BLAS — Basic Linear Algebra Subroutines

This module provides wrappers for some of the BLAS functions for linear algebra. Those BLAS functions that overwrite one of the input arrays have names ending in '!'.

Usually a function has 4 methods defined, one each for Float64, Float32, Complex128 and Complex64 arrays.

Utility Functions

copy!(n, X, incx, Y, incy)

Copy n elements of array X with stride incx to array Y with stride incy. Returns Y.

dot(n, X, incx, Y, incy)

Dot product of two vectors consisting of n elements of array X with stride incx and n elements of array Y with stride incy. There are no dot methods for Complex arrays.

nrm2(n, X, incx)

2-norm of a vector consisting of n elements of array X with stride incx.

axpy!(n, a, X, incx, Y, incy)

Overwrite Y with a*X + Y. Returns Y.

syrk!(uplo, trans, alpha, A, beta, C)

Rank-k update of the symmetric matrix C as alpha*A*A.' + beta*C or alpha*A.'*A + beta*C according to whether trans is ‘N’ or ‘T’. When uplo is ‘U’ the upper triangle of C is updated (‘L’ for lower triangle). Returns C.

syrk(uplo, trans, alpha, A)

Returns either the upper triangle or the lower triangle, according to uplo (‘U’ or ‘L’), of alpha*A*A.' or alpha*A.'*A, according to trans (‘N’ or ‘T’).

herk!(uplo, trans, alpha, A, beta, C)

Methods for complex arrays only. Rank-k update of the Hermitian matrix C as alpha*A*A' + beta*C or alpha*A'*A + beta*C according to whether trans is ‘N’ or ‘T’. When uplo is ‘U’ the upper triangle of C is updated (‘L’ for lower triangle). Returns C.

herk(uplo, trans, alpha, A)

Methods for complex arrays only. Returns either the upper triangle or the lower triangle, according to uplo (‘U’ or ‘L’), of alpha*A*A' or alpha*A'*A, according to trans (‘N’ or ‘T’).

gbmv!(trans, m, kl, ku, alpha, A, x, beta, y)

Update vector y as alpha*A*x + beta*y or alpha*A'*x + beta*y according to trans (‘N’ or ‘T’). The matrix A is a general band matrix of dimension m by size(A,2) with kl sub-diagonals and ku super-diagonals. Returns the updated y.

gbmv(trans, m, kl, ku, alpha, A, x, beta, y)

Returns alpha*A*x or alpha*A'*x according to trans (‘N’ or ‘T’). The matrix A is a general band matrix of dimension m by size(A,2) with kl sub-diagonals and ku super-diagonals.

sbmv!(uplo, k, alpha, A, x, beta, y)

Update vector y as alpha*A*x + beta*y where A is a a symmetric band matrix of order size(A,2) with k super-diagonals stored in the argument A. The storage layout for A is described the reference BLAS module, level-2 BLAS at <http://www.netlib.org/lapack/explore-html/>.

Returns the updated y.

sbmv(uplo, k, alpha, A, x)

Returns alpha*A*x where A is a symmetric band matrix of order size(A,2) with k super-diagonals stored in the argument A.

gemm!(tA, tB, alpha, A, B, beta, C)

Update C as alpha*A*B + beta*C or the other three variants according to tA (transpose A) and tB. Returns the updated C.

gemm(tA, tB, alpha, A, B)

Returns alpha*A*B or the other three variants according to tA (transpose A) and tB.