feat: add lapack/base/dppequ

lib/node_modules/@stdlib/lapack/base/dppequ/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.
+
+-->
+
+# dppequ
+
+> LAPACK routine to compute the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dppequ = require( '@stdlib/lapack/base/dppequ' );
+```
+
+#### dppequ( order, uplo, N, AP, S, out )
+
+Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm).
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+var S = new Float64Array( 3 );
+var out = new Float64Array( 2 );
+
+dppequ( 'row-major', 'lower', 3, AP, S, out );
+// S => <Float64Array>[ 1.0, ~0.58, ~0.33 ]
+// out => <Float64Array>[ ~0.33, 9.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **uplo**: specifies whether upper or lower triangle of `A` is stored ( `upper` or `lower` ).
+-   **AP**: array containing the upper or lower triangle of `A` in packed form stored in linear memory as a [`Float64Array`][mdn-float64array], expects `N * (  N + 1 ) / 2` indexed elements
+-   **S**: array to store the scale factors of `A` in linear memory as a [`Float64Array`][mdn-float64array], expects `N` indexed elements.
+-   **out**: the first element of `out` represents `scond`, the second element of out represents `amax`. if `scond` >= 0.1 and `amax` is not close to overflow/underflow it isn't worth scaling the matrix by `S`, if `amax` is close to underflow/overflow the matrix shoud be scaled. expects a [`Float64Array`][mdn-float64array] with 2 indexed elements.
+
+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 AP0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+var S0 = new Float64Array( 4 );
+var out0 = new Float64Array( 3 );
+
+// Create offset views...
+var AP1 = new Float64Array( AP0.buffer, AP0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var S1 = new Float64Array( S0.buffer, S0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dppequ( 'row-major', 'lower', 3, AP1, S1, out1 );
+// S0 => <Float64Array>[ 0.0, 1.0, ~0.58, ~0.33 ]
+// out => <Float64Array>[ ~0.33, 9.0 ]
+```
+
+#### dppequ.ndarray( order, uplo, N, AP, sap, oap, S, ss, os, out, so, oo )
+
+Computes the row and column scaling factors intended to equilibrate a symmetric positive definite matrix `A` in packed storage and reduce it's condition number (with respect to the two-norm) using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var AP = new Float64Array( [ 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+var S = new Float64Array( 3 );
+var out = new Float64Array( 2 );
+
+dppequ.ndarray( 'row-major', 'lower', 3, AP, 1, 0, S, 1, 0, out, 1, 0 );
+// S => <Float64Array>[ 1.0, ~0.58, ~0.33 ]
+// out => <Float64Array>[ ~0.33, 9.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **uplo**: specifies whether upper or lower triangle of `A` is stored ( `upper` or `lower` ).
+-   **AP**: array containing the upper or lower triangle of `A` in packed form stored in linear memory as a [`Float64Array`][mdn-float64array], expects `N * (  N + 1 ) / 2` indexed elements.
+-   **sap**: index increment for `AP`.
+-   **oap**: starting index of `AP`.
+-   **S**: array to store the scale factors of `A` in linear memory as a [`Float64Array`][mdn-float64array], expects `N` indexed elements.
+-   **ss**: index increment for `S`.
+-   **os**: starting index of `S`.
+-   **out**: the first element of `out` represents `scond`, the second element of out represents `amax`. if `scond` >= 0.1 and `amax` is not close to overflow/underflow it isn't worth scaling the matrix by `S`, if `amax` is close to underflow/overflow the matrix shoud be scaled. expects a [`Float64Array`][mdn-float64array] with 2 indexed elements.
+-   **so**: index increment for `out`.
+-   **oo**: starting index of `out`.
+
+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 AP = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 5.0, 6.0, 9.0 ] );
+var S = new Float64Array( 4 );
+var out = new Float64Array( 3 );
+
+dppequ.ndarray( 'row-major', 'lower', 3, AP, 1, 1, S, 1, 1, out, 1, 1 );
+// S => <Float64Array>[ 0.0, 1.0, ~0.58, ~0.33 ]
+// out => <Float64Array>[ 0.0, ~0.33, 9.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dppequ()` corresponds to the [LAPACK][LAPACK] function [`dppequ`][lapack-dppequ].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var dppequ = require( '@stdlib/lapack/base/dppequ' );
+
+var i;
+var j;
+
+// Specify matrix meta data:
+var shape = [ 3, 3 ];
+var order = 'row-major';
+var uplo = 'upper';
+var strides = shape2strides( shape, order );
+var offset = 0;
+
+// Define a symmetric positive definite matrix:
+var A = new Float64Array( [ 4.0, 1.0, 1.0, 1.0, 3.0, 0.0, 1.0, 0.0, 2.0 ] );
+console.log( ndarray2array( A, shape, strides, offset, order ) );
+
+// Convert the matrix to packed storage (upper triangle):
+var buf = [];
+for ( i = 0; i < shape[ 0 ]; i++ ) {
+    for ( j = i; j < shape[ 1 ]; j++ ) {
+        buf.push( A[ (i*strides[ 0 ]) + (j*strides[ 1 ]) + offset ] );
+    }
+}
+console.log( buf );
+
+var AP = new Float64Array( buf );
+var out = new Float64Array( 2 );
+var S = new Float64Array( shape[ 0 ] );
+var info = dppequ( order, uplo, shape[ 0 ], AP, S, out );
+
+console.log( 'info:', info );
+console.log( 'S:', S );
+console.log( 'out:', 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-dppequ]: https://www.netlib.org/lapack/explore-html/d4/d32/group__ppequ_gab707d51530c978eaae279e5728e4f54d.html#gab707d51530c978eaae279e5728e4f54d
+
+[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 -->