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* @license Apache-2.0
*
* Copyright (c) 2026 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' );
// MAIN //
/**
* Performs a matrix-matrix product of the form `B := alpha * A * X + beta * B` where `A` is a tridiagonal matrix, `B` and `X` are N by NRHS matrices, and `alpha` and `beta` are real scalars, each of which may be `0`, `1`, or `-1`.
*
* ## Notes
*
* - `DL` should have `N-1` indexed elements representing the sub-diagonal of `A`.
* - `D` should have `N` indexed elements representing the diagonal of `A`.
* - `DU` should have `N-1` indexed elements representing the super-diagonal of `A`.
* - `X` is an `N` by `NRHS` input matrix.
* - `B` is an `N` by `NRHS` input/output matrix.
* - `alpha` must be `0`, `1`, or `-1`; otherwise, it is assumed to be `0`.
* - `beta` must be `0`, `1`, or `-1`; otherwise, it is assumed to be `1`.
*
* @private
* @param {string} trans - specifies the operation applied to `A`
* @param {NonNegativeInteger} N - order of the matrix `A`
* @param {NonNegativeInteger} NRHS - number of right hand sides (columns of `X` and `B`)
* @param {number} alpha - scalar alpha
* @param {Float64Array} DL - sub-diagonal of `A`
* @param {integer} strideDL - stride length for `DL`
* @param {NonNegativeInteger} offsetDL - starting index of `DL`
* @param {Float64Array} D - diagonal of `A`
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index of `D`
* @param {Float64Array} DU - super-diagonal of `A`
* @param {integer} strideDU - stride length for `DU`
* @param {NonNegativeInteger} offsetDU - starting index of `DU`
* @param {Float64Array} X - input matrix `X`
* @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 of `X`
* @param {number} beta - scalar beta
* @param {Float64Array} B - input/output matrix `B`
* @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 of `B`
* @returns {Float64Array} `B`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var DL = new Float64Array( [ 1.0, 1.0 ] );
* var D = new Float64Array( [ 2.0, 3.0, 4.0 ] );
* var DU = new Float64Array( [ 1.0, 1.0 ] );
* var X = new Float64Array( [ 1.0, 1.0, 1.0 ] );
* var B = new Float64Array( [ 0.0, 0.0, 0.0 ] );
*
* dlagtm( 'no-transpose', 3, 1, 1.0, DL, 1, 0, D, 1, 0, DU, 1, 0, X, 1, 3, 0, 0.0, B, 1, 3, 0 );
* // B => <Float64Array>[ 3.0, 5.0, 5.0 ]
*/
function dlagtm( trans, N, NRHS, alpha, DL, strideDL, offsetDL, D, strideD, offsetD, DU, strideDU, offsetDU, X, strideX1, strideX2, offsetX, beta, B, strideB1, strideB2, offsetB ) {
var sd1;
var sd3;
var od1;
var od3;
var id1;
var id2;
var id3;
var d1;
var d3;
var rm;
var ib;
var ix;
var i0;
var i1;
var s;
var v;
if ( N === 0 ) {
return B;
}
// Determine whether the memory layout is row-major:
rm = isRowMajor( [ strideB1, strideB2 ] );
// Multiply B by beta if beta is not 1:
if ( beta === 0.0 ) {
ib = offsetB;
if ( rm ) {
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = 0; i0 < NRHS; i0++ ) {
B[ ib + (i0*strideB2) ] = 0.0;
}
ib += strideB1;
}
} else {
for ( i1 = 0; i1 < NRHS; i1++ ) {
for ( i0 = 0; i0 < N; i0++ ) {
B[ ib + (i0*strideB1) ] = 0.0;
}
ib += strideB2;
}
}
} else if ( beta === -1.0 ) {
ib = offsetB;
if ( rm ) {
for ( i1 = 0; i1 < N; i1++ ) {
for ( i0 = 0; i0 < NRHS; i0++ ) {
B[ ib + (i0*strideB2) ] = -B[ ib + (i0*strideB2) ];
}
ib += strideB1;
}
} else {
for ( i1 = 0; i1 < NRHS; i1++ ) {
for ( i0 = 0; i0 < N; i0++ ) {
B[ ib + (i0*strideB1) ] = -B[ ib + (i0*strideB1) ];
}
ib += strideB2;
}
}
}
// If beta === 1.0 or any other value, B remains unchanged
// Determine the sign from alpha:
if ( alpha === 1.0 ) {
s = 1.0;
} else if ( alpha === -1.0 ) {
s = -1.0;
} else {
// If alpha is not 1.0 or -1.0, treat as 0.0 (no multiplication):
return B;
}
// Resolve the tridiagonal arrays based on the transpose operation:
if ( trans === 'no-transpose' ) {
// A*X: DL is sub-diagonal, DU is super-diagonal
d1 = DL;
sd1 = strideDL;
od1 = offsetDL;
d3 = DU;
sd3 = strideDU;
od3 = offsetDU;
} else {
// A^T*X: roles of DL and DU are swapped
d1 = DU;
sd1 = strideDU;
od1 = offsetDU;
d3 = DL;
sd3 = strideDL;
od3 = offsetDL;
}
// Handle N === 1 separately (no sub-diagonal or super-diagonal contribution):
if ( N === 1 ) {
ib = offsetB;
ix = offsetX;
for ( i0 = 0; i0 < NRHS; i0++ ) {
B[ ib ] += s * D[ offsetD ] * X[ ix ];
ib += strideB2;
ix += strideX2;
}
return B;
}
// General case: N >= 2
if ( rm ) {
// Row-major: outer loop over rows, inner loop over columns
ib = offsetB;
ix = offsetX;
id2 = offsetD;
id3 = od3;
// First row:
for ( i0 = 0; i0 < NRHS; i0++ ) {
v = ( D[ id2 ] * X[ ix + (i0*strideX2) ] ) + ( d3[ id3 ] * X[ ix + strideX1 + (i0*strideX2) ] );
B[ ib + (i0*strideB2) ] += s * v;
}
ib += strideB1;
ix += strideX1;
id2 += strideD;
id3 += sd3;
id1 = od1;
// Interior rows:
for ( i1 = 1; i1 < N - 1; i1++ ) {
for ( i0 = 0; i0 < NRHS; i0++ ) {
v = d1[ id1 ] * X[ ix - strideX1 + (i0*strideX2) ];
v += D[ id2 ] * X[ ix + (i0*strideX2) ];
v += d3[ id3 ] * X[ ix + strideX1 + (i0*strideX2) ];
B[ ib + (i0*strideB2) ] += s * v;
}
ib += strideB1;
ix += strideX1;
id1 += sd1;
id2 += strideD;
id3 += sd3;
}
// Last row:
for ( i0 = 0; i0 < NRHS; i0++ ) {
v = ( d1[ id1 ] * X[ ix - strideX1 + (i0*strideX2) ] ) + ( D[ id2 ] * X[ ix + (i0*strideX2) ] );
B[ ib + (i0*strideB2) ] += s * v;
}
} else {
// Column-major: outer loop over columns, inner loop over rows
ib = offsetB;
ix = offsetX;
for ( i1 = 0; i1 < NRHS; i1++ ) {
id1 = od1;
id2 = offsetD;
id3 = od3;
// First row:
v = ( D[ id2 ] * X[ ix ] ) + ( d3[ id3 ] * X[ ix + strideX1 ] );
B[ ib ] += s * v;
id2 += strideD;
id3 += sd3;
// Interior rows:
for ( i0 = 1; i0 < N - 1; i0++ ) {
v = d1[ id1 ] * X[ ix + ((i0-1)*strideX1) ];
v += D[ id2 ] * X[ ix + (i0*strideX1) ];
v += d3[ id3 ] * X[ ix + ((i0+1)*strideX1) ];
B[ ib + (i0*strideB1) ] += s * v;
id1 += sd1;
id2 += strideD;
id3 += sd3;
}
// Last row:
v = ( d1[ id1 ] * X[ ix + ((N-2)*strideX1) ] ) + ( D[ id2 ] * X[ ix + ((N-1)*strideX1) ] );
B[ ib + ((N-1)*strideB1) ] += s * v;
ib += strideB2;
ix += strideX2;
}
}
return B;
}
// EXPORTS //
module.exports = dlagtm;
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