feat: add lapack/base/dlatrs

lib/node_modules/@stdlib/lapack/base/dlatrs/lib/dlange.js

@@ -0,0 +1,362 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var dlassq = require( '@stdlib/lapack/base/dlassq' ).ndarray;
+var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
+var loopOrder = require( '@stdlib/ndarray/base/nullary-loop-interchange-order' );
+var dasum = require( '@stdlib/blas/base/dasum' ).ndarray;
+var Float64Array = require( '@stdlib/array/float64' );
+var min = require( '@stdlib/math/base/special/min' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var abs = require( '@stdlib/math/base/special/abs' );
+
+
+// FUNCTIONS //
+
+/**
+* Returns the value of the one norm of a real matrix `A`.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @param {Float64Array} A - input array
+* @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 of `A`
+* @param {Float64Array} work - work array, should have `N` indexed elements if row-major layout is used
+* @param {integer} strideWork - stride length of `work`
+* @param {NonNegativeInteger} offsetWork - starting index of `work`
+* @returns {number} required norm value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
+* var work = new Float64Array( 4 );
+*
+* var out = oneNorm( 3, 4, A, 4, 1, 0, work, 1, 0 );
+* // returns 33.0
+*/
+function oneNorm( M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) { // eslint-disable-line max-len
+	var value;
+	var temp;
+	var ia1;
+	var ia2;
+	var sum;
+	var iw;
+	var i;
+	var j;
+
+	if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
+		iw = offsetWork;
+		for ( i = 0; i < N; i++ ) {
+			work[ iw ] = 0.0;
+			iw += strideWork;
+		}
+
+		ia1 = offsetA;
+		for ( j = 0; j < M; j++ ) {
+			ia2 = 0;
+			iw = offsetWork;
+			for ( i = 0; i < N; i++ ) {
+				work[ iw ] += abs( A[ ia1 + ia2 ] );
+				iw += strideWork;
+				ia2 += strideA2;
+			}
+			ia1 += strideA1;
+		}
+
+		value = 0.0;
+
+		iw = offsetWork;
+		for ( i = 0; i < N; i++ ) {
+			temp = work[ iw ];
+			if ( value < temp || isnan( temp ) ) {
+				value = temp;
+			}
+			iw += strideWork;
+		}
+	} else {
+		value = 0.0;
+		ia1 = offsetA;
+		for ( j = 0; j < N; j++ ) {
+			sum = dasum( M, A, strideA1, ia1 );
+			if ( value < sum || isnan( sum ) ) {
+				value = sum;
+			}
+			ia1 += strideA2;
+		}
+	}
+
+	return value;
+}
+
+/**
+* Returns the absolute value of the maximum element of a real matrix `A`.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @param {Float64Array} A - input array
+* @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 of `A`
+* @returns {number} required norm value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
+*
+* var out = maxAbs( 3, 4, A, 4, 1, 0 );
+* // returns 12.0
+*/
+function maxAbs( M, N, A, strideA1, strideA2, offsetA ) {
+	var value;
+	var temp;
+	var da0;
+	var da1;
+	var ia;
+	var sa;
+	var sh;
+	var S0;
+	var S1;
+	var o;
+	var i;
+	var j;
+
+	value = 0.0;
+
+	// Resolve the loop interchange order:
+	o = loopOrder( [ M, N ], [ strideA1, strideA2 ] );
+	sh = o.sh;
+	sa = o.sx;
+	S0 = sh[ 0 ];
+	S1 = sh[ 1 ];
+	da0 = sa[ 0 ];
+	da1 = sa[ 1 ] - ( S0*sa[0] );
+	ia = offsetA;
+
+	for ( i = 0; i < S1; i++ ) {
+		for ( j = 0; j < S0; j++ ) {
+			temp = A[ ia ];
+			if ( value < temp || isnan( temp ) ) {
+				value = temp;
+			}
+			ia += da0;
+		}
+		ia += da1;
+	}
+	return value;
+}
+
+/**
+* Returns the value of the infinity norm of a real matrix `A`.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @param {Float64Array} A - input array
+* @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 of `A`
+* @param {Float64Array} work - work array, should have `M` indexed elements if column-major layout is used
+* @param {integer} strideWork - stride length of `work`
+* @param {NonNegativeInteger} offsetWork - starting index of `work`
+* @returns {number} required norm value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
+* var work = new Float64Array( 3 );
+*
+* var out = infinityNorm( 3, 4, A, 4, 1, 0, work, 1, 0 );
+* // returns 30.0
+*/
+function infinityNorm( M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) { // eslint-disable-line max-len
+	var value;
+	var temp;
+	var sum;
+	var ia1;
+	var ia2;
+	var iw;
+	var i;
+	var j;
+
+	if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
+		value = 0.0;
+		ia1 = offsetA;
+		for ( j = 0; j < M; j++ ) {
+			sum = dasum( N, A, strideA2, ia1 );
+			if ( value < sum || isnan( sum ) ) {
+				value = sum;
+			}
+			ia1 += strideA1;
+		}
+	} else {
+		iw = offsetWork;
+		for ( i = 0; i < M; i++ ) {
+			work[ iw ] = 0.0;
+			iw += strideWork;
+		}
+
+		ia1 = offsetA;
+		for ( j = 0; j < N; j++ ) {
+			ia2 = 0;
+			iw = offsetWork;
+			for ( i = 0; i < M; i++ ) {
+				work[ iw ] += abs( A[ ia1 + ia2 ] );
+				iw += strideWork;
+				ia2 += strideA1;
+			}
+			ia1 += strideA2;
+		}
+
+		value = 0.0;
+
+		iw = offsetWork;
+		for ( i = 0; i < M; i++ ) {
+			temp = work[ iw ];
+			if ( value < temp || isnan( temp ) ) {
+				value = temp;
+			}
+			iw += strideWork;
+		}
+	}
+	return value;
+}
+
+/**
+* Returns the absolute value of the frobenius norm of a real matrix `A`.
+*
+* @private
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @param {Float64Array} A - input array
+* @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 of `A`
+* @returns {number} required norm value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
+*
+* var out = frobeniusNorm( 3, 4, A, 4, 1, 0 );
+* // returns ~25.5
+*/
+function frobeniusNorm( M, N, A, strideA1, strideA2, offsetA ) {
+	var out;
+	var da0;
+	var da1;
+	var S1;
+	var S2;
+	var ia;
+	var i;
+
+	out = new Float64Array( [ 0.0, 1.0 ] );
+
+	if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
+		S1 = M;
+		S2 = N;
+		da0 = strideA2;
+		da1 = strideA1;
+	} else {
+		S1 = N;
+		S2 = M;
+		da0 = strideA1;
+		da1 = strideA2;
+	}
+
+	ia = offsetA;
+	for ( i = 0; i < S1; i++ ) {
+		dlassq( S2, A, da0, ia, out[ 0 ], out[ 1 ], out, 1, 0 );
+		ia += da1;
+	}
+
+	return out[ 0 ] * sqrt( out[ 1 ] );
+}
+
+
+// MAIN //
+
+/**
+* Returns the value of the one norm, or the frobenius norm, or the infinity norm, or the element with the largest absolute value of a real matrix `A`.
+*
+* ## Notes
+*
+* -   use `norm` = `max` to calculate the element with the largest absolute value
+* -   use `norm` = `one` to calculate the one norm, work should have `N` indexed elements if row-major layout is used
+* -   use `norm` = `infinity` to calculate the infinity norm, work should have `M` indexed elements if column-major layout is used
+* -   use `norm` = `frobenius` to calculate the frobenius norm
+*
+* @private
+* @param {string} norm - specifies the type of norm to be calculated
+* @param {NonNegativeInteger} M - number of rows in `A`
+* @param {NonNegativeInteger} N - number of columns in `A`
+* @param {Float64Array} A - input array
+* @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 of `A`
+* @param {Float64Array} work - temporary workspace array
+* @param {integer} strideWork - stride length of `work`
+* @param {NonNegativeInteger} offsetWork - starting index of `work`
+* @returns {number} required norm value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var A = new Float64Array( [ 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
+* var work = new Float64Array( 3 );
+*
+* var out = dlange( 'frobenius', 3, 4, A, 4, 1, 0, work, 1, 0 );
+* // returns ~25.5
+*/
+function dlange( norm, M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ) { // eslint-disable-line max-len
+	if ( min( M, N ) === 0 ) {
+		return 0.0;
+	}
+
+	if ( norm === 'max' ) {
+		return maxAbs( M, N, A, strideA1, strideA2, offsetA );
+	}
+
+	if ( norm === 'one' ) {
+		return oneNorm( M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ); // eslint-disable-line max-len
+	}
+
+	if ( norm === 'infinity' ) {
+		return infinityNorm( M, N, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork ); // eslint-disable-line max-len
+	}
+
+	if ( norm === 'frobenius' ) {
+		return frobeniusNorm( M, N, A, strideA1, strideA2, offsetA );
+	}
+}
+
+
+// EXPORTS //
+
+module.exports = dlange;