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feat: add lapack/base/iladlc
PR-URL: #7083 Co-authored-by: Athan Reines <[email protected]> Reviewed-by: Athan Reines <[email protected]> Co-authored-by: stdlib-bot <[email protected]>
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‎lib/node_modules/@stdlib/lapack/base/iladlc/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# iladlc
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> Find the index of the last non-zero column in a matrix `A`.
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<section class="usage">
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## Usage
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```javascript
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var iladlc = require( '@stdlib/lapack/base/iladlc' );
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```
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#### iladlc( order, M, N, A, LDA )
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Returns the index of the last non-zero column in a matrix `A`.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 1.0, 2.0, 0.0, 3.0, 4.0, 0.0 ] );
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/*
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A = [
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[ 1.0, 2.0, 0.0 ],
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[ 3.0, 4.0, 0.0 ]
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]
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*/
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var out = iladlc( 'row-major', 2, 3, A, 3 );
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// returns 1
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **M**: number of rows in `A`.
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- **N**: number of columns in `A`.
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- **A**: input [`Float64Array`][mdn-float64array].
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial array:
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var A0 = new Float64Array( [ 9999.0, 1.0, 2.0, 0.0, 3.0, 4.0, 0.0 ] );
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// Create an offset view:
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var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var out = iladlc( 'row-major', 2, 3, A1, 3 );
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// returns 1
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```
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#### iladlc.ndarray( M, N, A, strideA1, strideA2, offsetA )
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Returns the index of the last non-zero column in a matrix `A` using alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 1.0, 2.0, 0.0, 3.0, 4.0, 0.0 ] );
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/*
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A = [
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[ 1.0, 2.0, 0.0 ],
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[ 3.0, 4.0, 0.0 ]
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]
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*/
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var out = iladlc.ndarray( 2, 3, A, 3, 1, 0 );
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// returns 1
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```
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The function has the following parameters:
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- **M**: number of rows in `A`.
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- **N**: number of columns in `A`.
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- **A**: input [`Float64Array`][mdn-float64array].
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- **strideA1**: stride of the first dimension of `A`.
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- **strideA2**: stride of the second dimension of `A`.
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- **offsetA**: starting index for `A`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example,
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 9999.0, 1.0, 2.0, 0.0, 3.0, 4.0, 0.0 ] );
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/*
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A = [
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[ 1.0, 2.0, 0.0 ],
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[ 3.0, 4.0, 0.0 ]
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]
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*/
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var out = iladlc.ndarray( 2, 3, A, 3, 1, 1 );
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// returns 1
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- This routine is commonly used throughout LAPACK to shrink work domains (e.g., before bulge-chasing, deflation, or when trimming Householder panels), thus ensuring that higher-level routines operate only on numerically relevant sub-matrices.
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- `iladlc()` corresponds to the [LAPACK][lapack] routine [`iladlc`][lapack-iladlc].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
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var Float64Array = require( '@stdlib/array/float64' );
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var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
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var iladlc = require( '@stdlib/lapack/base/iladlc' );
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var shape = [ 3, 3 ];
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var order = 'row-major';
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var strides = shape2strides( shape, order );
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var A = new Float64Array( [ 1.0, 2.0, 0.0, 3.0, 4.0, 0.0, 5.0, 6.0, 0.0 ] );
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console.log( ndarray2array( A, shape, strides, 0, order ) );
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var out = iladlc( order, shape[ 0 ], shape[ 1 ], A, strides[ 0 ] );
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console.log( out );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[lapack-iladlc]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d43/group__aux_o_t_h_e_rauxiliary_gab8b3783390380038c9d26de61d7aefb4.html
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/lapack/base/iladlc/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var zeros = require( '@stdlib/array/zeros' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var pkg = require( './../package.json' ).name;
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var iladlc = require( './../lib/iladlc.js' );
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// VARIABLES //
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var LAYOUTS = [
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'row-major',
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'column-major'
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];
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {string} order - storage layout
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* @param {PositiveInteger} N - number of elements along each dimension
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* @returns {Function} benchmark function
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*/
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function createBenchmark( order, N ) {
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var A = zeros( N*N, 'float64' );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var z;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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A[ 0 ] = i;
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z = iladlc( order, N, N, A, N );
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if ( isnan( z ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( z ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var min;
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var max;
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var ord;
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var N;
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var f;
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var i;
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var k;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( k = 0; k < LAYOUTS.length; k++ ) {
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ord = LAYOUTS[ k ];
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for ( i = min; i <= max; i++ ) {
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N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
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f = createBenchmark( ord, N );
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bench( pkg+'::square_matrix:order='+ord+',size='+(N*N), f );
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}
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}
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}
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main();

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