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249 changes: 249 additions & 0 deletions lib/node_modules/@stdlib/lapack/base/dlascl/README.md
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<!--

@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.

-->

# dlascl

> LAPACK routine to multiply a real M by N matrix `A` by a real scalar `CTO/CFROM`.
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@kgryte kgryte Jul 9, 2025

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Suggested change
> LAPACK routine to multiply a real M by N matrix `A` by a real scalar `CTO/CFROM`.
> LAPACK routine to multiply a double-precision floating-point M-by-N matrix `A` by a double-precision floating-point scalar.


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@kgryte kgryte Jul 9, 2025

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I suggest adding an intro section stating something like:

This routine multiplies each element of an M-by-N matrix A by a scalar \alpha

$$B = \alpha \cdot A = \alpha \cdot \begin{bmatrix} a_{11} a_{12} \ldots a_{0N} && ... \end{bmatrix} = \begin{bmatrix} \alpha a_{11} \alpha a_{12} \ldots \alpha a_{0N} && ... \end{bmatrix}$$

In order to more readily avoid underflow/overflow, this routine chooses to represent \alpha as the product of

$$\alpha = \beta \cdot \frac{1}{\gamma}$$

<section class="usage">

## Usage

```javascript
var dlascl = require( '@stdlib/lapack/base/dlascl' );
```

#### dlascl( order, type, KL, KU, CFROM, CTO, M, N, A, LDA )
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#### dlascl( order, type, KL, KU, CFROM, CTO, M, N, A, LDA )
#### dlascl( order, type, KL, KU, \gamma, \beta, M, N, A, LDA )

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Use the actual greek characters.

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In JSDoc, use gamma and beta.


Multiplies a real M by N matrix `A` by a real scalar `CTO/CFROM`.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]

dlascl( 'row-major', 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2 );
// A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
```

The function has the following parameters:

- **order**: storage layout.
- **type**: specifies the type of matrix `A` ( should be one of these: `general`, `upper`, `lower`, `upper-hessenberg`, `symmetric-banded-lower`, `symmetric-banded-upper` or `banded` ).
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- **type**: specifies the type of matrix `A` ( should be one of these: `general`, `upper`, `lower`, `upper-hessenberg`, `symmetric-banded-lower`, `symmetric-banded-upper` or `banded` ).
- **type**: specifies the type of matrix `A`. Must be one of the following: `'general'`, `'upper'`, `'lower'`, `'upper-hessenberg'`, `'symmetric-banded-lower'`, `'symmetric-banded-upper'`, or `'banded'`.

- **KL**: lower band width of `A`. Referenced only if type is `symmetric-banded-lower` or `banded`.
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- **KL**: lower band width of `A`. Referenced only if type is `symmetric-banded-lower` or `banded`.
- **KL**: lower bandwidth of `A` (i.e., the number of sub-diagonals). Referenced only if type is `symmetric-banded-lower` or `banded`.

- **KU**: upper band width of `A`. Referenced only if type is `symmetric-banded-upper` or `banded`.
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- **KU**: upper band width of `A`. Referenced only if type is `symmetric-banded-upper` or `banded`.
- **KU**: upper bandwidth of `A` (i.e., the number of super-diagonals). Referenced only if type is `symmetric-banded-upper` or `banded`.

- **CFROM**: the matrix `A` is multiplied by `CTO / CFROM`.
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- **CFROM**: the matrix `A` is multiplied by `CTO / CFROM`.
- **gamma**: the matrix `A` is multiplied by `beta/gamma`.

- **CTO**: the matrix `A` is multiplied by `CTO / CFROM`.
- **M**: number of rows in matrix `A`.
- **N**: number of columns in matrix `A`.
- **A**: input [`Float64Array`][mdn-float64array].
- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).

If `type` is `banded`, `symmetric-banded-lower` or `symmetric-banded-upper` the matrix should be stored in the [`Band storage`][lapack-band-storage] format.

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If `type` is `banded`, `symmetric-banded-lower` or `symmetric-banded-upper` the matrix should be stored in the [`Band storage`][lapack-band-storage] format.

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 -->

```javascript
var Float64Array = require( '@stdlib/array/float64' );

// Initial arrays...
var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );

// Create offset views...
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// Initial arrays...
var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
// Create offset views...
// Initial array:
var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
// Create offset view:

var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dlascl( 'row-major', 'general', 0, 0, 1.0, 2.0, 3, 2, A1, 2 );
// A0 => <Float64Array>[ 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
```

#### dlascl.ndarray( type, KL, KU, CFROM, CTO, M, N, A, strideA1, strideA2, offsetA )

Multiplies a real M by N matrix `A` by a real scalar `CTO/CFROM` using alternative indexing semantics.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]

dlascl.ndarray( 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2, 1, 0 );
// A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
```

The function has the following additional parameters:
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Suggested change
The function has the following additional parameters:
The function has the following parameters:


- **type**: specifies the type of matrix `A` ( should be one of these: `general`, `upper`, `lower`, `upper-hessenberg`, `symmetric-banded-lower`, `symmetric-banded-upper` or `banded` ).
- **KL**: lower band width of `A`. Referenced only if type is `symmetric-banded-lower` or `banded`.
- **KU**: upper band width of `A`. Referenced only if type is `symmetric-banded-upper` or `banded`.
- **CFROM**: the matrix `A` is multiplied by `CTO / CFROM`.
- **CTO**: the matrix `A` is multiplied by `CTO / CFROM`.
- **M**: number of rows in matrix `A`.
- **N**: number of columns in matrix `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`.

If `type` is `banded`, `symmetric-banded-lower` or `symmetric-banded-upper` the matrix should be stored in the [`Band storage`][lapack-band-storage] format.

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If `type` is `banded`, `symmetric-banded-lower` or `symmetric-banded-upper` the matrix should be stored in the [`Band storage`][lapack-band-storage] format.

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,

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );

dlascl.ndarray( 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2, 1, 1 );
// A => <Float64Array>[ 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

- `dlascl()` corresponds to the [LAPACK][lapack] routine [`dlascl`][lapack-dlascl].
- If `type` is `banded`, `symmetric-banded-lower` or `symmetric-banded-upper` the matrix should be stored in the [`Band storage`][lapack-band-storage] format.
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Suggested change
- If `type` is `banded`, `symmetric-banded-lower` or `symmetric-banded-upper` the matrix should be stored in the [`Band storage`][lapack-band-storage] format.
- If `type` is `'banded'`, `'symmetric-banded-lower'`, or `'symmetric-banded-upper'`, the matrix should be stored in the [band storage][lapack-band-storage] format.

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May be good to provide a brief schematic using math equations in terms of what is meant.


</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var Float64Array = require( '@stdlib/array/float64' );
var dlascl = require( '@stdlib/lapack/base/dlascl' );

// Define a matrix A (3x2 in row-major order):
var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
console.log( 'Initial A (row-major): ', A );

dlascl( 'row-major', 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2 );
console.log( 'Scaled A (row-major): ', A );
```

</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-dlascl]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d43/group__aux_o_t_h_e_rauxiliary_ga7bce4c35ec5a86ee0bfdd15c476d99c8.html

[lapack-band-storage]: https://www.netlib.org/lapack/lug/node124.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 -->
117 changes: 117 additions & 0 deletions lib/node_modules/@stdlib/lapack/base/dlascl/benchmark/benchmark.js
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/**
* @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 bench = require( '@stdlib/bench' );
var uniform = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var pow = require( '@stdlib/math/base/special/pow' );
var floor = require( '@stdlib/math/base/special/floor' );
var pkg = require( './../package.json' ).name;
var dlascl = require( './../lib/dlascl.js' );


// VARIABLES //

var LAYOUTS = [
'row-major',
'column-major'
];


// FUNCTIONS //

/**
* Creates a benchmark function.
*
* @private
* @param {string} order - storage layout
* @param {PositiveInteger} N - number of rows/columns
* @returns {Function} benchmark function
*/
function createBenchmark( order, N ) {
var LDA;
var A;

LDA = N;

A = uniform( N*N, -10.0, 10.0, {
'dtype': 'float64'
});
return benchmark;

/**
* Benchmark function.
*
* @private
* @param {Benchmark} b - benchmark instance
*/
function benchmark( b ) {
var z;
var i;

b.tic();
for ( i = 0; i < b.iterations; i++ ) {
z = dlascl( order, 'general', 0, 0, 1.0, 2.0, N, N, A, LDA );
if ( isnan( z[ i%z.length ] ) ) {
b.fail( 'should not return NaN' );
}
}
b.toc();
if ( isnan( z[ i%z.length ] ) ) {
b.fail( 'should not return NaN' );
}
b.pass( 'benchmark finished' );
b.end();
}
}


// MAIN //

/**
* Main execution sequence.
*
* @private
*/
function main() {
var min;
var max;
var ord;
var N;
var f;
var i;
var k;

min = 1; // 10^min
max = 6; // 10^max

for ( k = 0; k < LAYOUTS.length; k++ ) {
ord = LAYOUTS[ k ];
for ( i = min; i <= max; i++ ) {
N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
f = createBenchmark( ord, N );
bench( pkg+'::square_matrix:order='+ord+',size='+(N*N), f );
}
}
}

main();
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