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feat: add blas/ext/base/drss
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‎lib/node_modules/@stdlib/blas/ext/base/drss/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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# drss
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> Calculate the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays.
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<section class="intro">
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The [residual sum of squares][wikipedia-residual-sum-of-squares] (also referred to as the **sum of squared residuals** (SSR) and the **sum of squared errors** (SSE)) is defined as
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<!-- <equation class="equation" label="eq:residual_sum_of_squares" align="center" raw="d = \sum_{i=0}^{N-1} (y_i - x_i)^2" alt="Equation for residual sum of squares."> -->
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```math
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\mathop{\mathrm{RSS}} = \sum_{i=0}^{N-1} (y_i - x_i)^2
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```
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<!-- <div class="equation" align="center" data-raw-text="d = \sum_{i=0}^{N-1} (y_i - x_i)^2" data-equation="eq:residual_sum_of_squares">
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<img src="" alt="residual sum of squares.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var drss = require( '@stdlib/blas/ext/base/drss' );
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```
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#### drss( N, x, strideX, y, strideY )
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Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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var y = new Float64Array( [ 1.0, 1.0, -4.0 ] );
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var z = drss( x.length, x, 1, y, 1 );
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// returns 45.0
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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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- **x**: first input [`Float64Array`][@stdlib/array/float64].
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- **strideX**: stride length for `x`.
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- **y**: second input [`Float64Array`][@stdlib/array/float64].
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- **strideY**: stride length for `y`.
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The `N` and stride parameters determine which elements in strided arrays are accessed at runtime. For example, to compute the [residual sum of squares][wikipedia-residual-sum-of-squares] of every other element in `x` and `y`
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
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var y = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
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var z = drss( x.length, x, 1, y, 1 );
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// returns 72.0
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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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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var y0 = new Float64Array( [ 8.0, -2.0, 3.0, -2.0, 7.0, -2.0, 0.0, -1.0 ] );
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var z = drss( 4, x1, 2, y1, 2 );
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// returns 50.0
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```
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#### drss.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
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Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays and 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( [ 1.0, -2.0, 2.0 ] );
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var y = new Float64Array( [ 1.0, 1.0, -4.0 ] );
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var z = drss.ndarray( x.length, x, 1, 0, y, 1, 0 );
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// returns 45.0
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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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- **offsetY**: starting index for `y`.
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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 calculate the [residual sum of squares][wikipedia-residual-sum-of-squares] for every other element in `x` and `y` starting from the second 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, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, 6.0 ] );
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var y = new Float64Array( [ 8.0, -2.0, 3.0, -2.0, 7.0, -2.0, 0.0, -1.0, 4.0 ] );
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var z = drss.ndarray( 4, x, 2, 1, y, 2, 1 );
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// returns 50.0
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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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- If `N <= 0`, both functions return `0.0`.
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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 drss = require( '@stdlib/blas/ext/base/drss' );
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var opts = {
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'dtype': 'float64'
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};
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var x = discreteUniform( 10, -50, 50, opts );
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console.log( x );
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var y = discreteUniform( 10, -50, 50, opts );
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console.log( y );
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var d = drss( x.length, x, 1, y, 1 );
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console.log( d );
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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/drss.h"
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```
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#### stdlib_strided_drss( N, \*X, strideX, \*Y, strideY )
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Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays.
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```c
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const double x[] = { 1.0, -2.0, 2.0 };
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const double y[] = { 1.0, 1.0, -4.0 };
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double z = stdlib_strided_drss( 3, x, 1, y, 1 );
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// returns 45.0
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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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- **X**: `[in] double*` first input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **Y**: `[in] double*` second input array.
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- **strideY**: `[in] CBLAS_INT` stride length for `Y`.
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```c
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double stdlib_strided_drss( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );
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```
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<!--lint ignore maximum-heading-length-->
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#### stdlib_strided_drss_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY )
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<!--lint enable maximum-heading-length-->
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Computes the [residual sum of squares][wikipedia-residual-sum-of-squares] of two double-precision floating-point strided arrays and alternative indexing semantics.
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```c
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const double x[] = { 1.0, -2.0, 2.0 };
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const double y[] = { 1.0, 1.0, -4.0 };
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double v = stdlib_strided_drss_ndarray( 3, x, 1, 0, 1, 0 );
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// returns 45.0
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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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- **X**: `[in] double*` first 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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- **Y**: `[in] double*` second input array.
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- **strideY**: `[in] CBLAS_INT` stride length for `Y`.
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- **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
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```c
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double stdlib_strided_drss_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
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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/drss.h"
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#include <stdio.h>
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int main( void ) {
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// Create two strided arrays:
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const double x[] = { 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 };
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const double y[] = { 5.0, 12.0, -8.0, 15.0, 9.0, 0.0 };
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// Specify the number of elements:
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const int N = 5;
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// Specify the stride lengths:
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const int strideX = 1;
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const int strideY = 1;
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// Compute the residual sum of squares of `x` and `y`:
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double d = stdlib_strided_drss( N, x, strideX, y, strideY );
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// Print the result:
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printf( "drss: %lf\n", d );
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// Specify index offsets:
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const int offsetX = 1;
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const int offsetY = 1;
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// Compute the residual sum of squares of `x` and `y` with offsets:
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d = stdlib_strided_drss_ndarray( N, x, strideX, offsetX, y, strideY, offsetY );
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// Print the result:
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printf( "drss: %lf\n", d );
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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 class="references">
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</section>
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<!-- /.references -->
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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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[wikipedia-residual-sum-of-squares]: https://en.wikipedia.org/wiki/Residual_sum_of_squares
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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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</section>
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<!-- /.links -->

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