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dger

README.md

dger

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

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 ] );
      }
   }
}