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blas-base-dsyr

Perform the symmetric rank 1 operation `A = α*x*x^T + A`.

https://github.com/stdlib-js/blas-base-dsyr

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algebra array blas double dsyr float64 float64array javascript level-2 linear math mathematics ndarray node node-js nodejs stdlib subroutines
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Perform the symmetric rank 1 operation `A = α*x*x^T + A`.

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algebra array blas double dsyr float64 float64array javascript level-2 linear math mathematics ndarray node node-js nodejs stdlib subroutines
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README.md

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dsyr

NPM version Build Status Coverage Status <!-- dependencies -->

Perform the symmetric rank 1 operation A = α*x*x^T + A.

## Installation ```bash npm install @stdlib/blas-base-dsyr ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
## Usage ```javascript var dsyr = require( '@stdlib/blas-base-dsyr' ); ``` #### dsyr( order, uplo, N, α, x, sx, A, LDA ) Performs the symmetric rank 1 operation `A = α*x*x^T + A` where `α` is a scalar, `x` is an `N` element vector, and `A` is an `N` by `N` symmetric matrix. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] ); var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); dsyr( 'row-major', 'upper', 3, 1.0, x, 1, A, 3 ); // A => [ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ] ``` The function has the following parameters: - **order**: storage layout. - **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced. - **N**: number of elements along each dimension of `A`. - **α**: scalar constant. - **x**: input [`Float64Array`][mdn-float64array]. - **sx**: stride length for `x`. - **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array]. - **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`). The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of `x` in reverse order, ```javascript var Float64Array = require( '@stdlib/array-float64' ); var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] ); var x = new Float64Array( [ 3.0, 2.0, 1.0 ] ); dsyr( 'row-major', 'upper', 3, 1.0, x, -1, A, 3 ); // A => [ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ] ``` Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. ```javascript var Float64Array = require( '@stdlib/array-float64' ); // Initial arrays... var x0 = new Float64Array( [ 0.0, 3.0, 2.0, 1.0 ] ); var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] ); // Create offset views... var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element dsyr( 'row-major', 'upper', 3, 1.0, x1, -1, A, 3 ); // A => [ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ] ``` #### dsyr.ndarray( uplo, N, α, x, sx, ox, A, sa1, sa2, oa ) Performs the symmetric rank 1 operation `A = α*x*x^T + A`, using alternative indexing semantics and where `α` is a scalar, `x` is an `N` element vector, and `A` is an `N` by `N` symmetric matrix. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] ); var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); dsyr.ndarray( 'upper', 3, 1.0, x, 1, 0, A, 3, 1, 0 ); // A => [ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ] ``` The function has the following additional parameters: - **ox**: starting index for `x`. - **sa1**: stride of the first dimension of `A`. - **sa2**: stride of the second dimension of `A`. - **oa**: starting index for `A`. 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, ```javascript var Float64Array = require( '@stdlib/array-float64' ); var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] ); var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] ); dsyr.ndarray( 'upper', 3, 1.0, x, -2, 4, A, 3, 1, 0 ); // A => [ 26.0, 17.0, 8.0, 2.0, 10.0, 5.0, 3.0, 2.0, 2.0 ] ```
## Notes - `dsyr()` corresponds to the [BLAS][blas] level 2 function [`dsyr`][blas-dsyr].
## Examples ```javascript var discreteUniform = require( '@stdlib/random-array-discrete-uniform' ); var ones = require( '@stdlib/array-ones' ); var dsyr = require( '@stdlib/blas-base-dsyr' ); var opts = { 'dtype': 'float64' }; var N = 3; // Create N-by-N symmetric matrices: var A1 = ones( N*N, opts.dtype ); var A2 = ones( N*N, opts.dtype ); // Create a random vector: var x = discreteUniform( N, -10.0, 10.0, opts ); dsyr( 'row-major', 'upper', 3, 1.0, x, 1, A1, 3 ); console.log( A1 ); dsyr.ndarray( 'upper', 3, 1.0, x, 1, 0, A2, 3, 1, 0 ); console.log( A2 ); ```
## C APIs
### Usage ```c #include "stdlib/blas/base/dsyr.h" ``` #### c_dsyr( layout, uplo, N, alpha, \*X, sx, \*A, LDA ) Performs the symmetric rank 1 operation `A = α*x*x^T + A` where `α` is a scalar, `x` is an `N` element vector, and `A` is an `N` by `N` symmetric matrix. ```c #include "stdlib/blas/base/shared.h" double A[] = { 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 }; const double x[] = { 1.0, 2.0, 3.0 }; c_dsyr( CblasColMajor, CblasUpper, 3, 1.0, x, 1, A, 3 ); ``` The function accepts the following arguments: - **layout**: `[in] CBLAS_LAYOUT` storage layout. - **uplo**: `[in] CBLAS_UPLO` specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced. - **N**: `[in] CBLAS_INT` number of elements along each dimension of `A`. - **alpha**: `[in] double` scalar constant. - **X**: `[in] double*` input array. - **sx**: `[in] CBLAS_INT` stride length for `X`. - **A**: `[inout] double*` input matrix. - **LDA**: `[in] CBLAS_INT` stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`). ```c void c_dsyr( const CBLAS_LAYOUT layout, const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, double *A, const CBLAS_INT LDA ) ``` #### c_dsyr_ndarray( uplo, N, alpha, \*X, sx, ox, \*A, sa1, sa2, oa ) Performs the symmetric rank 1 operation `A = α*x*x^T + A`, using alternative indexing semantics and where `α` is a scalar, `x` is an `N` element vector, and `A` is an `N` by `N` symmetric matrix. ```c #include "stdlib/blas/base/shared.h" double A[] = { 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 }; const double x[] = { 1.0, 2.0, 3.0 }; c_dsyr_ndarray( CblasUpper, 3, 1.0, x, 1, 0, A, 3, 1, 0 ); ``` The function accepts the following arguments: - **uplo**: `[in] CBLAS_UPLO` specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced. - **N**: `[in] CBLAS_INT` number of elements along each dimension of `A`. - **alpha**: `[in] double` scalar constant. - **X**: `[in] double*` input array. - **sx**: `[in] CBLAS_INT` stride length for `X`. - **ox**: `[in] CBLAS_INT` starting index for `X`. - **A**: `[inout] double*` input matrix. - **sa1**: `[in] CBLAS_INT` stride of the first dimension of `A`. - **sa2**: `[in] CBLAS_INT` stride of the second dimension of `A`. - **oa**: `[in] CBLAS_INT` starting index for `A`. ```c void c_dsyr_ndarray( const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA ) ```
### Examples ```c #include "stdlib/blas/base/dsyr.h" #include "stdlib/blas/base/shared.h" #include int main( void ) { // Define 3x3 symmetric matrices stored in row-major layout: double A1[ 3*3 ] = { 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 }; double A2[ 3*3 ] = { 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 }; // Define a vector: const double x[ 3 ] = { 1.0, 2.0, 3.0 }; // Specify the number of elements along each dimension of `A1` and `A2`: const int N = 3; // Perform the symmetric rank 1 operation `A = α*x*x^T + A`: c_dsyr( CblasColMajor, CblasUpper, N, 1.0, x, 1, A1, N ); // Print the result: for ( int i = 0; i < N*N; i++ ) { printf( "A1[ %i ] = %lf\n", i, A1[ i ] ); } // Perform the symmetric rank 1 operation `A = α*x*x^T + A` using alternative indexing semantics: c_dsyr_ndarray( CblasUpper, N, 1.0, x, 1, 0, A2, N, 1, 0 ); // Print the result: for ( int i = 0; i < N*N; i++ ) { printf( "A2[ %i ] = %lf\n", i, A[ i ] ); } } ```

* * * ## Notice This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more. For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Standard library for JavaScript.

Citation (CITATION.cff) 

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
  metadata from this file.

type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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