Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 56x 29x 29x 29x 56x 27x 27x 27x 27x 56x 56x 56x 56x 52x 56x 8x 8x 24x 22x 22x 12x 12x 22x 22x 22x 24x 24x 24x 22x 24x 24x 8x 8x 48x 56x 37x 56x 21x 21x 63x 34x 34x 14x 14x 34x 34x 34x 50x 50x 50x 34x 63x 63x 21x 21x 27x 56x 19x 56x 19x 19x 57x 57x 57x 57x 57x 57x 57x 57x 30x 30x 57x 57x 57x 19x 19x 8x 8x 8x 56x 24x 24x 24x 24x 24x 24x 24x 24x 12x 12x 24x 24x 24x 8x 56x 3x 3x 3x 3x 3x | /**
* @license Apache-2.0
*
* Copyright (c) 2024 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.
*/
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
// MAIN //
/**
* Solves one of the systems of equations `A*x = b` or `A^T*x = b` where `b` and `x` are `N` element vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix.
*
* @private
* @param {string} uplo - specifies whether `A` is an upper or lower triangular matrix
* @param {string} trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
* @param {string} diag - specifies whether `A` has a unit diagonal
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {Float32Array} 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 {Float32Array} x - input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {Float32Array} `x`
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
* var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
*
* strsv( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
* // x => <Float32Array>[ 0.0, -4.0, 3.0 ]
*/
function strsv( uplo, trans, diag, N, A, strideA1, strideA2, offsetA, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
var nonunit;
var isrm;
var tmp;
var sa0;
var sa1;
var ix0;
var ix1;
var i0;
var i1;
var oa;
var ox;
// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
isrm = isRowMajor( [ strideA1, strideA2 ] );
nonunit = ( diag === 'non-unit' );
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2; // stride for innermost loop
sa1 = strideA1; // stride for outermost loop
} 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
}
ox = offsetX;
if (
( !isrm && trans === 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'lower' )
) {
ix1 = ox + ( ( N - 1 ) * strideX );
for ( i1 = N-1; i1 >= 0; i1-- ) {
if ( x[ ix1 ] !== 0.0 ) {
oa = offsetA + (sa1*i1);
if ( nonunit ) {
x[ ix1 ] = f32( x[ ix1 ] / A[ oa+(sa0*i1) ] );
}
tmp = x[ ix1 ];
ix0 = ix1;
for ( i0 = i1-1; i0 >= 0; i0-- ) {
ix0 -= strideX;
x[ ix0 ] = f32( x[ ix0 ] - f32( tmp * A[ oa+(sa0*i0) ] ) );
}
}
ix1 -= strideX;
}
return x;
}
if (
( !isrm && trans === 'no-transpose' && uplo === 'lower' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'upper' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
if ( x[ ix1 ] !== 0.0 ) {
oa = offsetA + (sa1*i1);
if ( nonunit ) {
x[ ix1 ] = f32( x[ ix1 ] / A[ oa+(sa0*i1) ] );
}
tmp = x[ ix1 ];
ix0 = ix1;
for ( i0 = i1+1; i0 < N; i0++ ) {
ix0 += strideX;
x[ ix0 ] = f32( x[ ix0 ] - f32( tmp * A[ oa+(sa0*i0) ] ) );
}
}
ix1 += strideX;
}
return x;
}
if (
( !isrm && trans !== 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans === 'no-transpose' && uplo === 'lower' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
tmp = x[ ix1 ];
oa = offsetA + (sa1*i1);
ix0 = ox;
for ( i0 = 0; i0 <= i1-1; i0++ ) {
tmp = f32( tmp - f32( x[ ix0 ] * A[ oa+(sa0*i0) ] ) );
ix0 += strideX;
}
if ( nonunit ) {
tmp = f32( tmp / A[ oa+(sa0*i1) ] );
}
x[ ix1 ] = tmp;
ix1 += strideX;
}
return x;
}
// ( !isrm && trans !== 'no-transpose' && uplo === 'lower' ) || ( isrm && trans === 'no-transpose' && uplo === 'upper' )
ox += ( N - 1 ) * strideX;
ix1 = ox;
for ( i1 = N-1; i1 >= 0; i1-- ) {
tmp = x[ ix1 ];
oa = offsetA + (sa1*i1);
ix0 = ox;
for ( i0 = N-1; i0 > i1; i0-- ) {
tmp = f32( tmp - f32( x[ ix0 ] * A[ oa+(sa0*i0) ] ) );
ix0 -= strideX;
}
if ( nonunit ) {
tmp = f32( tmp / A[ oa+(sa0*i1) ] );
}
x[ ix1 ] = tmp;
ix1 -= strideX;
}
return x;
}
// EXPORTS //
module.exports = strsv;
|