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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, max-params */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
// FUNCTIONS //
/**
* Fills a matrix with zeros.
*
* @private
* @param {NonNegativeInteger} M - number of rows
* @param {NonNegativeInteger} N - number of columns
* @param {Float64Array} X - matrix to fill
* @param {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @returns {Float64Array} input matrix
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* zeros( 2, 3, X, 3, 1, 0 );
* // X => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* zeros( 2, 3, X, 1, 2, 0 );
* // X => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*/
function zeros( M, N, X, strideX1, strideX2, offsetX ) { // TODO: consider moving to a separate package
var dx0;
var dx1;
var S0;
var S1;
var i0;
var i1;
var ix;
if ( isRowMajor( [ strideX1, strideX2 ] ) ) {
// For row-major matrices, the last dimension has the fastest changing index...
S0 = N;
S1 = M;
dx0 = strideX2; // offset increment for innermost loop
dx1 = strideX1 - ( S0*strideX2 ); // offset increment for outermost loop
} else { // column-major
// For column-major matrices, the first dimension has the fastest changing index...
S0 = M;
S1 = N;
dx0 = strideX1; // offset increment for innermost loop
dx1 = strideX2 - ( S0*strideX1 ); // offset increment for outermost loop
}
ix = offsetX;
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
X[ ix ] = 0.0;
ix += dx0;
}
ix += dx1;
}
return X;
}
/**
* Scales each element in a matrix by a scalar `β`.
*
* @private
* @param {NonNegativeInteger} M - number of rows
* @param {NonNegativeInteger} N - number of columns
* @param {number} beta - scalar
* @param {Float64Array} X - matrix to fill
* @param {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @returns {Float64Array} input matrix
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* scal( 2, 3, 5.0, X, 3, 1, 0 );
* // X => <Float64Array>[ 5.0, 10.0, 15.0, 20.0, 25.0, 30.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* scal( 2, 3, 5.0, X, 1, 2, 0 );
* // X => <Float64Array>[ 5.0, 10.0, 15.0, 20.0, 25.0, 30.0 ]
*/
function scal( M, N, beta, X, strideX1, strideX2, offsetX ) { // TODO: consider moving to a separate package
var dx0;
var dx1;
var S0;
var S1;
var i0;
var i1;
var ix;
if ( isRowMajor( [ strideX1, strideX2 ] ) ) {
// For row-major matrices, the last dimension has the fastest changing index...
S0 = N;
S1 = M;
dx0 = strideX2; // offset increment for innermost loop
dx1 = strideX1 - ( S0*strideX2 ); // offset increment for outermost loop
} else { // column-major
// For column-major matrices, the first dimension has the fastest changing index...
S0 = M;
S1 = N;
dx0 = strideX1; // offset increment for innermost loop
dx1 = strideX2 - ( S0*strideX1 ); // offset increment for outermost loop
}
ix = offsetX;
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
X[ ix ] *= beta;
ix += dx0;
}
ix += dx1;
}
return X;
}
// MAIN //
/**
* Performs the matrix-matrix operation `C = α*A*B + β*C` or `C = α*B*A + β*C` where `α` and `β` are scalars, `A` is a symmetric matrix and B and C are `M` by `N` matrices.
*
* @private
* @param {string} side - specifies whether `A` appears on the left or right of `B`
* @param {string} uplo - specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied
* @param {NonNegativeInteger} M - number of rows in the matrix `C`
* @param {NonNegativeInteger} N - number of columns in the matrix `C`
* @param {number} alpha - scalar constant
* @param {Float64Array} A - first 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 {Float64Array} B - second matrix
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @param {number} beta - scalar constant
* @param {Float64Array} C - third matrix
* @param {integer} strideC1 - stride of the first dimension of `C`
* @param {integer} strideC2 - stride of the second dimension of `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @returns {Float64Array} `C`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 3.0 ] );
* var B = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
* var C = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
*
* dsymm( 'left', 'lower', 3, 3, 1.0, A, 3, 1, 0, B, 3, 1, 0, 1.0, C, 3, 1, 0 );
* // C => <Float64Array>[ 4.0, 4.0, 4.0, 5.0, 5.0, 5.0, 6.0, 6.0, 6.0 ]
*/
function dsymm( side, uplo, M, N, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB, beta, C, strideC1, strideC2, offsetC ) {
var isrma;
var tmp;
var sa0;
var sa1;
var sb0;
var sb1;
var sc0;
var sc1;
var oa2;
var idx;
var oa;
var ob;
var i;
var j;
var k;
// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
isrma = isRowMajor( [ strideA1, strideA2 ] );
// Check whether we can early return...
if ( M === 0 || N === 0 || ( ( beta === 1.0 ) && ( alpha === 0.0 ) ) ) {
return C;
}
if ( isrma ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2; // stride for innermost loop
sa1 = strideA1; // stride for outermost loop
sb0 = strideB2;
sb1 = strideB1;
sc0 = strideC2;
sc1 = strideC1;
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1; // stride for innermost loop
sa1 = strideA2; // stride for outermost loop
sb0 = strideB1;
sb1 = strideB2;
sc0 = strideC1;
sc1 = strideC2;
}
if ( beta === 0.0 ) {
C = zeros( M, N, C, strideC1, strideC2, offsetC );
} else if ( beta !== 1.0 ) {
C = scal( M, N, beta, C, strideC1, strideC2, offsetC );
}
// Check whether we can early return...
if ( alpha === 0.0 ) {
return C;
}
oa = offsetA;
ob = offsetB;
if (
( isrma && side === 'left' && uplo === 'upper' ) ||
( !isrma && side === 'right' && uplo === 'lower' )
) {
for ( i = 0; i < M; i++ ) {
for ( j = 0; j < N; j++ ) {
tmp = 0.0;
for ( k = 0; k < i; k++ ) {
oa2 = A[ oa + ( k * sa1 ) + ( i * sa0 ) ];
tmp += oa2 * B[ ob + ( k * sb1 ) + ( j * sb0 ) ];
}
for ( k = i; k < M; k++ ) {
oa2 = A[ oa + ( i * sa1 ) + ( k * sa0 ) ];
tmp += oa2 * B[ ob + ( k * sb1 ) + ( j * sb0 ) ];
}
idx = offsetC + ( i * sc1 ) + ( j * sc0 );
C[ idx ] += alpha * tmp;
}
}
return C;
}
if (
( isrma && side === 'left' && uplo === 'lower' ) ||
( !isrma && side === 'right' && uplo === 'upper' )
) {
for ( i = 0; i < M; i++ ) {
for ( j = 0; j < N; j++ ) {
tmp = 0.0;
for ( k = 0; k < i; k++ ) {
oa2 = A[ oa + ( i * sa1 ) + ( k * sa0 ) ];
tmp += oa2 * B[ ob + ( k * sb1 ) + ( j * sb0 ) ];
}
for ( k = i; k < M; k++ ) {
oa2 = A[ oa + ( k * sa1 ) + ( i * sa0 ) ];
tmp += oa2 * B[ ob + ( k * sb1 ) + ( j * sb0 ) ];
}
idx = offsetC + ( i * sc1 ) + ( j * sc0 );
C[ idx ] += alpha * tmp;
}
}
return C;
}
if (
( isrma && side === 'right' && uplo === 'upper' ) ||
( !isrma && side === 'left' && uplo === 'lower' )
) {
for ( i = 0; i < M; i++ ) {
for ( j = 0; j < N; j++ ) {
tmp = 0.0;
for ( k = 0; k < j; k++ ) {
oa2 = A[ oa + ( k * sa1 ) + ( j * sa0 ) ];
tmp += B[ ob + ( i * sb1 ) + ( k * sb0 ) ] * oa2;
}
for ( k = j; k < N; k++ ) {
oa2 = A[ oa + ( j * sa1 ) + ( k * sa0 ) ];
tmp += B[ ob + ( i * sb1 ) + ( k * sb0 ) ] * oa2;
}
idx = offsetC + ( i * sc1 ) + ( j * sc0 );
C[ idx ] += alpha * tmp;
}
}
return C;
}
// ( isrma && side === 'right' && uplo === 'lower' ) || ( !isrma && side === 'left' && uplo === 'upper' )
for ( i = 0; i < M; i++ ) {
for ( j = 0; j < N; j++ ) {
tmp = 0.0;
for ( k = 0; k < j; k++ ) {
oa2 = A[ oa + ( j * sa1 ) + ( k * sa0 ) ];
tmp += B[ ob + ( i * sb1 ) + ( k * sb0 ) ] * oa2;
}
for ( k = j; k < N; k++ ) {
oa2 = A[ oa + ( k * sa1 ) + ( j * sa0 ) ];
tmp += B[ ob + ( i * sb1 ) + ( k * sb0 ) ] * oa2;
}
idx = offsetC + ( i * sc1 ) + ( j * sc0 );
C[ idx ] += alpha * tmp;
}
}
return C;
}
// EXPORTS //
module.exports = dsymm;
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