SF_LINALG

Quick access

Variables:

operator(.px.), operator(.x.)

Routines:

build_tridiag(), check_tridiag(), cross_product(), det(), deye(), deye_tridiag(), diag(), diagonal(), eig(), eigh(), eigh_jacobi(), eigvals(), eigvalsh(), eye(), get_tridiag(), inv(), inv_gj(), inv_her(), inv_sym(), inv_triang(), inv_tridiag(), kron(), kronecker_product(), lstsq(), mat_product(), ones(), operator(.kx.)(), outerprod(), p_eigh(), p_inv(), p_mat_product(), s3_product(), solve(), svd(), svdvals(), trace(), zeros(), zeye(), zeye_tridiag()

Used modules

• sf_blacs

Variables

• sf_linalg/operator (.px.) [public]

• sf_linalg/operator (.x.) [public]

Subroutines and functions

interface  sf_linalg/eig(a, eval, evec[, jobvl, jobvr])

Parameters:

• a (*,*) [real, complex, in]

• eval (*) [complex, out]

• evec (*,*) [complex, out]

Options:

• jobvl [character(len=1)]

• jobvr [character(len=1)]

interface  sf_linalg/eigh(am, bm, lam, c, a, e, d, u[, method, jobz, uplo, vl, vu, il, iu, tol, ev, irange, vrange])

Parameters:

• am (*,*) [real, complex, in] – LHS matrix: Am c = lam Bm c

• bm (*,*) [real, complex, in] – Bmt temporaries overwritten by dsygvd

• lam (*) [real, out] – eigenvalues: Am c = lam Bm c

• c (*,*) [real, complex, out] – eigenvectors: Am c = lam Bm c; c(i,j) = ith component of jth vec.

• a (*,*) [real, complex, inout/in,required] – M v = E v/v(i,j) = ith component of jth vec.

• e (size(a, 2) [real, inout] – eigenvalues

• d (*) [real, in,required]

• u (max(1, -1 + size(d) [real]

Options:

• method [character(len=*)]

• jobz [character(len=1)]

• uplo [character(len=1)]

• vl [real]

• vu [real]

• il [integer]

• iu [integer]

• tol [real]

• ev (*,*) [real]

• irange (2) [integer]

• vrange (2) [integer]

interface  sf_linalg/p_eigh(a, w, nblock[, method, jobz, uplo, vl, vu, il, iu, tol])

Parameters:

• a (*,*) [real, complex, inout/in,required] – M v = E v/v(i,j) = ith component of jth vec.

• w (size(a, 2) [real, inout] – eigenvalues

• nblock [integer]

Options:

• method [character(len=*)]

• jobz [character(len=1)]

• uplo [character(len=1)]

• vl [real]

• vu [real]

• il [integer]

• iu [integer]

• tol [real]

interface  sf_linalg/eigh_jacobi(a, d, v, nrot, u, sweep)

Parameters:

• a (*,*) [real, complex, inout]

• d (size(a, 1) [real, out]

• v (size(a, 1,size(a, 2) [real, out]

• nrot [integer, out]

• u (size(a, 1,size(a, 2) [complex, out]

• sweep [integer]

interface  sf_linalg/eigvals(a)

Parameters:

a (*,*) [real, complex, in]

interface  sf_linalg/eigvalsh(a)

Parameters:

a (*,*) [real, complex, in]

interface  sf_linalg/svdvals(a)

Parameters:

a (*,*) [real, complex, in]

interface  sf_linalg/svd(a, s, u, vtransp)

Parameters:

• a (*,*) [real, complex, in] – use a temporary as dgesvd destroys its input

• s (*) [real, out] – has size min(m, n) –> sigma matrix is (n x m) with sigma_ii = s_i

• u (*,*) [real, complex, out]

• vtransp (*,*) [real, complex, out]

interface  sf_linalg/inv(am)

Parameters:

am (*,*) [real, complex, inout] – matrix to be inverted

interface  sf_linalg/p_inv(a, nblock)

Parameters:

• a (*,*) [real, complex, inout]

• nblock [integer]

interface  sf_linalg/inv_sym(a[, uplo])

Parameters:

a (*,*) [real, complex]

Options:

uplo [character(len=*)]

interface  sf_linalg/inv_her(a[, uplo])

Parameters:

a (*,*) [complex]

Options:

uplo [character(len=*)]

interface  sf_linalg/inv_triang(a[, uplo, diag])

Parameters:

a (*,*) [real, complex]

Options:

• uplo [character(len=1)]

• diag [character(len=1)] – not a unit triangular matrix

interface  sf_linalg/inv_gj(a)

Parameters:

a (*,*) [real, complex, inout] – cmplx

interface  sf_linalg/solve(a, b[, trans])

Parameters:

• a (*,*) [real, complex, in]

• b (various shapes) [real, complex, inout]

Options:

trans [character(len=1)]

interface  sf_linalg/lstsq(a, b)

Parameters:

• a (*,*) [real, complex, in]

• b (*) [real, complex, in] – only one right-hand side

interface  sf_linalg/inv_tridiag(sub_, diag_, over_, inv, ainv, amat, nb, n[, n, nb])

Options:

• n [integer, optional/default=1 + shape(sub, 0)]

• nb [integer, optional/default=1 + shape(sub, 0)]

Parameters:

• sub_ (various shapes) [real, complex]

• diag_ (various shapes) [real, complex]

• over_ (various shapes) [real, complex]

• inv (n) [real, complex]

• ainv (nb,n,n) [real, complex]

• amat (*,*) [real, complex, inout]

interface  sf_linalg/check_tridiag(amat, nblock, nsize)

Parameters:

• amat (*,*) [real, complex]

• nblock [integer, in,required]

• nsize [integer, in,required]

interface  sf_linalg/get_tridiag(amat, sub, diag, nblock, nsize[, over])

Parameters:

• amat (*,*) [real, complex, in,required]

• sub (various shapes) [real, complex]

• diag (various shapes) [real, complex]

• nblock [integer, in,required/default=1 + shape(sub, 0)]

• nsize [integer, in,required]

Options:

over (various shapes) [real, complex]

interface  sf_linalg/build_tridiag(sub, diag[, over, nblock, nsize])

Parameters:

• sub (various shapes) [real, complex]

• diag (various shapes) [real, complex, in,required]

Options:

• over (various shapes) [real, complex]

• nblock [integer, optional/default=1 + shape(sub, 0)]

• nsize [integer]

interface  sf_linalg/det(a)

Parameters:

a (*,*) [real, complex, in]

interface  sf_linalg/deye(n, i, j)

Parameters:

• n [integer, in]

• i [integer, in]

• j [integer, in]

interface  sf_linalg/zeye(n, i, j)

Parameters:

• n [integer, in]

• i [integer, in]

• j [integer, in]

interface  sf_linalg/eye(n, i, j)

Parameters:

• n [integer, in]

• i [integer, in]

• j [integer, in]

interface  sf_linalg/diag(x)

Parameters:

x (*) [real, complex, in]

interface  sf_linalg/diagonal(a)

Parameters:

a (*,*) [real, complex, in]

interface  sf_linalg/trace(a)

Parameters:

a (*,*) [real, complex, in]

interface  sf_linalg/zeros(n, n1, n2, n3, n4, n5, n6, n7)

Parameters:

• n [integer, in]

• n1 [integer, in]

• n2 [integer, in]

• n3 [integer, in]

• n4 [integer, in]

• n5 [integer, in]

• n6 [integer, in]

• n7 [integer, in]

interface  sf_linalg/ones(n, n1, n2, n3, n4, n5, n6, n7)

Parameters:

• n [integer, in]

• n1 [integer, in]

• n2 [integer, in]

• n3 [integer, in]

• n4 [integer, in]

• n5 [integer, in]

• n6 [integer, in]

• n7 [integer, in]

interface  sf_linalg/kron(a, b)

Parameters:

• a (*,*) [integer, real, complex, in]

• b (*,*) [integer, real, complex, in]

interface  sf_linalg/kronecker_product(a, b)

Parameters:

• a (*,*) [integer, real, complex, in]

• b (*,*) [integer, real, complex, in]

interface  sf_linalg/operator(.kx.)(a, b)

Parameters:

• a (*,*) [integer, real, complex, in]

• b (*,*) [integer, real, complex, in]

interface  sf_linalg/outerprod(a, b)

Parameters:

• a (*) [real, complex, in]

• b (*) [real, complex, in]

interface  sf_linalg/cross_product(a, b)

Parameters:

• a (3) [real, complex]

• b (3) [real, complex]

interface  sf_linalg/s3_product(a, b, c)

Parameters:

• a (3) [real, complex, in]

• b (3) [real, complex, in]

• c (3) [real, complex, in]

interface  sf_linalg/mat_product(a, b, c[, alfa, beta])

Parameters:

• a (*,*) [real, complex, inout] – [N,K]

• b (*,*) [real, complex, inout] – [K,M]

• c (*,*) [real, complex, inout] – [N,M]

Options:

• alfa [real, complex]

• beta [real, complex]

interface  sf_linalg/p_mat_product(a, b, c, nblock[, alfa, beta])

Parameters:

• a (*,*) [real, complex, inout] – [N,K]

• b (*,*) [real, complex, inout] – [K,M]

• c (*,*) [real, complex, inout] – [N,M]

• nblock [integer]

Options:

• alfa [real]

• beta [real]

function  sf_linalg/deye_tridiag(nblock, n)

Parameters:

• nblock [integer]

• n [integer]

Return:

eye_block (nblock,n,n) [real]

function  sf_linalg/zeye_tridiag(nblock, n)

Parameters:

• nblock [integer]

• n [integer]

Return:

eye_block (nblock,n,n) [complex]