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‎lib/node_modules/@stdlib/lapack/base/dlange/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dlange
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> Compute an `LU` factorization of a real tridiagonal matrix `A` using elimination with partial pivoting and row interchanges.
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<section class="intro">
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The `dlange` routine computes the value of a specified norm of a real M-by-N matrix `A`. The norm to be computed is selected using the parameter `norm`, which may specify the **Max norm**, **One norm**, **Infinity norm**, or **Frobenius norm**.
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The supported norms are:
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- **Max Absolute Value** (`norm` = `'max'`): returns the largest absolute element in `A`.
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<!-- <equation class="equation" label="eq:lu_decomposition" align="center" raw="\|A\|_{\max} = \max_{i,j} |a_{i,j}|" alt="Maximum absolute value of a matrix."> -->
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```math
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\|A\|_{\max} = \max_{i,j} |a_{i,j}|
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```
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<!-- </equation> -->
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- **One Norm** (`norm` = `'one'`): returns the maximum absolute column sum in `A`.
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<!-- <equation class="equation" label="eq:lu_decomposition" align="center" raw="\|A\|_1 = \max_j \sum_{i=1}^M |a_{i,j}|" alt="Definition of one norm of a matrix."> -->
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```math
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\|A\|_1 = \max_j \sum_{i=1}^M |a_{i,j}|
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```
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<!-- </equation> -->
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- **Infinity Norm** (`norm` = `'infinity'`): returns the maximum absolute row sum in `A`.
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<!-- <equation class="equation" label="eq:lu_decomposition" align="center" raw="\|A\|_{\infty} = \max_i \sum_{j=1}^N |a_{i,j}|" alt="Definition of infinity norm of a matrix."> -->
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```math
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\|A\|_{\infty} = \max_i \sum_{j=1}^N |a_{i,j}|
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```
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<!-- </equation> -->
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- **Frobenius Norm** (`norm` = `'frobenius'`): returns the square root of the sum of the squares of all elements in `A`.
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<!-- <equation class="equation" label="eq:lu_decomposition" align="center" raw="\|A\|_F = \left(\sum_{i=1}^M \sum_{j=1}^N |a_{i,j}|^2 \right)^{1/2}" alt="Definition of frobenius norm of a matrix."> -->
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```math
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\|A\|_F = \left(\sum_{i=1}^M \sum_{j=1}^N |a_{i,j}|^2 \right)^{1/2}
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```
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var dlange = require( '@stdlib/lapack/base/dlange' );
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```
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#### dlange( N, DL, D, DU, DU2, IPIV )
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Computes 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`.
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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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 ] );
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/*
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A = [
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[ 1.0, 4.0, 7.0, 10.0 ],
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[ 2.0, 5.0, 8.0, 11.0 ],
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[ 3.0, 6.0, 9.0, 12.0 ]
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]
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*/
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var work = new Float64Array( 3 );
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var out = dlange( 'row-major', 'frobenius', 3, 4, A, 4, work );
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// returns ~25.5
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **norm**: specifies the type of norm to be calculated, should be one of the following: `max`, `one`, `frobenius` or `infinity`.
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- **M**: number of rows in `A`.
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- **N**: number of columns in `A`.
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- **A**: input [`Float64Array`][mdn-float64array].
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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- **work**: [`Float64Array`][mdn-float64array] used to compute the infinity norm, should have `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array.
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments, max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A0 = new Float64Array( [ 0.0, 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
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var work0 = new Float64Array( 4 );
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/*
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A = [
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[ 1.0, 4.0, 7.0, 10.0 ],
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[ 2.0, 5.0, 8.0, 11.0 ],
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[ 3.0, 6.0, 9.0, 12.0 ]
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]
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*/
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// Create offset views...
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var A = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var work = new Float64Array( work0.buffer, work0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var out = dlange( 'row-major', 'frobenius', 3, 4, A, 4, work );
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// returns ~25.5
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```
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<!-- lint disable maximum-heading-length -->
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#### dlange.ndarray( norm, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork )
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Computes 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` using alternative indexing semantics.
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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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 ] );
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/*
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A = [
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[ 1.0, 4.0, 7.0, 10.0 ],
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[ 2.0, 5.0, 8.0, 11.0 ],
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[ 3.0, 6.0, 9.0, 12.0 ]
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]
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*/
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var work = new Float64Array( 3 );
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var out = dlange.ndarray( 'frobenius', 3, 4, A, 4, 1, 0, work, 1, 0 );
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// returns ~25.5
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```
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The function has the following additional parameters:
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- **norm**: specifies the type of norm to be calculated, should be one of the following: `max`, `one`, `frobenius` or `infinity`.
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- **M**: number of rows in `A`.
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- **N**: number of columns in `A`.
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- **A**: input [`Float64Array`][mdn-float64array].
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- **strideA1**: stride of the first dimension of `A`.
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- **strideA2**: stride of the second dimension of `A`.
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- **offsetA**: starting index for `A`.
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- **work**: [`Float64Array`][mdn-float64array] used to compute the infinity norm, should have `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array.
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- **strideWork**: stride length of `work`.
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- **offsetWork**: starting index of `work`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 ] );
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/*
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A = [
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[ 1.0, 4.0, 7.0, 10.0 ],
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[ 2.0, 5.0, 8.0, 11.0 ],
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[ 3.0, 6.0, 9.0, 12.0 ]
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]
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*/
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var work = new Float64Array( 4 );
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var out = dlange.ndarray( 'frobenius', 3, 4, A, 4, 1, 1, work, 1, 1 );
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// returns ~25.5
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- `dlange()` corresponds to the [LAPACK][LAPACK] routine [`dlange`][lapack-dlange].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var numel = require( '@stdlib/ndarray/base/numel' );
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var dlange = require( '@stdlib/lapack/base/dlange' );
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// Specify matrix meta data:
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var shape = [ 3, 4 ];
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var strides = [ 4, 1 ];
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var offset = 0;
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var N = numel( shape );
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var order = 'row-major';
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// Create a matrix stored in linear memory:
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var A = uniform( N, -10, 10, {
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'dtype': 'float64'
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});
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console.log( ndarray2array( A, shape, strides, offset, order ) );
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var work = new Float64Array( shape[ 0 ] );
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// Calculate the infinity norm:
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var out = dlange( order, 'infinity', shape[ 0 ], shape[ 1 ], A, strides[ 0 ], work );
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console.log( 'Infinity norm: ', out );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[lapack-dlange]: https://www.netlib.org/lapack/explore-html/d8/d2e/group__lange_ga8581d687290b36c6e24fe76b3be7caa3.html
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/lapack/base/dlange/docs/types/index.d.ts‎

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* @param N - number of columns in `A`
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* @param A - input array
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* @param LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
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* @param work - only used to compute the infinity norm, expects `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
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* @param work - only used to compute the infinity norm, should have `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
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* @returns required norm value
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*
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* @example
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* @param strideA1 - stride of the first dimension of `A`
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* @param strideA2 - stride of the second dimension of `A`
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* @param offsetA - starting index of `A`
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* @param work - only used to compute the infinity norm, expects `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
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* @param work - only used to compute the infinity norm, should have `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
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* @param strideWork - stride length of `work`
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* @param offsetWork - starting index of `work`
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* @returns required norm value
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* @param A - input array
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* @param LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
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* @param work - only used to compute the infinity norm, expects `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
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* @param work - only used to compute the infinity norm, should have `M` indexed elements if computing the infinity norm otherwise it's fine to pass a dummy array
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* @returns required norm value
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*
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* @example

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