Press n or j to go to the next uncovered block, b, p or k for the previous block.
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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.
*/
'use strict';
// MODULES //
var dlamch = require( '@stdlib/lapack/base/dlamch' );
var dswap = require( '@stdlib/blas/base/dswap' );
var dger = require( '@stdlib/blas/base/dger' );
var abs = require( '@stdlib/math/base/special/abs' );
var max = require( '@stdlib/math/base/special/max' );
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
// MAIN //
/**
* Computes the LU factorization with complete pivoting of the general n-by-n matrix `A`.
*
* ## Notes
*
* - `A` should have dimension (LDA, N) and is overwritten with the factors L and U from the factorization A = `P*L*U*Q`; the unit diagonal elements of L are not stored.
* - If U(k, k) appears to be less than `SMIN`, U(k, k) is given the value of `SMIN`, i.e., giving a nonsingular perturbed system.
* - `IPIV` should have `N` elements and is overwritten with the pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
* - `JPIV` should have `N` elements and is overwritten with the pivot indices; for 1 <= i <= N, column i of the matrix has been interchanged with column JPIV(i).
* - Returns 0 on successful exit and if returns `k`, U(k, k) is likely to produce overflow if we try to solve for x in Ax = b. So U is perturbed to avoid the overflow.
*
* @private
* @param {PositiveInteger} 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 - index offset for `A`
* @param {Int32Array} IPIV - vector of pivot indices for rows
* @param {integer} strideIPIV - stride length for `IPIV`
* @param {NonNegativeInteger} offsetIPIV - index offset for `IPIV`
* @param {Int32Array} JPIV - vector of pivot indices for columns
* @param {integer} strideJPIV - stride length for `JPIV`
* @param {NonNegativeInteger} offsetJPIV - index offset for `JPIV`
* @returns {integer} - status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var Int32Array = require( '@stdlib/array/int32' );
*
* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 10.0 ] );
* var IPIV = new Int32Array( 3 );
* var JPIV = new Int32Array( 3 );
*
* dgetc2( 3, A, 1, 3, 0, IPIV, 1, 0, JPIV, 1, 0 );
* // A => <Float64Array>[ 10, 0.7, 0.8, 3, ~-1.1, ~0.36, 6, ~-0.2, ~0.27 ]
* // JPIV = <Int32Array>[ 3, 3, 3 ]
* // IPIV = <Int32Array>[ 3, 3, 3 ]
*/
function dgetc2( N, A, strideA1, strideA2, offsetA, IPIV, strideIPIV, offsetIPIV, JPIV, strideJPIV, offsetJPIV ) { // eslint-disable-line max-params, max-len
var smlnum;
var info;
var smin;
var xmax;
var eps;
var ipv;
var jpv;
var sA1;
var sA2;
var ip;
var jp;
var oA;
var i;
var j;
sA1 = strideA1;
sA2 = strideA2;
oA = offsetA;
info = 0;
// Quick return if possible
if ( N === 0 ) {
return info;
}
// Set constants to control overflow
eps = dlamch( 'P' );
smlnum = dlamch( 'S' ) / eps;
// Handle the case N=1 by itself
if ( N === 1 ) {
IPIV[ offsetIPIV ] = 1;
JPIV[ offsetJPIV ] = 1;
if ( abs( A[ oA ] )< smlnum ) {
info = 1;
A[ oA ] = smlnum;
}
return info;
}
// Factorize A using complete pivoting.
// Set pivots less than SMIN to SMIN.
for ( i = 0; i < N - 1; i++ ) {
// Find max element in matrix A
xmax = 0.0;
if ( isRowMajor( [ sA1, sA2 ] ) ) {
for ( ip = i; ip < N; ip++ ) {
for ( jp = i; jp < N; jp++ ) {
if ( abs( A[ oA + ( sA1*ip ) + ( sA2*jp ) ] ) >= xmax ) {
xmax = abs( A[ oA + ( sA1*ip ) + ( sA2*jp ) ] );
ipv = ip;
jpv = jp;
}
}
}
} else { // column-major
for ( jp = i; jp < N; jp++ ) {
for ( ip = i; ip < N; ip++ ) {
if ( abs( A[ oA + ( sA1*ip ) + ( sA2*jp ) ]) >= xmax ) {
xmax = abs( A[ oA + ( sA1*ip ) + ( sA2*jp ) ] );
ipv = ip;
jpv = jp;
}
}
}
}
if ( i === 0 ) {
smin = max( eps*xmax, smlnum );
}
// Swap rows
if ( ipv !== i ) {
dswap.ndarray( N, A, sA2, oA + ( sA1*ipv ), A, sA2, oA+( sA1*i ) );
}
IPIV[ offsetIPIV + ( i*strideIPIV ) ] = ipv+1;
// Swap columns
if ( jpv !== i ) {
dswap.ndarray( N, A, sA1, oA + ( sA2*jpv ), A, sA1, oA+( sA2*i ) );
}
JPIV[ offsetJPIV + ( i*strideJPIV ) ] = jpv+1;
// Check for singularity
for ( j = i+1; j < N; j++ ) {
A[ oA + ( j*sA1 ) + ( i*sA2 ) ] /= A[ oA + ( i*( sA1 + sA2 ) ) ];
}
dger.ndarray( N - i-1, N - i-1, -1, A, sA1, oA + ( ( i + 1 )*sA1 ) + ( i*sA2 ), A, sA2, oA + ( i*sA1 ) + ( ( i + 1 )*sA2 ), A, sA1, sA2, oA + ( ( i + 1 )*( sA1 + sA2 ) ) ); // eslint-disable-line max-len
}
if ( abs( A[ ( oA ) + ( ( N - 1 )*( sA1 + sA2 ) ) ] ) < smin ) {
info = N;
A[ ( oA ) + ( ( N - 1 )*( sA1 + sA2 ) ) ] = smin;
}
IPIV[ offsetIPIV + ( ( N - 1 )*strideIPIV ) ] = N;
JPIV[ offsetJPIV + ( ( N - 1 )*strideJPIV ) ] = N;
return info;
}
// EXPORTS //
module.exports = dgetc2;
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