feat: add lapack/base/dlacn2

lib/node_modules/@stdlib/lapack/base/dlacn2/README.md

@@ -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.
+
+-->
+
+# dlacn2
+
+> LAPACK routine to estimate the one-norm of a square matrix `A`, using reverse communication for evaluating matrix-vector products.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlacn2 = require( '@stdlib/lapack/base/dlacn2' );
+```
+
+#### dlacn2( N, V, X, ISGN, EST, KASE, ISAVE )
+
+Estimates the one-norm of a square matrix `A`, using alternative indexing semantics and reverse communication for evaluating matrix-vector products.
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var V = new Float64Array( [ 5.0, 3.0, 1.0, 5.0 ] );
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN = new Int32Array( [ 1, 1, 1, 1 ] );
+var EST = new Float64Array( [ 10 ] );
+var KASE = new Int32Array( [ 1 ] );
+var ISAVE = new Int32Array( [ 2, 3, 1 ] );
+
+dlacn2( 4, V, X, ISGN, EST, KASE, ISAVE );
+// X => <Float64Array>[ 0.0, 0.0, 0.0, 1.0 ]
+// V => <Float64Array>[ 5.0, 3.0, 1.0, 5.0 ]
+// EST => <Float64Array>[ 10.0 ]
+// KASE => <Int32Array>[ 1 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of rows/columns in `A`.
+-   **V**: workspace [`Float64Array`][mdn-float64array] having `N` indexed elements, used internally to store intermediate vectors.
+-   **X**: input/output [`Float64Array`][mdn-float64array] having `N` indexed elements, contains the current or next matrix-vector product.
+-   **ISGN**: [`Int32Array`][mdn-int32array] having `N` indexed elements, stores the sign of each element in `X` during iterations.
+-   **EST**: single-element [`Float64Array`][mdn-float64array], on output, contains the estimated one-norm of the matrix `A`.
+-   **KASE**: single-element [`Int32Array`][mdn-int32array] that controls the reverse communication.
+-   **ISAVE**: [`Int32Array`][mdn-int32array] having 3 indexed elements, used internally to maintain state across multiple calls.
+
+The reverse communication takes place using `KASE`, it may have any of these values:
+
+-   `0`: estimation is complete.
+-   `1`: caller must compute `A * X` and store the result back in `X`.
+-   `2`: caller must compute `A^T * X` (transpose) and store the result back in `X`.
+
+`V` is over written by `A * W` where `EST` contains `norm( A ) / norm( W )`. (W is not returned).
+
+`ISAVE` has the following three elements:
+
+-   the first indexed element of `ISAVE` is used to determine the control flow for the algorithm.
+-   the second indexed element of `ISAVE` holds the index of the largest absolute value in `X`.
+-   the third indexed element of `ISAVE` counts the number of refinement iterations in the algorithm.
+
+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 Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var V0 = new Float64Array( [ 0.0, 5.0, 3.0, 1.0, 5.0 ] );
+var X0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN0 = new Int32Array( [ 0, 1, 1, 1, 1 ] );
+var EST0 = new Float64Array( [ 0.0, 10.0 ] );
+var KASE0 = new Int32Array( [ 0, 1 ] );
+var ISAVE0 = new Int32Array( [ 0, 2, 3, 1 ] );
+
+// Create offset views...
+var V = new Float64Array( V0.buffer, V0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var X = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var ISGN = new Int32Array( ISGN0.buffer, ISGN0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var EST = new Float64Array( EST0.buffer, EST0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var KASE = new Int32Array( KASE0.buffer, KASE0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var ISAVE = new Int32Array( ISAVE0.buffer, ISAVE0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlacn2( 4, V, X, ISGN, EST, KASE, ISAVE );
+// X0 => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 1.0 ]
+// V0 => <Float64Array>[ 0.0, 5.0, 3.0, 1.0, 5.0 ]
+// EST0 => <Float64Array>[ 0.0, 10.0 ]
+// KASE0 => <Int32Array>[ 0, 1 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dlacn2.ndarray( N, V, sv, ov, X, sx, ox, ISGN, sisgn, oisgn, EST, oe, KASE, ok, ISAVE, sisave, oisave )
+
+Estimates the one-norm of a square matrix `A`, using alternative indexing semantics and reverse communication for evaluating matrix-vector products.
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var V = new Float64Array( [ 5.0, 3.0, 1.0, 5.0 ] );
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN = new Int32Array( [ 1, 1, 1, 1 ] );
+var EST = new Float64Array( [ 10 ] );
+var KASE = new Int32Array( [ 1 ] );
+var ISAVE = new Int32Array( [ 2, 3, 1 ] );
+
+dlacn2.ndarray( 4, V, 1, 0, X, 1, 0, ISGN, 1, 0, EST, 0, KASE, 0, ISAVE, 1, 0 );
+// X => <Float64Array>[ 0.0, 0.0, 0.0, 1.0 ]
+// V => <Float64Array>[ 5.0, 3.0, 1.0, 5.0 ]
+// EST => <Float64Array>[ 10.0 ]
+// KASE => <Int32Array>[ 1 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of rows/columns in `A`.
+-   **V**: workspace [`Float64Array`][mdn-float64array] having `N` indexed elements, used internally to store intermediate vectors.
+-   **sv**: stride length for `V`.
+-   **ov**: starting index for `V`.
+-   **X**: input/output [`Float64Array`][mdn-float64array] having `N` indexed elements, contains the current or next matrix-vector product.
+-   **sx**: stride length for `X`.
+-   **ox**: starting index for `X`.
+-   **ISGN**: [`Int32Array`][mdn-int32array] having `N` indexed elements, stores the sign of each element in `X` during iterations.
+-   **sisgn**: stride length for `ISGN`.
+-   **oisgn**: starting index for `ISGN`.
+-   **EST**: single-element [`Float64Array`][mdn-float64array], on output, contains the estimated one-norm of the matrix `A`.
+-   **oe**: starting index for `EST`.
+-   **KASE**: single-element [`Int32Array`][mdn-int32array] that controls the reverse communication.
+-   **ok**: starting index for `KASE`.
+-   **ISAVE**: [`Int32Array`][mdn-int32array] having 3 indexed elements, used internally to maintain state across multiple calls.
+-   **sisave**: stride length for `ISAVE`.
+-   **oisave**: starting index for `ISAVE`.
+
+The reverse communication takes place using `KASE`, it may have any of these values:
+
+-   `0`: estimation is complete.
+-   `1`: caller must compute `A * X` and store the result back in `X`.
+-   `2`: caller must compute `A^T * X` (transpose) and store the result back in `X`.
+
+`V` is over written by `A * W` where `EST` contains `norm( A ) / norm( W )`. (W is not returned).
+
+`ISAVE` has the following three elements:
+
+-   the first indexed element of `ISAVE` is used to determine the control flow for the algorithm.
+-   the second indexed element of `ISAVE` holds the index of the largest absolute value in `X`.
+-   the third indexed element of `ISAVE` counts the number of refinement iterations in the algorithm.
+
+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 Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var V = new Float64Array( [ 0.0, 5.0, 3.0, 1.0, 5.0 ] );
+var X = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN = new Int32Array( [ 0, 1, 1, 1, 1 ] );
+var EST = new Float64Array( [ 0.0, 10.0 ] );
+var KASE = new Int32Array( [ 0, 1 ] );
+var ISAVE = new Int32Array( [ 0, 2, 3, 1 ] );
+
+dlacn2.ndarray( 4, V, 1, 1, X, 1, 1, ISGN, 1, 1, EST, 1, KASE, 1, ISAVE, 1, 1 );
+// X => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 1.0 ]
+// V => <Float64Array>[ 0.0, 5.0, 3.0, 1.0, 5.0 ]
+// EST => <Float64Array>[ 0.0, 10.0 ]
+// KASE => <Int32Array>[ 0, 1 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlacn2()` corresponds to the [LAPACK][LAPACK] function [`dlacn2`][lapack-dlacn2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+<!-- eslint-disable array-element-newline -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var dgemv = require( '@stdlib/blas/base/dgemv' );
+var dcopy = require( '@stdlib/blas/base/dcopy' );
+var dlacn2 = require( '@stdlib/lapack/base/dlacn2' );
+
+// Specify matrix meta data:
+var shape = [ 4, 4 ];
+var strides = [ 4, 1 ];
+var offset = 0;
+var order = 'row-major';
+
+// Create a matrix stored in linear memory:
+var A = new Float64Array([
+    1.0, -2.0, 0.0, 0.0,
+    3.0, 4.0, -5.0, 0.0,
+    0.0, 6.0, 7.0, -8.0,
+    0.0, 0.0, 9.0, 10.0
+]);
+
+console.log( ndarray2array( A, shape, strides, offset, order ) );
+
+var KASE = new Int32Array( 1 );
+var EST = new Float64Array( 1 );
+var ISGN = new Int32Array( 4 );
+var ISAVE = new Int32Array( 3 );
+var X = new Float64Array( 4 );
+var V = new Float64Array( 4 );
+
+var work = new Float64Array( 4 );
+
+while ( true ) {
+    dlacn2( 4, V, X, ISGN, EST, KASE, ISAVE );
+
+    if ( KASE[ 0 ] === 0 ) {
+        break;
+    }
+    else if ( KASE[ 0 ] === 1 ) {
+        dgemv( 'row-major', 'no-transpose', shape[ 0 ], shape[ 1 ], 1.0, A, strides[ 0 ], X, 1, 0, work, 1 );
+        dcopy( shape[ 0 ], work, 1, X, 1 );
+    } else if ( KASE[ 0 ] === 2 ) {
+        dgemv( 'row-major', 'transpose', shape[ 0 ], shape[ 1 ], 1.0, A, strides[ 0 ], X, 1, 0, work, 1 );
+        dcopy( shape[ 0 ], work, 1, X, 1 );
+    }
+}
+
+console.log( 'estimated norm: ', EST[ 0 ] );
+console.log( 'V: ', V );
+```
+
+</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-dlacn2]: https://netlib.org/lapack/explore-html/d6/d2d/group__lacn2_gabc1e7463e250c9e43596bfcbfa83c1de.html#gabc1e7463e250c9e43596bfcbfa83c1de
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-int32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Int32Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->