 1 ) { - m = ( N - 1 ) % M; + m = ( N-1 ) % M; // If we have a remainder, run a clean-up loop... if ( m > 0 ) { @@ -80,10 +80,10 @@ function dtrapezoid( N, x, strideX, offsetX, y, strideY, offsetY ) { iy += 1; } } - if ( N - 1 < M ) { + if ( N-1 < M ) { return sum * 0.5; } - for ( i = m; i < N - 1; i += M ) { + for ( i = m; i < N-1; i += M ) { sum += ( ( x[ix+1]-x[ix] ) * ( y[iy]+y[iy+1] ) ) + ( ( x[ix+2]-x[ix+1] ) * ( y[iy+1]+y[iy+2] ) ) + ( ( x[ix+3]-x[ix+2] ) * ( y[iy+2]+y[iy+3] ) ) +