Perform the symmetric rank 1 operation
A = α*x*x^T + A.
var gsyr = require( '@stdlib/blas/base/gsyr' );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.
var A = [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ];
var x = [ 1.0, 2.0, 3.0 ];
gsyr( '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
Ashould be referenced. - N: number of elements along each dimension of
A. - α: scalar constant.
- x: input array.
- sx: stride length for
x. - A: input matrix stored in linear memory.
- LDA: stride of the first dimension of
A(a.k.a., leading dimension of the matrixA).
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,
var A = [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ];
var x = [ 3.0, 2.0, 1.0 ];
gsyr( '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 views.
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
gsyr( 'row-major', 'upper', 3, 1.0, x1, -1, A, 3 );
// A => <Float64Array>[ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ]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.
var A = [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ];
var x = [ 1.0, 2.0, 3.0 ];
gsyr.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 views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
var A = [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ];
var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
gsyr.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 ]gsyr()corresponds to the BLAS level 2 functiondsyrwith the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (dsyr,ssyr, etc.) are likely to be significantly more performant.- Both functions support array-like objects having getter and setter accessors for array element access (e.g.,
@stdlib/array/base/accessor).
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ones = require( '@stdlib/array/ones' );
var gsyr = require( '@stdlib/blas/base/gsyr' );
var opts = {
'dtype': 'generic'
};
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 );
gsyr( 'row-major', 'upper', 3, 1.0, x, 1, A1, 3 );
console.log( A1 );
gsyr.ndarray( 'upper', 3, 1.0, x, 1, 0, A2, 3, 1, 0 );
console.log( A2 );