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feat: add lapack/base/dgttrf
PR-URL: #5754 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/dgttrf/README.md

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‎lib/node_modules/@stdlib/lapack/base/dgttrf/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 uniform = require( '@stdlib/random/array/uniform' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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var pkg = require( './../package.json' ).name;
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var dgttrf = require( './../lib/dgttrf.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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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 {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var IPIV = new Int32Array( len );
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var DU2 = new Float64Array( len-2 );
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var DL = uniform( len-1, 0.0, 100.0, options );
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var DU = uniform( len-1, 0.0, 100.0, options );
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var D = uniform( len, 0.0, 100.0, options );
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return benchmark;
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function benchmark( b ) {
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var d;
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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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d = dgttrf( len, DL, D, DU, DU2, IPIV );
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if ( d < 0 ) {
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b.fail( 'should return a success status code' );
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}
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}
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b.toc();
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if ( d < 0 ) {
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b.fail( 'should return a success status code' );
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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 len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

‎lib/node_modules/@stdlib/lapack/base/dgttrf/benchmark/benchmark.ndarray.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 uniform = require( '@stdlib/random/array/uniform' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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var pkg = require( './../package.json' ).name;
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var dgttrf = require( './../lib/ndarray.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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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 {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var IPIV = new Int32Array( len );
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var DU2 = new Float64Array( len-2 );
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var DL = uniform( len-1, 0.0, 100.0, options );
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var DU = uniform( len-1, 0.0, 100.0, options );
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var D = uniform( len, 0.0, 100.0, options );
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return benchmark;
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function benchmark( b ) {
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var d;
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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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d = dgttrf( len, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0 ); // eslint-disable-line max-len
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if ( d < 0 ) {
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b.fail( 'should return a success status code' );
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}
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}
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b.toc();
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if ( d < 0 ) {
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b.fail( 'should return a success status code' );
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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 len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':ndarray:len='+len, f );
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}
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}
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main();

‎lib/node_modules/@stdlib/lapack/base/dgttrf/docs/repl.txt

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{{alias}}( N, DL, D, DU, DU2, IPIV )
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Computes an LU factorization of a real tridiagonal matrix `A` using
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elimination with partial pivoting and row interchanges.
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Indexing is relative to the first index. To introduce an offset, use typed
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array views.
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The function mutates `DL`, `D`, `DU`, `DU2`, and `IPIV`.
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Parameters
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----------
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N: integer
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Number of rows/columns in `A`.
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DL: Float64Array
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The first sub diagonal of `A`. Should have `N-1` indexed elements. `DL`
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is overwritten by the multipliers that define the matrix `L` from the LU
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factorization of `A`.
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D: Float64Array
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The diagonal of `A`. Should have `N` indexed elements. `D` is
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overwritten by the diagonal elements of the upper triangular matrix `U`
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from the LU factorization of `A`.
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DU: Float64Array
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The first super-diagonal of `A`. Should have `N-1` indexed elements.
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`DU` is overwritten by the elements of the first super-diagonal of `U`.
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DU2: Float64Array
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The second super-diagonal of `U`. Should have `N-2` indexed elements.
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`DU2` is overwritten by the elements of the second super-diagonal of
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`U`.
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IPIV: Int32Array
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Vector of pivot indices. Should have `N` indexed elements.
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Returns
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-------
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info: integer
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Status code. The status code indicates the following conditions:
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- if equal to zero, then the factorization was successful.
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- if greater than zero, then `U(k, k)` is exactly zero the factorization
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has been completed, but the factor `U` is exactly singular, and division
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by zero will occur if it is used to solve a system of equations where
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`k = StatusCode`.
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Examples
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--------
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> var DL = new {{alias:@stdlib/array/float64}}( [ 1.0, 1.0 ] );
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> var D = new {{alias:@stdlib/array/float64}}( [ 2.0, 3.0, 1.0 ] );
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> var DU = new {{alias:@stdlib/array/float64}}( [ 1.0, 1.0 ] );
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> var DU2 = new {{alias:@stdlib/array/float64}}( 1 );
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> var IPIV = new {{alias:@stdlib/array/int32}}( 3 );
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> {{alias}}( 3, DL, D, DU, DU2, IPIV )
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0
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> DL
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<Float64Array>[ 0.5, 0.4 ]
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> D
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<Float64Array>[ 2.0, 2.5, 0.6 ]
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> DU
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<Float64Array>[ 1.0, 1.0 ]
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> DU2
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<Float64Array>[ 0.0 ]
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> IPIV
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<Int32Array>[ 0, 1, 2 ]
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// Using typed array views:
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> var DL0 = new {{alias:@stdlib/array/float64}}( [ 0.0, 1.0, 1.0 ] );
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> var D0 = new {{alias:@stdlib/array/float64}}( [ 0.0, 2.0, 3.0, 1.0 ] );
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> var DU0 = new {{alias:@stdlib/array/float64}}( [ 0.0, 1.0, 1.0 ] );
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> var DU20 = new {{alias:@stdlib/array/float64}}( 2 );
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> var IPIV0 = new {{alias:@stdlib/array/int32}}( 4 );
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> DL = new Float64Array( DL0.buffer, DL0.BYTES_PER_ELEMENT*1 );
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> D = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 );
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> DU = new Float64Array( DU0.buffer, DU0.BYTES_PER_ELEMENT*1 );
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> DU2 = new Float64Array( DU20.buffer, DU20.BYTES_PER_ELEMENT*1 );
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> IPIV = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 );
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> {{alias}}( 3, DL, D, DU, DU2, IPIV )
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0
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> DL0
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<Float64Array>[ 0.0, 0.5, 0.4 ]
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> D0
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<Float64Array>[ 0.0, 2.0, 2.5, 0.6 ]
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> DU0
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<Float64Array>[ 0.0, 1.0, 1.0 ]
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> DU20
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<Float64Array>[ 0.0, 0.0 ]
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> IPIV0
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<Int32Array>[ 0, 0, 1, 2 ]
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{{alias}}.ndarray(N, DL,sdl,odl, D,sd,od, DU,sdu,odu, DU2,sdu2,odu2, IPIV,si,oi)
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Computes an LU factorization of a real tridiagonal matrix `A` using
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elimination with partial pivoting and row interchanges and alternative
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indexing semantics.
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While typed array views mandate a view offset based on the underlying
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buffer, the offset parameters support indexing semantics based on starting
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indices.
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The function mutates `DL`, `D`, `DU`, `DU2`, and `IPIV`.
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Parameters
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----------
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N: integer
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Number of rows/columns in `A`.
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DL: Float64Array
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The first sub diagonal of `A`. Should have `N-1` indexed elements. `DL`
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is overwritten by the multipliers that define the matrix `L` from the LU
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factorization of `A`.
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sdl: integer
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Stride length for `DL`.
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odl: integer
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Starting index for `DL`.
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D: Float64Array
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The diagonal of `A`. Should have `N` indexed elements. `D` is
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overwritten by the diagonal elements of the upper triangular matrix `U`
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from the LU factorization of `A`.
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sd: integer
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Stride length for `D`.
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od: integer
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Starting index for `D`.
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DU: Float64Array
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The first super-diagonal of `A`. Should have `N-1` indexed elements.
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`DU` is overwritten by the elements of the first super-diagonal of `U`.
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sdu: integer
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Stride length for `DU`.
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odu: integer
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Starting index for `DU2`.
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DU2: Float64Array
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The second super-diagonal of `U`. Should have `N-2` indexed elements.
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`DU2` is overwritten by the elements of the second super-diagonal of
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`U`.
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sdu2: integer
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Stride length for `DU2`.
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odu2: integer
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Starting index for `DU2`.
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IPIV: Int32Array
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Vector of pivot indices. Should have `N` indexed elements.
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si: integer
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Stride length for `IPIV`.
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oi: integer
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Starting index for `IPIV`.
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Returns
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-------
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info: integer
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Status code. The status code indicates the following conditions:
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- if equal to zero, then the factorization was successful.
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- if greater than zero, then `U(k, k)` is exactly zero the factorization
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has been completed, but the factor `U` is exactly singular, and division
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by zero will occur if it is used to solve a system of equations where
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`k = StatusCode`.
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Examples
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--------
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> var DL = new {{alias:@stdlib/array/float64}}( [ 1.0, 1.0 ] );
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> var D = new {{alias:@stdlib/array/float64}}( [ 2.0, 3.0, 1.0 ] );
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> var DU = new {{alias:@stdlib/array/float64}}( [ 1.0, 1.0 ] );
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> var DU2 = new {{alias:@stdlib/array/float64}}( 1 );
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> var IPIV = new {{alias:@stdlib/array/int32}}( 3 );
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> {{alias}}.ndarray( 3, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0 )
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0
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> DL
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<Float64Array>[ 0.5, 0.4 ]
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> D
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<Float64Array>[ 2.0, 2.5, 0.6 ]
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> DU
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<Float64Array>[ 1.0, 1.0 ]
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> DU2
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<Float64Array>[ 0.0 ]
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> IPIV
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<Int32Array>[ 0, 1, 2 ]
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See Also
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--------
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