feat: add lapack/base/dlange

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

@@ -0,0 +1,351 @@
+<!--
+
+@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.
+
+-->
+
+# dlange
+
+> LAPACK routine to compute 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`.
+
+<section class="intro">
+
+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**.
+
+The supported norms are:
+
+-   **Max Absolute Value** (`norm` = `'max'`): returns the largest absolute element in `A`.
+
+<!-- <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."> -->
+
+```math
+\|A\|_{\max} = \max_{i,j} |a_{i,j}|
+```
+
+<!-- </equation> -->
+
+-   **One Norm** (`norm` = `'one'`): returns the maximum absolute column sum in `A`.
+
+<!-- <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."> -->
+
+```math
+\|A\|_1 = \max_j \sum_{i=1}^M |a_{i,j}|
+```
+
+<!-- </equation> -->
+
+-   **Infinity Norm** (`norm` = `'infinity'`): returns the maximum absolute row sum in `A`.
+
+<!-- <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."> -->
+
+```math
+\|A\|_{\infty} = \max_i \sum_{j=1}^N |a_{i,j}|
+```
+
+<!-- </equation> -->
+
+-   **Frobenius Norm** (`norm` = `'frobenius'`): returns the square root of the sum of the squares of all elements in `A`.
+
+<!-- <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."> -->
+
+```math
+\|A\|_F = \left(\sum_{i=1}^M \sum_{j=1}^N |a_{i,j}|^2 \right)^{1/2}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlange = require( '@stdlib/lapack/base/dlange' );
+```
+
+#### dlange( norm, M, N, A, LDA, work )
+
+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`.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+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 ] );
+
+/*
+    A = [
+        [ 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( 'row-major', 'frobenius', 3, 4, A, 4, work );
+// returns ~25.5
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **norm**: specifies the type of norm to be calculated, should be one of the following: `max`, `one`, `frobenius` or `infinity`.
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **work**: [`Float64Array`][mdn-float64array] used as a temporary workspace.
+
+`work` should have `N` indexed elements if calculating the one norm in a row-major layout and `M` indexed elements if calculating the infinity norm in column-major layout, in all other cases it is fine to pass a dummy [`Float64Array`][mdn-float64array].
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments, max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+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 ] );
+var work0 = new Float64Array( 4 );
+
+/*
+    A = [
+        [ 1.0, 4.0, 7.0, 10.0 ],
+        [ 2.0, 5.0, 8.0, 11.0 ],
+        [ 3.0, 6.0, 9.0, 12.0 ]
+    ]
+*/
+
+// Create offset views...
+var A = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var work = new Float64Array( work0.buffer, work0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var out = dlange( 'row-major', 'frobenius', 3, 4, A, 4, work );
+// returns ~25.5
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dlange.ndarray( norm, A, strideA1, strideA2, offsetA, work, strideWork, offsetWork )
+
+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.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+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 ] );
+
+/*
+    A = [
+        [ 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.ndarray( 'frobenius', 3, 4, A, 4, 1, 0, work, 1, 0 );
+// returns ~25.5
+```
+
+The function has the following additional parameters:
+
+-   **norm**: specifies the type of norm to be calculated, should be one of the following: `max`, `one`, `frobenius` or `infinity`.
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **strideA1**: stride of the first dimension of `A`.
+-   **strideA2**: stride of the second dimension of `A`.
+-   **offsetA**: starting index for `A`.
+-   **work**: [`Float64Array`][mdn-float64array] used as a temporary workspace
+-   **strideWork**: stride length of `work`.
+-   **offsetWork**: starting index of `work`.
+
+`work` should have `N` indexed elements if calculating the one norm in a row-major layout and `M` indexed elements if calculating the infinity norm in column-major layout, in all other cases it is fine to pass a dummy [`Float64Array`][mdn-float64array].
+
+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,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+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 ] );
+
+/*
+    A = [
+        [ 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 = dlange.ndarray( 'frobenius', 3, 4, A, 4, 1, 1, work, 1, 1 );
+// returns ~25.5
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlange()` corresponds to the [LAPACK][LAPACK] routine [`dlange`][lapack-dlange].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var numel = require( '@stdlib/ndarray/base/numel' );
+var dlange = require( '@stdlib/lapack/base/dlange' );
+
+// Specify matrix meta data:
+var shape = [ 3, 4 ];
+var strides = [ 4, 1 ];
+var offset = 0;
+var N = numel( shape );
+var order = 'row-major';
+
+// Create a matrix stored in linear memory:
+var A = uniform( N, -10, 10, {
+    'dtype': 'float64'
+});
+console.log( ndarray2array( A, shape, strides, offset, order ) );
+
+var work = new Float64Array( shape[ 0 ] );
+
+// Calculate the infinity norm:
+var out = dlange( order, 'infinity', shape[ 0 ], shape[ 1 ], A, strides[ 0 ], work );
+console.log( 'Infinity norm: ', out );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dlange]: https://www.netlib.org/lapack/explore-html/d8/d2e/group__lange_ga8581d687290b36c6e24fe76b3be7caa3.html
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->