dger

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

Installation

npm install @stdlib/blas-base-dger

Usage

var dger = require( '@stdlib/blas-base-dger' );

dger( ord, M, N, α, x, sx, y, sy, A, lda )

Performs the rank 1 operation A = α*x*y^T + A, where α is a scalar, x is an M element vector, y is an N element vector, and A is an M by N matrix.

var Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dger( 'row-major', 2, 3, 1.0, x, 1, y, 1, A, 3 );
// A => <Float64Array>[ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]

The function has the following parameters:

• ord: storage layout.
• M: number of rows in the matrix A.
• N: number of columns in the matrix A.
• α: scalar constant.
• x: an M element Float64Array.
• sx: stride length for x.
• y: an N element Float64Array.
• sy: stride length for y.
• A: input matrix stored in linear memory as a Float64Array.
• lda: stride of the first dimension of A (a.k.a., leading dimension of the matrix A).

The stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to iterate over every other element in x and y,

var Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 0.0, 1.0, 0.0 ] );
var y = new Float64Array( [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ] );

dger( 'column-major', 2, 3, 1.0, x, 2, y, 2, A, 2 );
// A => <Float64Array>[ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
var y0 = new Float64Array( [ 0.0, 1.0, 1.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dger( 'column-major', 2, 3, 1.0, x1, -1, y1, -1, A, 2 );
// A => <Float64Array>[ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

dger.ndarray( M, N, α, x, sx, ox, y, sy, oy, A, sa1, sa2, oa )

Performs the rank 1 operation A = α*x*y^T + A, using alternative indexing semantics and where α is a scalar, x is an M element vector, y is an N element vector, and A is an M by N matrix.

var Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dger.ndarray( 2, 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
// A => <Float64Array>[ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]

The function has the following additional parameters:

• sa1: stride of the first dimension of A.
• sa2: stride of the second dimension of A.
• oa: starting index for A.
• ox: starting index for x.
• oy: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,

var Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 0.0, 0.0, 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );
var x = new Float64Array( [ 0.0, 1.0, 0.0, 1.0, 0.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ] );

dger.ndarray( 2, 3, 1.0, x, 2, 1, y, 2, 1, A, 1, 2, 2 );
// A => <Float64Array>[ 0.0, 0.0, 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

Notes

• dger() corresponds to the BLAS level 2 function dger.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dger = require( '@stdlib/blas-base-dger' );

var opts = {
    'dtype': 'float64'
};

var M = 3;
var N = 5;

var A = discreteUniform( M*N, 0, 255, opts );
var x = discreteUniform( M, 0, 255, opts );
var y = discreteUniform( N, 0, 255, opts );

dger( 'row-major', M, N, 1.0, x, 1, y, 1, A, N );
console.log( A );

dger.ndarray( M, N, 1.0, x, 1, 0, y, 1, 0, A, 1, M, 0 );
console.log(A);

C APIs

Usage

#include "stdlib/blas/base/dger.h"

c_dger( layout, M, N, alpha, *X, strideX, *Y, strideY, *A, LDA )

Performs the rank 1 operation A = alpha*x*y^T + A, where alpha is a scalar, X is an M element vector, Y is an N element vector, and A is an M-by-N matrix.

#include "stdlib/blas/base/shared.h"

double A[ 3*4 ] = {
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0
};

const double x[ 3 ] = { 1.0, 4.0, 0.0 };
const double y[ 4 ] = { 0.0, 1.0, 2.0, 3.0 };

c_dger( CblasRowMajor, 3, 4, 1.0, x, 1, y, 1, A, 4 );

The function accepts the following arguments:

• layout: [in] CBLAS_LAYOUT storage layout.
• M: [in] CBLAS_INT number of rows in the matrix A.
• N: [in] CBLAS_INT number of columns in the matrix A.
• alpha: [in] double scalar constant.
• X: [in] double* an M element vector.
• strideX: [in] CBLAS_INT stride length for X.
• Y: [in] double* an N element vector.
• strideY: [in] CBLAS_INT stride length for Y.
• 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).

void c_dger( const CBLAS_LAYOUT layout, const CBLAS_INT M, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY, double *A, const CBLAS_INT LDA );

c_dger_ndarray( M, N, alpha, *X, sx, ox, *Y, sy, oy, *A, sa1, sa2, oa )

Performs the rank 1 operation A = alpha*x*y^T + A, using alternative indexing semantics and where alpha is a scalar, X is an M element vector, Y is an N element vector, and A is an M-by-N matrix.

#include "stdlib/blas/base/shared.h"

double A[ 3*4 ] = {
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0,
   0.0, 0.0, 0.0, 0.0
};

const double x[ 3 ] = { 1.0, 4.0, 0.0 };
const double y[ 4 ] = { 0.0, 1.0, 2.0, 3.0 };

c_dger_ndarray( 3, 4, 1.0, x, 1, 0, y, 1, 0, A, 4, 1, 0 );

The function accepts the following arguments:

• layout: [in] CBLAS_LAYOUT storage layout.
• M: [in] CBLAS_INT number of rows in the matrix A.
• N: [in] CBLAS_INT number of columns in the matrix A.
• alpha: [in] double scalar constant.
• X: [in] double* an M element vector.
• sx: [in] CBLAS_INT stride length for X.
• ox: [in] CBLAS_INT starting index for X.
• Y: [in] double* an N element vector.
• sy: [in] CBLAS_INT stride length for Y.
• oy: [in] CBLAS_INT starting index for Y.
• 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.

void c_dger( onst CBLAS_INT M, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA );

Examples

#include "stdlib/blas/base/dger.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
   // Define a 3x4 matrix stored in row-major order:
   double A[ 3*4 ] = {
      0.0, 0.0, 0.0, 0.0,
      0.0, 0.0, 0.0, 0.0,
      0.0, 0.0, 0.0, 0.0
   };
   // Define `x` and `y^T` vectors:
   const double x[ 3 ] = { 1.0, 4.0, 0.0 };      // M
   const double y[ 4 ] = { 0.0, 1.0, 2.0, 3.0 }; // N

   // Specify the number of rows and columns:
   const int M = 3;
   const int N = 4;

   // Specify stride lengths:
   const int strideX = 1;
   const int strideY = 1;

   // Perform operation:
   c_dger( CblasRowMajor, M, N, 1.0, x, strideX, y, strideY, A, N );

   // Print the result:
   for ( int i = 0; i < M; i++ ) {
      for ( int j = 0; j < N; j++ ) {
         printf( "A[%i,%i] = %lf\n", i, j, A[ (i*N)+j ] );
      }
   }
}

Notice

This package is part of 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, see the main project repository.

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License

See LICENSE.

Copyright

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