feat: add blas/ext/base/zlogspace

lib/node_modules/@stdlib/blas/ext/base/zlogspace/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.
+
+-->
+
+# zlogspace
+
+> Fill a double-precision complex floating-point strided array with logarithmically spaced values over a specified interval.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var zlogspace = require( '@stdlib/blas/ext/base/zlogspace' );
+```
+
+#### zlogspace( N, base, start, stop, endpoint, x, strideX )
+
+Fills a double-precision complex floating-point strided array with logarithmically spaced values over a specified interval.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var x = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+var strt = new Complex128( 0.0, 0.0 );
+var stp = new Complex128( 2.0, 0.0 );
+
+zlogspace( x.length, 10.0, strt, stp, true, x, 1 );
+// x => <Complex128Array>[ 1.0, 0.0, 10.0, 0.0, 100.0, 0.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **base**: base of the logarithmic scale.
+-   **start**: exponent of the starting value, where the starting value is given by `base^start`.
+-   **stop**: exponent of the final value, where the final value is given by `base^stop`.
+-   **endpoint**: boolean indicating whether to include the `base^stop` value when writing values to the input array. If `true`, the input array is filled with logarithmically spaced values over the closed interval `[base^start, base^stop]`. If `false`, the input array is filled with logarithmically spaced values over the half-open interval `[base^start, base^stop)`.
+-   **x**: input [`Complex128Array`][@stdlib/array/complex128].
+-   **strideX**: stride length.
+
+The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to fill every other element:
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var x = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+var strt = new Complex128( 0.0, 0.0 );
+var stp = new Complex128( 3.0, 0.0 );
+
+zlogspace( 4, 10.0, strt, stp, true, x, 2 );
+// x => <Complex128Array>[ 1.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 100.0, 0.0, 0.0, 0.0, 1000.0, 0.0, 0.0, 0.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+// Initial array...
+var x0 = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create an offset view...
+var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+// Fill every other element...
+var strt = new Complex128( 0.0, 0.0 );
+var stp = new Complex128( 2.0, 0.0 );
+
+zlogspace( 3, 10.0, strt, stp, true, x1, 2 );
+// x0 => <Complex128Array>[ 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 100.0, 0.0 ]
+```
+
+#### zlogspace.ndarray( N, base, start, stop, endpoint, x, strideX, offsetX )
+
+Fills a double-precision complex floating-point strided array with logarithmically spaced values over a specified interval using alternative indexing semantics.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var x = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+var strt = new Complex128( 0.0, 0.0 );
+var stp = new Complex128( 2.0, 0.0 );
+
+zlogspace.ndarray( x.length, 10.0, strt, stp, true, x, 1, 0 );
+// x => <Complex128Array>[ 1.0, 0.0, 10.0, 0.0, 100.0, 0.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to access only the last three elements:
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+var x = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+var strt = new Complex128( 0.0, 0.0 );
+var stp = new Complex128( 2.0, 0.0 );
+
+zlogspace.ndarray( 3, 10.0, strt, stp, true, x, 1, x.length-3 );
+// x => <Complex128Array>[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 10.0, 0.0, 100.0, 0.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Let `M` be the number of generated values (which is either `N` or `N+1` depending on whether `endpoint` is `true` or `false`, respectively). The complex increment between exponents is thus given by
+
+    ```text
+    Δ = (stop-start)/(M-1)
+    ```
+
+    and the generated values are equal to `base^(start+Δ*i)` for `i = 0, 1, ..., M-1`, where exponentiation is performed in the complex sense.
+
+-   When the number of generated values is greater than `1` and `endpoint` is `true`, the set of values written to a provided input array is guaranteed to include the `base^start` and `base^stop` values. Beware, however, that values between `base^start` and `base^stop` are subject to floating-point rounding errors. Hence,
+
+    ```javascript
+    var Complex128Array = require( '@stdlib/array/complex128' );
+    var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+    var x = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+    var strt = new Complex128( 0.0, 0.0 );
+    var stp = new Complex128( 1.0, 0.0 );
+
+    zlogspace( 3, 10.0, strt, stp, true, x, 1 );
+    // x => <Complex128Array>[ 1.0, 0.0, ~3.162, 0.0, 10.0, 0.0 ]
+    ```
+
+    where `x[1]` is only guaranteed to be approximately equal to the square root of `10`.
+
+-   When `N = 1` and `endpoint` is `false`, only the `base^start` value is written to a provided input array. When `N = 1` and `endpoint` is `true`, only the `base^stop` value is written to a provided input array.
+
+-   Generated values follow a logarithmic spiral in the complex plane, where imaginary components of `start` and `stop` control phase rotation. If `Re(start) < Re(stop)`, the magnitudes of the generated values are in ascending order; otherwise, the magnitudes are in descending order.
+
+-   If `N <= 0`, both functions return `x` unchanged.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var logEach = require( '@stdlib/console/log-each' );
+var zlogspace = require( '@stdlib/blas/ext/base/zlogspace' );
+
+var x = new Complex128Array( 6 );
+
+var strt = new Complex128( 0.0, 0.0 );
+var stp = new Complex128( 5.0, 0.0 );
+
+zlogspace( x.length, 10.0, strt, stp, true, x, 1 );
+logEach( '%s', x );
+```
+
+</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
+#include "stdlib/blas/ext/base/zlogspace.h"
+```
+
+#### stdlib_strided_zlogspace( N, base, start, stop, endpoint, \*X, strideX )
+
+Fills a double-precision complex floating-point strided array with logarithmically spaced values over a specified interval.
+
+```c
+#include "stdlib/complex/float64/ctor.h"
+#include <stdbool.h>
+
+double x[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+stdlib_strided_zlogspace( 4, 10.0, stdlib_complex128( 0.0, 0.0 ), stdlib_complex128( 3.0, 0.0 ), true, (stdlib_complex128_t *)x, 1 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **base**: `[in] double` base of the logarithmic scale.
+-   **start**: `[in] stdlib_complex128_t` exponent of the starting value.
+-   **stop**: `[in] stdlib_complex128_t` exponent of the final value.
+-   **endpoint**: `[in] bool` boolean indicating whether to include the `base^stop` value when writing values to the input array. If `true`, the input array is filled with logarithmically spaced values over the closed interval `[base^start, base^stop]`. If `false`, the input array is filled with logarithmically spaced values over the half-open interval `[base^start, base^stop)`.
+-   **X**: `[out] stdlib_complex128_t*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length.
+
+```c
+void stdlib_strided_zlogspace( const CBLAS_INT N, const double base, const stdlib_complex128_t start, const stdlib_complex128_t stop, const bool endpoint, stdlib_complex128_t *X, const CBLAS_INT strideX );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### stdlib_strided_zlogspace_ndarray( N, base, start, stop, endpoint, \*X, strideX, offsetX )
+
+<!-- lint enable maximum-heading-length -->
+
+Fills a double-precision complex floating-point strided array with logarithmically spaced values over a specified interval using alternative indexing semantics.
+
+```c
+#include "stdlib/complex/float64/ctor.h"
+#include <stdbool.h>
+
+double x[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+stdlib_strided_zlogspace_ndarray( 4, 10.0, stdlib_complex128( 0.0, 0.0 ), stdlib_complex128( 3.0, 0.0 ), true, (stdlib_complex128_t *)x, 1, 0 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **base**: `[in] double` base of the logarithmic scale.
+-   **start**: `[in] stdlib_complex128_t` exponent of the starting value.
+-   **stop**: `[in] stdlib_complex128_t` exponent of the final value.
+-   **endpoint**: `[in] bool` boolean indicating whether to include the `base^stop` value when writing values to the input array. If `true`, the input array is filled with logarithmically spaced values over the closed interval `[base^start, base^stop]`. If `false`, the input array is filled with logarithmically spaced values over the half-open interval `[base^start, base^stop)`.
+-   **X**: `[out] stdlib_complex128_t*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length.
+-   **offsetX**: `[in] CBLAS_INT` starting index.
+
+```c
+void stdlib_strided_zlogspace_ndarray( const CBLAS_INT N, const double base, const stdlib_complex128_t start, const stdlib_complex128_t stop, const bool endpoint, stdlib_complex128_t *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
+```
+
+</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
+#include "stdlib/blas/ext/base/zlogspace.h"
+#include "stdlib/complex/float64/ctor.h"
+#include <stdio.h>
+#include <stdbool.h>
+
+int main( void ) {
+    // Create a strided array of interleaved real and imaginary components:
+    double x[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
+
+    // Specify the number of indexed elements:
+    const int N = 8;
+
+    // Specify a stride:
+    const int strideX = 1;
+
+    // Fill the array:
+    stdlib_strided_zlogspace( N, 10.0, stdlib_complex128( 0.0, 0.0 ), stdlib_complex128( 2.0, 0.0 ), true, (stdlib_complex128_t *)x, strideX );
+
+    // Print the result:
+    for ( int i = 0; i < N; i++ ) {
+        printf( "x[ %i ] = %lf + %lfi\n", i, x[ i*2 ], x[ i*2+1 ] );
+    }
+}
+```
+
+</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">
+
+[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->