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feat: add lapack/base/dlascl
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‎lib/node_modules/@stdlib/lapack/base/dlascl/lib/base.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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/* eslint-disable max-statements, max-len */
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'use strict';
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// MODULES //
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var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var dlamch = require( '@stdlib/lapack/base/dlamch' );
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var loopOrder = require( '@stdlib/ndarray/base/nullary-loop-interchange-order' );
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var max = require( '@stdlib/math/base/special/fast/max' );
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var min = require( '@stdlib/math/base/special/fast/min' );
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// VARIABLES //
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var smlnum = dlamch( 'safe minimum' );
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var bignum = 1.0 / smlnum;
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// MAIN //
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/**
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* Performs a series of row interchanges on a matrix `A` using pivot indices stored in `IPIV`.
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*
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* @private
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* @param {string} type - specifies the type of matrix `A`
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* @param {NonNegativeInteger} KL - lower band width of `A`. Referenced only if type is `symmetric-banded-lower` or `banded`.
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* @param {NonNegativeInteger} KU - upper band width of `A`. Referenced only if type is `symmetric-banded-upper` or `banded`.
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* @param {number} CFROM - selected elements in `A` are multiplied by `CTO / CFROM`
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* @param {number} CTO - selected elements in `A` are multiplied by `CTO / CFROM`
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* @param {NonNegativeInteger} M - number of rows in matrix `A`
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* @param {NonNegativeInteger} N - number of columns in matrix `A`
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* @param {Float64Array} A - input matrix
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* @param {integer} strideA1 - stride of the first dimension of `A`
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* @param {integer} strideA2 - stride of the second dimension of `A`
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* @param {NonNegativeInteger} offsetA - starting index for `A`
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* @returns {Float64Array} scaled matrix `A`
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
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*
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* dlascl( 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2, 1, 0 );
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* // A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
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*/
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function dlascl( type, KL, KU, CFROM, CTO, M, N, A, strideA1, strideA2, offsetA ) { // eslint-disable-line max-params
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var cfromc;
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var cfrom1;
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var ctoc;
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var cto1;
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var done;
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var mul;
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var da1;
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var da0;
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var S1;
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var S0;
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var ia;
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var i0;
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var i1;
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var k3;
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var k4;
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var k1;
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var k2;
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var sh;
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var sa;
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var o;
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if ( N === 0 || M === 0 ) {
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return A;
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}
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done = false;
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cfromc = CFROM;
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ctoc = CTO;
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while ( !done ) {
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cfrom1 = CTO * smlnum;
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if ( cfrom1 === cfromc ) {
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// cfromc is Infinity, multiply by a correctly signed zero for finite ctoc or NaN
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mul = ctoc / cfromc;
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done = true;
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cto1 = ctoc;
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} else {
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cto1 = ctoc / bignum;
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if ( cto1 === ctoc ) {
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// ctoc is either zero or Infinity, thus ctoc itself is a correct multiplication factor
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mul = ctoc;
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done = true;
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cfromc = 1.0;
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} else if ( abs( cfrom1 ) > abs( ctoc ) && ctoc !== 0.0 ) {
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mul = smlnum;
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done = false;
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ctoc = cto1;
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} else if ( abs( cto1 ) > abs( cfromc ) ) {
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mul = bignum;
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done = false;
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ctoc = cto1;
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} else {
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mul = ctoc / cfromc;
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done = true;
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}
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}
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if ( type === 'general' ) {
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// Full matrix
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// Resolve the loop interchange order:
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o = loopOrder( [ M, N ], [ strideA1, strideA2 ] );
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sh = o.sh;
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sa = o.sx;
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// Extract loop variables for purposes of loop interchange: dimensions and loop offset (pointer) increments...
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S0 = sh[ 0 ];
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S1 = sh[ 1 ];
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da0 = sa[ 0 ];
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da1 = sa[ 1 ] - ( S0*sa[0] );
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// Set the pointers to the first indexed elements in the respective matrices...
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ia = offsetA;
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// Iterate over the matrix dimensions...
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for ( i1 = 0; i1 < S1; i1++ ) {
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for ( i0 = 0; i0 < S0; i0++ ) {
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A[ ia ] *= mul;
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ia += da0;
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}
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ia += da1;
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}
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}
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if ( type === 'upper' ) {
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// Upper triangular matrix
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ia = offsetA;
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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for ( i1 = 0; i1 < M; i1++ ) {
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for ( i0 = i1; i0 < N; i0++ ) {
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A[ ia+(i0*strideA2) ] *= mul;
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}
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ia += strideA1;
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}
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} else {
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for ( i1 = 0; i1 < N; i1++ ) {
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for ( i0 = 0; i0 <= min( i1, M-1 ); i0++ ) {
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A[ ia+(i0*strideA1) ] *= mul;
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}
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ia += strideA2;
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}
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}
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}
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if ( type === 'lower' ) {
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// Lower triangular matrix
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ia = offsetA;
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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for ( i1 = 0; i1 < M; i1++ ) {
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for ( i0 = 0; i0 <= min( i1, N-1 ); i0++ ) {
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A[ ia+(i0*strideA2) ] *= mul;
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}
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ia += strideA1;
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}
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} else {
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for ( i1 = 0; i1 < N; i1++ ) {
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for ( i0 = i1; i0 < M; i0++ ) {
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A[ ia+(i0*strideA1) ] *= mul;
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}
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ia += strideA2;
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}
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}
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}
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if ( type === 'upper-hessenberg' ) {
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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ia = offsetA;
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for ( i1 = 0; i1 < M; i1++ ) {
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for ( i0 = 0; i0 <= min( i1+1, N-1 ); i0++ ) {
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A[ ia+(i0*strideA2) ] *= mul;
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}
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ia += strideA1;
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}
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} else {
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ia = offsetA;
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for ( i0 = 0; i0 < N; i0++ ) {
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for ( i1 = 0; i1 <= min( i0+1, M-1 ); i1++ ) {
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A[ ia+(i1*strideA1) ] *= mul;
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}
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ia += strideA2;
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}
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}
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}
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if ( type === 'symmetric-banded-lower' ) {
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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ia = offsetA;
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k3 = KL + 1;
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k4 = N;
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for ( i1 = 0; i1 < M; i1++ ) {
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for ( i0 = max( 0, i1 - KL ); i0 < min( k4, i1 + 1 ); i0++ ) {
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A[ ia+( ( i1-i0 ) * strideA2) ] *= mul;
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}
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ia += strideA1;
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}
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} else {
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ia = offsetA;
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for ( i1 = 0; i1 < N; i1++ ) {
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for ( i0 = 0; i0 < min( k3, k4 - i1 ); i0++ ) {
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A[ ia+(i0*strideA1) ] *= mul;
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}
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ia += strideA2;
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}
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}
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}
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if ( type === 'symmetric-banded-upper' ) {
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k1 = KU + 1;
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ia = offsetA;
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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for ( i1 = 0; i1 < M; i1++ ) {
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for ( i0 = i1; i0 < min( N, i1 + k1 ); i0++ ) {
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A[ ia + ( (i0-i1) * strideA2) ] *= mul;
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}
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ia += strideA1;
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}
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} else {
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for ( i1 = 0; i1 < N; i1++ ) {
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for ( i0 = max( k1 - i1, 0 ); i0 < k1; i0++ ) {
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A[ ia+(i0*strideA1) ] *= mul;
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}
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ia += strideA2;
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}
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}
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}
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if ( type === 'banded' ) {
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k1 = KL + KU + 2;
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k2 = KL + 1;
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k3 = ( 2 * KL ) + KU + 1;
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k4 = KL + KU + 1 + M;
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ia = offsetA;
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if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
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for ( i1 = 0; i1 < M; i1++ ) {
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for ( i0 = max( 0, i1 - KL ); i0 <= min( N - 1, i1 + KU ); i0++ ) {
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A[ ia + ( ( i0 - i1 + KL ) * strideA2 ) ] *= mul;
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}
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ia += strideA1;
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}
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} else {
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for ( i1 = 0; i1 < N; i1++ ) {
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for ( i0 = max( k1 - i1, k2 ); i0 <= min( k3, k4-i1 ); i0++ ) {
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A[ ia+(i0*strideA1) ] *= mul;
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}
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ia += strideA2;
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}
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}
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}
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}
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return A;
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}
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// EXPORTS //
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module.exports = dlascl;

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