feat: add lapack/base/dptcon

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# dptcon
+
+> Compute the reciprocal of the condition number of a real symmetric positive definite tridiagonal matrix using the factorization `A = L*D*L^T`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dptcon = require( '@stdlib/lapack/base/dptcon' );
+```
+
+#### dptcon( N, D, E, anorm, rcond, work )
+
+Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal matrix using the factorization `A = L*D*L^T`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 3.0, 2.0, 1.0 ] );
+var E = new Float64Array( [ 1.0, 1.0 ] );
+var rcond = new Float64Array( 1 );
+var work = new Float64Array( 3 );
+
+var out = dptcon( 3, D, E, 3.0, rcond, work );
+// returns 0
+```
+
+The function has the following parameters:
+
+- **N**: order of matrix `A`.
+- **D**: the `N` diagonal elements of `A` as a [`Float64Array`][mdn-float64array].
+- **E**: the N-1 off-diagonal elements of `U` or `L` from the factorization `A`.
+- **anorm**: the 1-norm of `A`.
+- **rcond**: an output [`Float64Array`][mdn-float64array] containing the reciprocal of the condition number of `A`
+- **work**: a workspace array.
+
+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 D0 = new Float64Array( [ 0.0, 3.0, 2.0, 1.0 ] );
+var E0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var RCOND0 = new Float64Array( [ 0.0, 0.0 ] );
+var WORK0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0] );
+
+// Create offset views...
+var D1 = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var E1 = new Float64Array( E0.buffer, E0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var RCOND1 = new Float64Array( RCOND0.buffer, RCOND0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var WORK1 = new Float64Array( WORK0.buffer, WORK0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dptcon( 3, D1, E1, 3.0, RCOND1, WORK1 );
+// RCOND0 => <Float64Array>[ 0.0, 0.07692307692307693 ]
+// WORK0 => <Float64Array>[ 0.0, 4.333333333333333, 4.0, 3.0 ]
+```
+
+#### dptcon.ndarray( N, D, sd, od, E, se, oe, anorm, rc, or, work, sw, ow )
+
+Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal matrix using the factorization `A = L*D*L^T` and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 3.0, 2.0, 1.0 ] );
+var E = new Float64Array( [ 1.0, 1.0 ] );
+var rcond = new Float64Array( 1 );
+var work = new Float64Array( 3 );
+
+var out = dptcon.ndarray( 3, D, 1, 0, E, 1, 0, 3.0, rcond, 0, work, 1, 0 );
+// returns 0
+```
+
+The function has the following additional parameters:
+
+- **sd**: stride length for `D`.
+- **od**: starting index for `D`.
+- **se**: stride length for `E`.
+- **oe**: starting index for `E`.
+- **or**: starting index for `rcond`.
+- **sw**: stride length for `work`.
+- **ow**: starting index for `work`.
+
+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 D = new Float64Array( [ 0.0, 3.0, 2.0, 1.0 ] );
+var E = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var rcond = new Float64Array( 1 );
+var work = new Float64Array( 3 );
+
+var out = dptcon.ndarray( 3, D, 1, 1, E, 1, 1, 3.0, rcond, 0, work, 1, 0 );
+// returns 0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+- Both functions mutate the input arrays `D` and `E`.
+
+- Both functions return a status code indicating success or failure. A status code indicates the following conditions:
+
+ - `0`: the execution was successful.
+ - `<0`: the k-th argument had an illegal value, where `-k` equals the status code value.
+
+- `dptcon()` corresponds to the [LAPACK][LAPACK] routine [`dptcon`][lapack-dptcon].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dptcon = require( '@stdlib/lapack/base/dptcon' );
+
+var D = new Float64Array( [ 3.0, 2.0, 1.0 ] );
+var E = new Float64Array( [ 1.0, 1.0 ] );
+var rcond = new Float64Array( 1 );
+var work = new Float64Array( 3 );
+
+var out = dptcon( 3, D, E, 3.0, rcond, work );
+console.log( out );
+console.log( rcond );
+console.log( work );
+```
+
+</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-dptcon]: https://www.netlib.org/lapack/explore-html/d1/d85/group__ptcon_gafc28b3de543d210d9dd7ad6dd9373071.html#gafc28b3de543d210d9dd7ad6dd9373071
+
+[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 -->

lib/node_modules/@stdlib/lapack/base/dptcon/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 Float64Array = require( '@stdlib/array/float64' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var pkg = require( './../package.json' ).name;
+var dptcon = require( './../lib/dptcon.js' );
+
+
+// VARIABLES //
+
+var options = {
+ 'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+ var rcond = new Float64Array( 1 );
+ var work = new Float64Array( len );
+ var D = uniform( len, 0.0, 100.0, options );
+ var E = uniform( len - 1, 0.0, 100.0, options );
+ return benchmark;
+
+ function benchmark( b ) {
+ var d;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ d = dptcon( len, D, E, 3.0, rcond, work );
+ if ( isnan( d ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( d ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var len;
+ var min;
+ var max;
+ var f;
+ var i;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( i = min; i <= max; i++ ) {
+ len = pow( 10, i );
+ f = createBenchmark( len );
+ bench( pkg+':len='+len, f );
+ }
+}
+
+main();