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* @license Apache-2.0
*
* Copyright (c) 2025 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.
*/
/* eslint-disable max-len */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var abs = require( '@stdlib/math/base/special/abs' );
var dlamch = require( '@stdlib/lapack/base/dlamch' );
var loopOrder = require( '@stdlib/ndarray/base/nullary-loop-interchange-order' );
var max = require( '@stdlib/math/base/special/fast/max' );
var min = require( '@stdlib/math/base/special/fast/min' );
// VARIABLES //
var smlnum = dlamch( 'safe minimum' );
var bignum = 1.0 / smlnum;
// FUNCTIONS //
/**
* Multiplies a real M by N general matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );
*
* scaleGeneral( 3, 2, A, 2, 1, 0, 2.0 );
* // A => <Float64Array>[ 2.0, 8.0, 4.0, 10.0, 6.0, 12.0 ]
*/
function scaleGeneral( M, N, A, strideA1, strideA2, offsetA, mul ) {
var da1;
var da0;
var S1;
var S0;
var ia;
var i0;
var i1;
var o;
// Resolve the loop interchange order:
o = loopOrder( [ M, N ], [ strideA1, strideA2 ] );
S0 = o.sh[ 0 ];
S1 = o.sh[ 1 ];
da0 = o.sx[ 0 ];
da1 = o.sx[ 1 ] - ( S0 * o.sx[ 0 ] );
// Set the pointers to the first indexed elements in the respective matrices...
ia = offsetA;
// Iterate over the matrix dimensions...
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
A[ ia ] *= mul;
ia += da0;
}
ia += da1;
}
}
/**
* Multiplies a real M by N upper triangular matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {boolean} isrm - boolean indicating if the matrix is row-major
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 4.0, 0.0, 3.0, 5.0, 0.0, 0.0, 6.0 ] );
*
* scaleUpper( 3, 3, A, 3, 1, 0, true, 2.0 );
* // A => <Float64Array>[ 2.0, 4.0, 8.0, 0.0, 6.0, 10.0, 0.0, 0.0, 12.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 0.0, 0.0, 2.0, 3.0, 0.0, 4.0, 5.0, 6.0 ] );
*
* scaleUpper( 3, 3, A, 1, 3, 0, false, 2.0 );
* // A => <Float64Array>[ 2.0, 0.0, 0.0, 4.0, 6.0, 0.0, 8.0, 10.0, 12.0 ]
*/
function scaleUpper( M, N, A, strideA1, strideA2, offsetA, isrm, mul ) {
var ia;
var i0;
var i1;
ia = offsetA;
if ( isrm ) {
for ( i1 = 0; i1 < M; i1++ ) {
for ( i0 = i1; i0 < N; i0++ ) {
A[ ia + ( i0 * strideA2 ) ] *= mul;
}
ia += strideA1;
}
} else {
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = 0; i0 <= min( i1, M - 1 ); i0++ ) {
A[ ia + ( i0 * strideA1 ) ] *= mul;
}
ia += strideA2;
}
}
}
/**
* Multiplies a real M by N lower triangular matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {boolean} isrm - boolean indicating if the matrix is row-major
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 0.0, 0.0, 2.0, 4.0, 0.0, 3.0, 5.0, 6.0 ] );
*
* scaleLower( 3, 3, A, 3, 1, 0, true, 2.0 );
* // A => <Float64Array>[ 2.0, 0.0, 0.0, 4.0, 8.0, 0.0, 6.0, 10.0, 12.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 4.0, 5.0, 0.0, 0.0, 6.0 ] );
*
* scaleLower( 3, 3, A, 1, 3, 0, false, 2.0 );
* // A => <Float64Array>[ 2.0, 4.0, 6.0, 0.0, 8.0, 10.0, 0.0, 0.0, 12.0 ]
*/
function scaleLower( M, N, A, strideA1, strideA2, offsetA, isrm, mul ) {
var ia;
var i0;
var i1;
ia = offsetA;
if ( isrm ) {
for ( i1 = 0; i1 < M; i1++ ) {
for ( i0 = 0; i0 <= min( i1, N - 1 ); i0++ ) {
A[ ia + ( i0 * strideA2 ) ] *= mul;
}
ia += strideA1;
}
} else {
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = i1; i0 < M; i0++ ) {
A[ ia + ( i0 * strideA1 ) ] *= mul;
}
ia += strideA2;
}
}
}
/**
* Multiplies a real M by N upper Hessenberg matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {boolean} isrm - boolean indicating if the matrix is row-major
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 0.0, 9.0, 10.0, 11.0, 0.0, 0.0, 12.0, 13.0 ] );
*
* scaleUpperHHessenberg( 4, 4, A, 4, 1, 0, true, 2.0 );
* // A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 0.0, 18.0, 20.0, 22.0, 0.0, 0.0, 24.0, 26.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 5.0, 0.0, 0.0, 2.0, 6.0, 9.0, 0.0, 3.0, 7.0, 10.0, 12.0, 4.0, 8.0, 11.0, 13.0 ] );
*
* scaleUpperHHessenberg( 4, 4, A, 1, 4, 0, false, 2.0 );
* // A => <Float64Array>[ 2.0, 10.0, 0.0, 0.0, 4.0, 12.0, 18.0, 0.0, 6.0, 14.0, 20.0, 24.0, 8.0, 16.0, 22.0, 26.0 ]
*/
function scaleUpperHHessenberg( M, N, A, strideA1, strideA2, offsetA, isrm, mul ) {
var ia;
var i0;
var i1;
if ( isrm ) {
ia = offsetA;
for ( i1 = 0; i1 < M; i1++ ) {
for ( i0 = max( i1 - 1, 0 ); i0 < N; i0++ ) {
A[ ia + ( i0 * strideA2 ) ] *= mul;
}
ia += strideA1;
}
} else {
ia = offsetA;
for ( i0 = 0; i0 < N; i0++ ) {
for ( i1 = 0; i1 <= min( i0 + 1, M - 1 ); i1++ ) {
A[ ia + ( i1 * strideA1 ) ] *= mul;
}
ia += strideA2;
}
}
}
/**
* Multiplies a real M by N symmetric banded lower matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} KL - lower band width of `A`
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {boolean} isrm - boolean indicating if the matrix is row-major
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.1, 2.2, 3.3, 4.4, 5.5, 6.1, 7.2, 8.3, 9.4, 0.0, 10.1, 11.2, 12.3, 0.0, 0.0 ] );
*
* scaleSymmetricBandedLower( 2, 5, 5, A, 5, 1, 0, true, 10.0 );
* // A => <Float64Array>[ 11.0, 22.0, 33.0, 44.0, 55.0, 61.0, 72.0, 83.0, 94.0, 0.0, 101.0, 112.0, 123.0, 0.0, 0.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.1, 6.1, 10.1, 2.2, 7.2, 11.2, 3.3, 8.3, 12.3, 4.4, 9.4, 0.0, 5.5, 0.0, 0.0 ] );
*
* scaleSymmetricBandedLower( 2, 5, 5, A, 1, 3, 0, false, 10.0 );
* // A => <Float64Array>[ 11.0, 61.0, 101.0, 22.0, 72.0, 112.0, 33.0, 83.0, 123.0, 44.0, 94.0, 0.0, 55.0, 0.0, 0.0 ]
*/
function scaleSymmetricBandedLower( KL, M, N, A, strideA1, strideA2, offsetA, isrm, mul ) {
var ia;
var i0;
var i1;
var k3;
var k4;
ia = offsetA;
k3 = KL + 1;
k4 = N;
if ( isrm ) {
for ( i1 = 0; i1 < M; i1++ ) {
for ( i0 = 0; i0 < ( N - i1 ); i0++ ) {
A[ ia + ( i0 * strideA2 ) ] *= mul;
}
ia += strideA1;
}
} else {
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = 0; i0 < min( k3, k4 - i1 ); i0++ ) {
A[ ia + ( i0 * strideA1 ) ] *= mul;
}
ia += strideA2;
}
}
}
/**
* Multiplies a real M by N symmetric banded upper matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} KU - upper band width of `A`
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {boolean} isrm - boolean indicating if the matrix is row-major
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 0.0, 0.0, 10.1, 11.2, 12.3, 0.0, 6.1, 7.2, 8.3, 9.4, 1.1, 2.2, 3.3, 4.4, 5.5 ] );
*
* scaleSymmetricBandedUpper( 2, 5, 5, A, 5, 1, 0, true, 10.0 );
* // A => <Float64Array>[ 0.0, 0.0, 101.0, 112.0, 123.0, 0.0, 61.0, 72.0, 83.0, 94.0, 11.0, 22.0, 33.0, 44.0, 55.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 0.0, 0.0, 1.1, 0.0, 6.1, 2.2, 10.1, 7.2, 3.3, 11.2, 8.3, 4.4, 12.3, 9.4, 5.5 ] );
*
* scaleSymmetricBandedUpper( 2, 5, 5, A, 1, 3, 0, false, 10.0 );
* // A => <Float64Array>[ 0.0, 0.0, 11.0, 0.0, 61.0, 22.0, 101.0, 72.0, 33.0, 112.0, 83.0, 44.0, 123.0, 94.0, 55.0 ]
*/
function scaleSymmetricBandedUpper( KU, M, N, A, strideA1, strideA2, offsetA, isrm, mul ) {
var ia;
var i0;
var i1;
ia = offsetA;
if ( isrm ) {
for ( i1 = 0; i1 <= KU; i1++ ) {
for ( i0 = max( KU - i1, 0 ); i0 < N; i0++ ) {
A[ ia + ( i0 * strideA2 ) ] *= mul;
}
ia += strideA1;
}
} else {
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = max( KU - i1, 0 ); i0 <= KU; i0++ ) {
A[ ia + ( i0 * strideA1 ) ] *= mul;
}
ia += strideA2;
}
}
}
/**
* Multiplies a real M by N banded matrix `A` by a real scalar `mul`.
*
* @private
* @param {NonNegativeInteger} KL - lower band width of `A`
* @param {NonNegativeInteger} KU - upper band width of `A`
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {number} mul - scalar multiplier
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.2, 2.3, 3.4, 4.5, 1.1, 2.2, 3.3, 4.4, 5.5, 2.1, 3.2, 4.3, 5.4, 0.0, 3.1, 4.2, 5.3, 0.0, 0.0 ] );
*
* scaleBanded( 2, 1, 5, 5, A, 5, 1, 0, 10.0 );
* // A => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 12.0, 23.0, 34.0, 45.0, 11.0, 22.0, 33.0, 44.0, 55.0, 21.0, 32.0, 43.0, 54.0, 0.0, 31.0, 42.0, 53.0, 0.0, 0.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 0.0, 0.0, 0.0, 1.1, 2.1, 3.1, 0.0, 0.0, 1.2, 2.2, 3.2, 4.2, 0.0, 0.0, 2.3, 3.3, 4.3, 5.3, 0.0, 0.0, 3.4, 4.4, 5.4, 0.0, 0.0, 0.0, 4.5, 5.5, 0.0, 0.0 ] );
*
* scaleBanded( 2, 1, 5, 5, A, 1, 6, 0, 10.0 );
* // A => <Float64Array>[ 0.0, 0.0, 0.0, 11.0, 21.0, 31.0, 0.0, 0.0, 12.0, 22.0, 32.0, 42.0, 0.0, 0.0, 23.0, 33.0, 43.0, 53.0, 0.0, 0.0, 34.0, 44.0, 54.0, 0.0, 0.0, 0.0, 45.0, 55.0, 0.0, 0.0 ]
*/
function scaleBanded( KL, KU, M, N, A, strideA1, strideA2, offsetA, mul ) {
var ia;
var i0;
var i1;
var k1;
var k2;
var k3;
var k4;
k1 = KL + KU;
k2 = KL;
k3 = ( 2 * KL ) + KU;
k4 = KL + KU + M - 1;
ia = offsetA;
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = max( k1 - i1, k2 ); i0 <= min( k3, k4 - i1 ); i0++ ) {
A[ ia + ( i0 * strideA1 ) ] *= mul;
}
ia += strideA2;
}
}
// MAIN //
/**
* Multiplies a real M by N matrix `A` by a real scalar `CTO/CFROM`.
*
* @param {string} type - specifies the type of matrix `A`
* @param {NonNegativeInteger} KL - lower band width of `A`. Referenced only if type is `symmetric-banded-lower` or `banded`.
* @param {NonNegativeInteger} KU - upper band width of `A`. Referenced only if type is `symmetric-banded-upper` or `banded`.
* @param {number} CFROM - the matrix `A` is multiplied by `CTO / CFROM`
* @param {number} CTO - the matrix `A` is multiplied by `CTO / CFROM`
* @param {NonNegativeInteger} M - number of rows in matrix `A`
* @param {NonNegativeInteger} N - number of columns in matrix `A`
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @returns {Float64Array} scaled matrix `A`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* 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 ] ]
*
* dlascl( 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2, 1, 0 );
* // A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
*/
function dlascl( type, KL, KU, CFROM, CTO, M, N, A, strideA1, strideA2, offsetA ) { // eslint-disable-line max-params
var cfromc;
var cfrom1;
var isrm;
var ctoc;
var cto1;
var done;
var mul;
if ( N === 0 || M === 0 ) {
return A;
}
done = false;
cfromc = CFROM;
ctoc = CTO;
isrm = isRowMajor( [ strideA1, strideA2 ] );
while ( !done ) {
cfrom1 = CTO * smlnum;
if ( cfrom1 === cfromc ) {
// cfromc is Infinity, multiply by a correctly signed zero for finite ctoc or NaN
mul = ctoc / cfromc;
done = true;
cto1 = ctoc;
} else {
cto1 = ctoc / bignum;
if ( cto1 === ctoc ) {
// ctoc is either zero or Infinity, thus ctoc itself is a correct multiplication factor
mul = ctoc;
done = true;
cfromc = 1.0;
} else if ( abs( cfrom1 ) > abs( ctoc ) && ctoc !== 0.0 ) {
mul = smlnum;
done = false;
ctoc = cto1;
} else if ( abs( cto1 ) > abs( cfromc ) ) {
mul = bignum;
done = false;
ctoc = cto1;
} else {
mul = ctoc / cfromc;
done = true;
}
}
if ( type === 'general' ) {
scaleGeneral( M, N, A, strideA1, strideA2, offsetA, mul );
continue;
}
if ( type === 'upper' ) {
scaleUpper( M, N, A, strideA1, strideA2, offsetA, isrm, mul );
continue;
}
if ( type === 'lower' ) {
scaleLower( M, N, A, strideA1, strideA2, offsetA, isrm, mul );
continue;
}
if ( type === 'upper-hessenberg' ) {
scaleUpperHHessenberg( M, N, A, strideA1, strideA2, offsetA, isrm, mul );
continue;
}
if ( type === 'symmetric-banded-lower' ) {
scaleSymmetricBandedLower( KL, M, N, A, strideA1, strideA2, offsetA, isrm, mul );
continue;
}
if ( type === 'symmetric-banded-upper' ) {
scaleSymmetricBandedUpper( KU, M, N, A, strideA1, strideA2, offsetA, isrm, mul );
continue;
}
if ( type === 'banded' ) {
scaleBanded( KL, KU, M, N, A, strideA1, strideA2, offsetA, mul );
continue;
}
}
return A;
}
// EXPORTS //
module.exports = dlascl;
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