feat: add blas/ext/base/gtoeplitz

lib/node_modules/@stdlib/blas/ext/base/gtoeplitz/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# gtoeplitz
+
+> Generate a Toeplitz matrix.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gtoeplitz = require( '@stdlib/blas/ext/base/gtoeplitz' );
+```
+
+#### gtoeplitz( order, N, r, strideR, c, strideC, out, ldo )
+
+Generates a Toeplitz matrix.
+
+```javascript
+var r = [ 1.0, 2.0, 3.0 ];
+var c = [ 1.0, 4.0, 5.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gtoeplitz( 'row-major', 3, r, 1, c, 1, out, 3 );
+// out => [ 1.0, 2.0, 3.0, 4.0, 1.0, 2.0, 5.0, 4.0, 1.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: row-major (C-style) or column-major (Fortran-style) order.
+-   **N**: number of indexed elements in both `r` and `c`.
+-   **r**: first row of the matrix ([`Array`][mdn-array] or [`typed array`][mdn-typed-array]).
+-   **strideR**: stride length for `r`.
+-   **c**: first column of the matrix ([`Array`][mdn-array] or [`typed array`][mdn-typed-array]).
+-   **strideC**: stride length for `c`.
+-   **out**: output matrix.
+-   **ldo**: stride between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of the matrix `out`). Must be greater than or equal to `max(1,N)`.
+
+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' );
+
+// Initial arrays:
+var r0 = new Float64Array( [ 999.0, 1.0, 2.0, 3.0 ] );
+var c0 = new Float64Array( [ 999.0, 1.0, 4.0, 5.0 ] );
+var out0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create offset views:
+var r1 = new Float64Array( r0.buffer, r0.BYTES_PER_ELEMENT*1 );
+var c1 = new Float64Array( c0.buffer, c0.BYTES_PER_ELEMENT*1 );
+var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 );
+
+gtoeplitz( 'row-major', 3, r1, 1, c1, 1, out1, 3 );
+// out0 => <Float64Array>[ 0.0, 1.0, 2.0, 3.0, 4.0, 1.0, 2.0, 5.0, 4.0, 1.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### gtoeplitz.ndarray( N, r, strideR, offsetR, c, strideC, offsetC, out, strideOut1, strideOut2, offsetOut )
+
+<!-- lint enable maximum-heading-length -->
+
+Generates a Toeplitz matrix using alternative indexing semantics.
+
+```javascript
+var r = [ 1.0, 2.0, 3.0 ];
+var c = [ 1.0, 4.0, 5.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gtoeplitz.ndarray( 3, r, 1, 0, c, 1, 0, out, 3, 1, 0 );
+// out => [ 1.0, 2.0, 3.0, 4.0, 1.0, 2.0, 5.0, 4.0, 1.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetR**: starting index for `r`.
+-   **offsetC**: starting index for `c`.
+-   **strideOut1**: stride length for the first dimension of `out`.
+-   **strideOut2**: stride length for the second dimension of `out`.
+-   **offsetOut**: starting index for `out`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, offset parameters support indexing semantics based on starting indices. For example, to use every other element from the input arrays starting from the second element:
+
+```javascript
+var r = [ 0.0, 1.0, 0.0, 2.0, 0.0, 3.0 ];
+var c = [ 0.0, 1.0, 0.0, 4.0, 0.0, 5.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gtoeplitz.ndarray( 3, r, 2, 1, c, 2, 1, out, 3, 1, 0 );
+// out => [ 1.0, 2.0, 3.0, 4.0, 1.0, 2.0, 5.0, 4.0, 1.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `out` unchanged.
+-   If `r[0]` and `c[0]` differ, `c[0]` is used for the diagonal.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var zeros = require( '@stdlib/array/zeros' );
+var gtoeplitz = require( '@stdlib/blas/ext/base/gtoeplitz' );
+
+var N = 4;
+var order = 'row-major';
+var shape = [ N, N ];
+var strides = shape2strides( shape, order );
+
+var r = discreteUniform( N, 0, 10, {
+    'dtype': 'generic'
+});
+console.log( 'r:', r );
+
+var c = discreteUniform( N, 0, 10, {
+    'dtype': 'generic'
+});
+console.log( 'c:', c );
+
+var out = zeros( N*N, 'generic' );
+
+gtoeplitz( order, N, r, 1, c, 1, out, N );
+console.log( ndarray2array( out, shape, strides, 0, order ) );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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">
+
+[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/ext/base/gtoeplitz/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 zeros = require( '@stdlib/array/zeros' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var gtoeplitz = require( './../lib/main.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out = zeros( len * len, options.dtype );
+	var r = uniform( len, -10.0, 10.0, options );
+	var c = uniform( len, -10.0, 10.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			r[ 0 ] += 0.1;
+			v = gtoeplitz( 'row-major', len, r, 1, c, 1, out, len );
+			if ( isnan( v[ i%v.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( v[ i%v.length ] ) ) {
+			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 = 3; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( format( '%s:len=%d', pkg, len ), f );
+	}
+}
+
+main();