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feat: add blas/ext/base/ddiff
PR-URL: #10376 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#163
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‎lib/node_modules/@stdlib/blas/ext/base/ddiff/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# ddiff
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> Calculate the k-th discrete forward difference of a double-precision floating-point strided array.
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<section class="usage">
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## Usage
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```javascript
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var ddiff = require( '@stdlib/blas/ext/base/ddiff' );
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```
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<!-- lint disable maximum-heading-length -->
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#### ddiff( N, k, x, strideX, N1, prepend, strideP, N2, append, strideA, out, strideOut, workspace, strideW )
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Calculates the k-th discrete forward difference of a double-precision floating-point strided array.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
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var p = new Float64Array( [ 1.0 ] );
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var a = new Float64Array( [ 11.0 ] );
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var out = new Float64Array( 6 );
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var w = new Float64Array( 6 );
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ddiff( x.length, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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console.log( out );
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// out => <Float64Array>[ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **k**: number of times to recursively compute differences.
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- **x**: input [`Float64Array`][@stdlib/array/float64].
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- **strideX**: stride length for `x`.
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- **N1**: number of indexed elements to `prepend`.
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- **prepend**: a [`Float64Array`][@stdlib/array/float64] containing values to prepend prior to computing differences.
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- **strideP**: stride length for `prepend`.
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- **N2**: number of indexed elements to `append`.
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- **append**: a [`Float64Array`][@stdlib/array/float64] containing values to append prior to computing differences.
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- **strideA**: stride length for `append`.
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- **out**: output [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - k` elements.
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- **strideOut**: stride length for `out`.
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- **workspace**: workspace [`Float64Array`][@stdlib/array/float64]. Must have `N + N1 + N2 - 1` elements.
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- **strideW**: stride length for `workspace`.
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The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to differences of every other element:
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
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var p = new Float64Array( [ 1.0 ] );
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var a = new Float64Array( [ 11.0 ] );
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var out = new Float64Array( 4 );
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var w = new Float64Array( 4 );
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ddiff( 3, 1, x, 2, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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console.log( out );
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// out => <Float64Array>[ 1.0, 4.0, 4.0, 1.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial array...
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var x0 = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
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// Create an offset view...
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var p = new Float64Array( [ 1.0 ] );
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var a = new Float64Array( [ 11.0 ] );
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var out = new Float64Array( 5 );
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var w = new Float64Array( 5 );
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ddiff( x1.length, 1, x1, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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console.log( out );
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// out => <Float64Array>[ 3.0, 2.0, 2.0, 2.0, 1.0 ]
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```
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<!-- lint disable maximum-heading-length -->
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#### ddiff.ndarray( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut, workspace, strideW, offsetW )
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Calculates the k-th discrete forward difference of a double-precision floating-point strided array using alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
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var p = new Float64Array( [ 1.0 ] );
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var a = new Float64Array( [ 11.0 ] );
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var out = new Float64Array( 6 );
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var w = new Float64Array( 6 );
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ddiff.ndarray( x.length, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
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console.log( out );
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// out => <Float64Array>[ 1.0, 2.0, 2.0, 2.0, 2.0, 1.0 ]
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `x`.
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- **offsetP**: starting index for `prepend`.
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- **offsetA**: starting index for `append`.
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- **offsetOut**: starting index for `out`.
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- **offsetW**: starting index for `workspace`.
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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, to access only the last three elements:
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 2.0, 4.0, 6.0, 8.0, 10.0 ] );
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var p = new Float64Array( [ 1.0 ] );
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var a = new Float64Array( [ 11.0 ] );
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var out = new Float64Array( 4 );
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var w = new Float64Array( 4 );
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ddiff.ndarray( 3, 1, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
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console.log( out );
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// out => <Float64Array>[ 5.0, 2.0, 2.0, 1.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- When `k <= 1`, the workspace array is unused and thus ignored.
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- If `N <= 0`, both functions return the output array unchanged.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var Float64Array = require( '@stdlib/array/float64' );
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var ddiff = require( '@stdlib/blas/ext/base/ddiff' );
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var x = discreteUniform( 10, -100, 100, {
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'dtype': 'float64'
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});
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console.log( 'Input array: ', x );
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var p = discreteUniform( 2, -100, 100, {
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'dtype': 'float64'
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});
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console.log( 'Prepend array: ', p );
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var a = discreteUniform( 2, -100, 100, {
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'dtype': 'float64'
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});
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console.log( 'Append array: ', a );
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var out = new Float64Array( 10 );
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var w = new Float64Array( 13 );
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ddiff( x.length, 4, x, 1, 2, p, 1, 2, a, 1, out, 1, w, 1 );
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console.log( 'Output: ', out );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/blas/ext/base/ddiff.h"
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```
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<!-- lint disable maximum-heading-length -->
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#### stdlib_strided_ddiff( N, k, \*X, strideX, N1, \*Prepend, strideP, N2, \*Append, strideA, \*Out, strideOut, \*Workspace, strideW )
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Calculates the k-th discrete forward difference of a double-precision floating-point strided array.
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```c
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const double x[] = { 2.0, 4.0, 6.0, 8.0, 10.0 };
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const double p[] = { 1.0 };
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const double a[] = { 11.0 };
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double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
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double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
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stdlib_strided_ddiff( 5, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **k**: `[in] CBLAS_INT` number of times to recursively compute differences.
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- **X**: `[in] double*` input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **N1**: `[in] CBLAS_INT` number of indexed elements for `Prepend`.
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- **Prepend**: `[in] double*` array containing values to prepend prior to computing differences.
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- **strideP**: `[in] CBLAS_INT` stride length for `Prepend`.
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- **N2**: `[in] CBLAS_INT` number of indexed elements for `Append`.
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- **Append**: `[in] double*` array containing values to append prior to computing differences.
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- **strideA**: `[in] CBLAS_INT` stride length for `Append`.
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- **Out**: `[out] double*` output array. Must have `N + N1 + N2 - k` elements.
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- **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
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- **Workspace**: `[out] double*` workspace array. Must have `N + N1 + N2 - 1` elements.
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- **strideW**: `[in] CBLAS_INT` stride length for `Workspace`.
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```c
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void stdlib_strided_ddiff( const CBLAS_INT N, const CBLAS_INT k, const double *X, const CBLAS_INT strideX, const CBLAS_INT N1, const double *Prepend, const CBLAS_INT strideP, const CBLAS_INT N2, const double *Append, const CBLAS_INT strideA, double *Out, const CBLAS_INT strideOut, double *Workspace, const CBLAS_INT strideW );
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```
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<!-- lint disable maximum-heading-length -->
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#### stdlib_strided_ddiff_ndarray( N, k, \*X, strideX, offsetX, N1, \*Prepend, strideP, offsetP, N2, \*Append, strideA, offsetA, \*Out, strideOut, offsetOut, \*Workspace, strideW, offsetW )
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Calculates the k-th discrete forward difference of a double-precision floating-point strided array using alternative indexing semantics.
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```c
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const double x[] = { 2.0, 4.0, 6.0, 8.0, 10.0 };
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const double p[] = { 1.0 };
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const double a[] = { 11.0 };
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double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
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double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
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stdlib_strided_ddiff_ndarray( 5, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **k**: `[in] CBLAS_INT` number of times to recursively compute differences.
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- **X**: `[in] double*` input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
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- **N1**: `[in] CBLAS_INT` number of indexed elements for `Prepend`.
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- **Prepend**: `[in] double*` array containing values to prepend prior to computing differences.
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- **strideP**: `[in] CBLAS_INT` stride length for `Prepend`.
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- **offsetP**: `[in] CBLAS_INT` starting index for `Prepend`.
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- **N2**: `[in] CBLAS_INT` number of indexed elements for `Append`.
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- **Append**: `[in] double*` array containing values to append prior to computing differences.
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- **strideA**: `[in] CBLAS_INT` stride length for `Append`.
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- **offsetA**: `[in] CBLAS_INT` starting index for `Append`.
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- **Out**: `[out] double*` output array. Must have `N + N1 + N2 - k` elements.
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- **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
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- **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.
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- **Workspace**: `[out] double*` workspace array. Must have `N + N1 + N2 - 1` elements.
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- **strideW**: `[in] CBLAS_INT` stride length for `Workspace`.
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- **offsetW**: `[in] CBLAS_INT` starting index for `Workspace`.
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```c
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void stdlib_strided_ddiff_ndarray( const CBLAS_INT N, const CBLAS_INT k, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const CBLAS_INT N1, const double *Prepend, const CBLAS_INT strideP, const CBLAS_INT offsetP, const CBLAS_INT N2, const double *Append, const CBLAS_INT strideA, const CBLAS_INT offsetA, double *Out, const CBLAS_INT strideOut, const CBLAS_INT offsetOut, double *Workspace, const CBLAS_INT strideW, const CBLAS_INT offsetW );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/blas/ext/base/ddiff.h"
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#include <stdio.h>
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int main( void ) {
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// Create a strided array:
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const double x[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };
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// Define a list of values to prepend:
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const double p[] = { -1.0 };
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// Define a list of values to append:
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const double a[] = { 10.0 };
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// Define an output array:
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double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
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// Define a workspace:
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double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
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// Compute forward differences:
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stdlib_strided_ddiff( 8, 3, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
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// Print the result:
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for ( int i = 0; i < 7; i++ ) {
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printf( "out[ %i ] = %lf\n", i, out[ i ] );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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