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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 isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
var max = require( '@stdlib/math/base/special/max' );
var format = require( '@stdlib/string/format' );
var isStorage = require( './is_storage.js' );
var isDirection = require( './is_direction.js' );
var base = require( './base.js' );
// MAIN //
/**
* Forms the triangular factor T of a real block reflector H of order N, which is defined as a product of K elementary reflectors.
*
* ## Notes
*
* - If `direct` = 'forward', `H = H(1) H(2) . . . H(k)` and `T` is upper triangular.
* - If `direct` = 'backward', `H = H(k) . . . H(2) H(1)` and `T` is lower triangular.
* - If `storev` = 'columnwise', the vector which defines the elementary reflector `H(i)` is stored in the i-th column of the array `V`, and `H = I - V * T * V**T`.
* - If `storev` = 'rowwise', the vector which defines the elementary reflector `H(i)` is stored in the i-th row of the array `V`, and `H = I - V**T * T * V`.
*
* @param {string} order - storage layout
* @param {string} direct - specifies the order in which the elementary reflectors are multiplied to form the block reflector `H`
* @param {string} storev - specifies how the vectors which define the elementary reflectors are stored
* @param {NonNegativeInteger} N - order of the block reflector `H`
* @param {NonNegativeInteger} K - order of the triangular factor `T` (the number of elementary reflectors)
* @param {Float64Array} V - matrix of reflector vectors
* @param {PositiveInteger} LDV - leading dimension of `V`
* @param {Float64Array} TAU - array of scalar factors of the elementary reflector `H(i)`y
* @param {Float64Array} T - output triangular matrix
* @param {PositiveInteger} LDT - leading dimension of `T`
* @throws {TypeError} first argument must be a valid order
* @throws {TypeError} second argument must be a valid direction
* @throws {TypeError} third argument must be a valid storage layout
* @throws {RangeError} seventh argument must be a valid `LDV`
* @throws {RangeError} tenth argument must be a valid `LDT`
* @returns {Float64Array} `T`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var V = new Float64Array( [ 1.0, 0.2, 0.3, -0.4, 0.5, 0.0, 1.0, -0.6, 0.7, -0.8, 0.0, 0.0, 1.0, 0.9, 1.1 ] );
* var TAU = new Float64Array( [ 1.2, 0.7, 1.5 ] );
* var T = new Float64Array( 9 );
*
* dlarft( 'row-major', 'forward', 'rowwise', 5, 3, V, 5, TAU, T, 3 );
* // T => <Float64Array>[ ~1.2, ~0.5544, ~-0.17514, 0.0, 0.7, 0.8925, 0.0, 0.0, 1.5 ]
*/
function dlarft( order, direct, storev, N, K, V, LDV, TAU, T, LDT ) {
var strideV1;
var strideV2;
var strideT1;
var strideT2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( !isDirection( direct ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a direction. Value: `%s`.', direct ) );
}
if ( !isStorage( storev ) ) {
throw new TypeError( format( 'invalid argument. Third argument must be a valid storage layout. Value: `%s`.', storev ) );
}
if ( isColumnMajor( order ) ) {
if ( storev === 'columnwise' && LDV < max( 1, N ) ) {
throw new RangeError( format( 'invalid argument. Seventh argument must be at least max(1,%d). Value: `%d`.', N, LDV ) );
}
if ( storev === 'rowwise' && LDV < K ) {
throw new RangeError( format( 'invalid argument. Seventh argument must be at least %d. Value: `%d`.', K, LDV ) );
}
strideV1 = 1;
strideV2 = LDV;
strideT1 = 1;
strideT2 = LDT;
} else { // order === 'row-major'
strideV1 = LDV;
strideV2 = 1;
strideT1 = LDT;
strideT2 = 1;
}
if ( LDT < K ) {
throw new RangeError( format( 'invalid argument. Tenth argument must be at least %d. Value: `%d`.', K, LDT ) );
}
base( direct, storev, N, K, V, strideV1, strideV2, 0, TAU, 1, 0, T, strideT1, strideT2, 0 );
return T;
}
// EXPORTS //
module.exports = dlarft;
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