scalapackfx_module Module Reference

High level Fortran wrappers for the SCALAPACK library. More...

Data Types
interface	scalafx_creatematrix
	Creates a distributed matrix and allocates local storage. More...
interface	scalafx_pheev
	Solves Hermitian eigenvalue problem by the QR algorithm. More...
interface	scalafx_pheevd
	Solves Hermitian eigenvalue problem by the divide and conquer algorithm. More...
interface	scalafx_phegst
	Reduces Hermitian definite generalized eigenvalue problem to standard form. More...
interface	scalafx_phegv
	Solves generalized Hermitian eigenvalue problem by the QR algorithm. More...
interface	scalafx_phegvd
	Solves generalized Hermitian eigenvalue problem by the divide and conquer algorithm. More...
interface	scalafx_ppotrf
	Cholesky factorization of a symmetric/Hermitian positive definite matrix. More...
interface	scalafx_psyev
	Solves symmetric eigenvalue problem by the QR algorithm. More...
interface	scalafx_psyevd
	Solves symmetric eigenvalue problem by the divide and conquer algorithm. More...
interface	scalafx_psygst
	Reduces symmetric definite generalized eigenvalue problem to standard form. More...
interface	scalafx_psygv
	Solves generalized symmetric eigenvalue problem by the QR algorithm. More...
interface	scalafx_psygvd
	Solves generalized symmetric eigenvalue problem by the divide and conquer algorithm. More...
interface	scalafx_ptrsm
	Solves triangular matrix equation. More...

Public Member Functions
subroutine, public	scalafx_getdescriptor (mygrid, mm, nn, mb, nb, desc, rsrc, csrc, info)
	Returns descriptor and size for the local part of a distributed matrix.
subroutine, public	scalafx_getlocalshape (mygrid, desc, nrowloc, ncolloc)
	Returns the shape of the local part of a distributed array.
subroutine, public	scalafx_infog2l (mygrid, desc, grow, gcol, lrow, lcol, rsrc, csrc)
	Maps global position in a distributed matrix to local one.

Private Member Functions
subroutine	scalafx_ppotrf_real (aa, desca, uplo, ia, ja, info)
	Computes the Cholesky factorization of a Hermitian positive definite matrix.
subroutine	scalafx_ppotrf_dreal (aa, desca, uplo, ia, ja, info)
	Computes the Cholesky factorization of a Hermitian positive definite matrix.
subroutine	scalafx_ppotrf_complex (aa, desca, uplo, ia, ja, info)
	Computes the Cholesky factorization of a Hermitian positive definite matrix.
subroutine	scalafx_ppotrf_dcomplex (aa, desca, uplo, ia, ja, info)
	Computes the Cholesky factorization of a Hermitian positive definite matrix.
subroutine	scalafx_psygst_real (ibtype, aa, desca, bb, descb, scale, uplo, ia, ja, ib, jb, info)
	Reduces Hermitian-definite generalized eigenvalue problem to standard form.
subroutine	scalafx_psygst_dreal (ibtype, aa, desca, bb, descb, scale, uplo, ia, ja, ib, jb, info)
	Reduces Hermitian-definite generalized eigenvalue problem to standard form.
subroutine	scalafx_phegst_complex (ibtype, aa, desca, bb, descb, scale, uplo, ia, ja, ib, jb, info)
	Reduces Hermitian-definite generalized eigenvalue problem to standard form.
subroutine	scalafx_phegst_dcomplex (ibtype, aa, desca, bb, descb, scale, uplo, ia, ja, ib, jb, info)
	Reduces Hermitian-definite generalized eigenvalue problem to standard form.
subroutine	scalafx_psyev_real (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, info)
	Solves real eigenvalue problem.
subroutine	scalafx_psyev_dreal (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, info)
	Solves real eigenvalue problem.
subroutine	scalafx_pheev_complex (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, rwork, info)
	Solves complex eigenvalue problem.
subroutine	scalafx_pheev_dcomplex (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, rwork, info)
	Solves complex eigenvalue problem.
subroutine	scalafx_psygv_real (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, skipchol, info)
	Solves symmetric generalized eigenvalue problem by the QR algorithm.
subroutine	scalafx_psygv_dreal (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, skipchol, info)
	Solves symmetric generalized eigenvalue problem by the QR algorithm.
subroutine	scalafx_phegv_complex (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, rwork, skipchol, info)
	Solves Hermitian generalized eigenvalue problem by the QR algorithm.
subroutine	scalafx_phegv_dcomplex (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, rwork, skipchol, info)
	Solves Hermitian generalized eigenvalue problem by the QR algorithm.
subroutine	scalafx_psyevd_real (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, iwork, allocfix, info)
	Solves symmetric eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_psyevd_dreal (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, iwork, allocfix, info)
	Solves symmetric eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_pheevd_complex (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, rwork, iwork, allocfix, info)
	Solves Hermitian eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_pheevd_dcomplex (aa, desca, ww, zz, descz, jobz, uplo, ia, ja, iz, jz, work, rwork, iwork, allocfix, info)
	Solves Hermitian eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_psygvd_real (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, iwork, allocfix, skipchol, info)
	Solves real generalized eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_psygvd_dreal (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, iwork, allocfix, skipchol, info)
	Solves real generalized eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_phegvd_complex (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, rwork, iwork, allocfix, skipchol, info)
	Solves Hermitian eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_phegvd_dcomplex (aa, desca, bb, descb, ww, zz, descz, jobz, uplo, ia, ja, ib, jb, iz, jz, work, rwork, iwork, allocfix, skipchol, info)
	Solves Hermitian eigenvalue problem by the divide and conquer algorithm.
subroutine	scalafx_ptrsm_real (aa, desca, bb, descb, side, uplo, transa, diag, alpha, ia, ja, ib, jb)
	Solves triangular matrix equation.
subroutine	scalafx_ptrsm_dreal (aa, desca, bb, descb, side, uplo, transa, diag, alpha, ia, ja, ib, jb)
	Solves triangular matrix equation.
subroutine	scalafx_ptrsm_complex (aa, desca, bb, descb, side, uplo, transa, diag, alpha, ia, ja, ib, jb)
	Solves triangular matrix equation.
subroutine	scalafx_ptrsm_dcomplex (aa, desca, bb, descb, side, uplo, transa, diag, alpha, ia, ja, ib, jb)
	Solves triangular matrix equation.
subroutine	scalafx_creatematrix_int (mygrid, mm, nn, mb, nb, mtxloc, desc, rsrc, csrc, info)
	Creates a distributed matrix and allocates local storage.
subroutine	scalafx_creatematrix_real (mygrid, mm, nn, mb, nb, mtxloc, desc, rsrc, csrc, info)
	Creates a distributed matrix and allocates local storage.
subroutine	scalafx_creatematrix_dreal (mygrid, mm, nn, mb, nb, mtxloc, desc, rsrc, csrc, info)
	Creates a distributed matrix and allocates local storage.
subroutine	scalafx_creatematrix_complex (mygrid, mm, nn, mb, nb, mtxloc, desc, rsrc, csrc, info)
	Creates a distributed matrix and allocates local storage.
subroutine	scalafx_creatematrix_dcomplex (mygrid, mm, nn, mb, nb, mtxloc, desc, rsrc, csrc, info)
	Creates a distributed matrix and allocates local storage.

Detailed Description

High level Fortran wrappers for the SCALAPACK library.

Member Function/Subroutine Documentation

subroutine scalapackfx_module::scalafx_creatematrix_complex ( type(blacsgrid), intent(in)  mygrid, integer, intent(in)  mm, integer, intent(in)  nn, integer, intent(in)  mb, integer, intent(in)  nb, complex(sp), dimension(:,:), intent(out), allocatable  mtxloc, integer, dimension(dlen_), intent(out)  desc, integer, intent(in), optional  rsrc, integer, intent(in), optional  csrc, integer, intent(out), optional  info  )

private

Creates a distributed matrix and allocates local storage.

Parameters

mygrid	BLACS descriptor.
mm	Number of rows of global matrix.
nn	Number of columns of global matrix.
mb	Row block size.
nb	Column block size.
desc	Matrix descriptor on exit.
mtxloc	Allocated local matrix on exit.
rsrc	Process row, over which first row is distributed (default: master row).
csrc	Process column, over which first column is distributed (default: master column).
info	Info flag.

subroutine scalapackfx_module::scalafx_creatematrix_dcomplex ( type(blacsgrid), intent(in)  mygrid, integer, intent(in)  mm, integer, intent(in)  nn, integer, intent(in)  mb, integer, intent(in)  nb, complex(dp), dimension(:,:), intent(out), allocatable  mtxloc, integer, dimension(dlen_), intent(out)  desc, integer, intent(in), optional  rsrc, integer, intent(in), optional  csrc, integer, intent(out), optional  info  )

private

Creates a distributed matrix and allocates local storage.

Parameters

mygrid	BLACS descriptor.
mm	Number of rows of global matrix.
nn	Number of columns of global matrix.
mb	Row block size.
nb	Column block size.
desc	Matrix descriptor on exit.
mtxloc	Allocated local matrix on exit.
rsrc	Process row, over which first row is distributed (default: master row).
csrc	Process column, over which first column is distributed (default: master column).
info	Info flag.

subroutine scalapackfx_module::scalafx_creatematrix_dreal ( type(blacsgrid), intent(in)  mygrid, integer, intent(in)  mm, integer, intent(in)  nn, integer, intent(in)  mb, integer, intent(in)  nb, real(dp), dimension(:,:), intent(out), allocatable  mtxloc, integer, dimension(dlen_), intent(out)  desc, integer, intent(in), optional  rsrc, integer, intent(in), optional  csrc, integer, intent(out), optional  info  )

private

Creates a distributed matrix and allocates local storage.

Parameters

mygrid	BLACS descriptor.
mm	Number of rows of global matrix.
nn	Number of columns of global matrix.
mb	Row block size.
nb	Column block size.
desc	Matrix descriptor on exit.
mtxloc	Allocated local matrix on exit.
rsrc	Process row, over which first row is distributed (default: master row).
csrc	Process column, over which first column is distributed (default: master column).
info	Info flag.

subroutine scalapackfx_module::scalafx_creatematrix_int ( type(blacsgrid), intent(in)  mygrid, integer, intent(in)  mm, integer, intent(in)  nn, integer, intent(in)  mb, integer, intent(in)  nb, integer, dimension(:,:), intent(out), allocatable  mtxloc, integer, dimension(dlen_), intent(out)  desc, integer, intent(in), optional  rsrc, integer, intent(in), optional  csrc, integer, intent(out), optional  info  )

private

Creates a distributed matrix and allocates local storage.

Parameters

mygrid	BLACS descriptor.
mm	Number of rows of global matrix.
nn	Number of columns of global matrix.
mb	Row block size.
nb	Column block size.
desc	Matrix descriptor on exit.
mtxloc	Allocated local matrix on exit.
rsrc	Process row, over which first row is distributed (default: master row).
csrc	Process column, over which first column is distributed (default: master column).
info	Info flag.

subroutine scalapackfx_module::scalafx_creatematrix_real ( type(blacsgrid), intent(in)  mygrid, integer, intent(in)  mm, integer, intent(in)  nn, integer, intent(in)  mb, integer, intent(in)  nb, real(sp), dimension(:,:), intent(out), allocatable  mtxloc, integer, dimension(dlen_), intent(out)  desc, integer, intent(in), optional  rsrc, integer, intent(in), optional  csrc, integer, intent(out), optional  info  )

private

Creates a distributed matrix and allocates local storage.

Parameters

mygrid	BLACS descriptor.
mm	Number of rows of global matrix.
nn	Number of columns of global matrix.
mb	Row block size.
nb	Column block size.
desc	Matrix descriptor on exit.
mtxloc	Allocated local matrix on exit.
rsrc	Process row, over which first row is distributed (default: master row).
csrc	Process column, over which first column is distributed (default: master column).
info	Info flag.

subroutine, public scalapackfx_module::scalafx_getdescriptor	(	type(blacsgrid), intent(in)	mygrid,
		integer, intent(in)	mm,
		integer, intent(in)	nn,
		integer, intent(in)	mb,
		integer, intent(in)	nb,
		integer, dimension(dlen_), intent(out)	desc,
		integer, intent(in), optional	rsrc,
		integer, intent(in), optional	csrc,
		integer, intent(out), optional	info
	)

Returns descriptor and size for the local part of a distributed matrix.

Parameters

mygrid	BLACS descriptor.
mm	Number of rows of global matrix.
nn	Number of columns of global matrix.
mb	Row block size.
nb	Column block size.
desc	Matrix descriptor on exit.
nrowloc	Number of rows for local matrix.
ncolloc	Number of columns for local matrix.
rsrc	Process row, over which first row is distributed (default: master row).
csrc	Process column, over which first column is distributed (default: master column).
info	Info flag.

subroutine, public scalapackfx_module::scalafx_getlocalshape	(	type(blacsgrid), intent(in)	mygrid,
		integer, dimension(dlen_), intent(in)	desc,
		integer, intent(out)	nrowloc,
		integer, intent(out)	ncolloc
	)

Returns the shape of the local part of a distributed array.

Parameters

mygrid	BLACS grid descriptor.
desc	Global matrix descriptor.
nrowloc	Nr. of local rows.
ncolloc	Nr. of local columns.

subroutine, public scalapackfx_module::scalafx_infog2l	(	type(blacsgrid), intent(in)	mygrid,
		integer, dimension(dlen_), intent(in)	desc,
		integer, intent(in)	grow,
		integer, intent(in)	gcol,
		integer, intent(out)	lrow,
		integer, intent(out)	lcol,
		integer, intent(out)	rsrc,
		integer, intent(out)	csrc
	)

Maps global position in a distributed matrix to local one.

Parameters

mygrid	BLACS descriptor.
desc	Descriptor of the distributed matrix.
grow	Global row index.
gcol	Global column index.
lrow	Local row index on output.
lcol	Local column index on output.
rsrc	Row of the process owning the local matrix.
csrc	Column of the process owning the local matrix.

subroutine scalapackfx_module::scalafx_pheev_complex ( complex(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:), intent(out)  ww, complex(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(sp), dimension(:), intent(inout), optional, allocatable  work, real(sp), dimension(:), intent(inout), optional, allocatable  rwork, integer, intent(out), optional  info  )

private

Solves complex eigenvalue problem.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated automatically)
rwork	Real working array (if not specified, allocated automatically)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?heev).

subroutine scalapackfx_module::scalafx_pheev_dcomplex ( complex(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:), intent(out)  ww, complex(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(dp), dimension(:), intent(inout), optional, allocatable  work, real(dp), dimension(:), intent(inout), optional, allocatable  rwork, integer, intent(out), optional  info  )

private

Solves complex eigenvalue problem.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated automatically)
rwork	Real working array (if not specified, allocated automatically)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?heev).

subroutine scalapackfx_module::scalafx_pheevd_complex ( complex(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:), intent(out)  ww, complex(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(sp), dimension(:), intent(inout), optional, allocatable  work, real(sp), dimension(:), intent(inout), optional, allocatable  rwork, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, integer, intent(out), optional  info  )

private

Solves Hermitian eigenvalue problem by the divide and conquer algorithm.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated automatically)
rwork	Real working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

Note

Unfortunately, SCALAPACK seems to return the wrong real work space sizes for many cases. This routine (when allocfix had been set to true) tries to improve on it by two ways:

• It queries also the QR routine (p?heev) for workspace size and takes this, if bigger than returned by p?heevd. That should ensure that the pzunmtr() routine does not encounter any difficulties.

• It additionally enlarges the real workspace size by the amount of memory needed by the pdlasrt() routine, to make sure this would not fail either.

Those fixes are empirical, may lead to oversized workspace allocations and probably would not even fix the allocation problem, but are the best we could find so far.

See Also

SCALAPACK documentation (routine p?heevd).

subroutine scalapackfx_module::scalafx_pheevd_dcomplex ( complex(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:), intent(out)  ww, complex(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(dp), dimension(:), intent(inout), optional, allocatable  work, real(dp), dimension(:), intent(inout), optional, allocatable  rwork, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, integer, intent(out), optional  info  )

private

Solves Hermitian eigenvalue problem by the divide and conquer algorithm.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated automatically)
rwork	Real working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

Note

Unfortunately, SCALAPACK seems to return the wrong real work space sizes for many cases. This routine (when allocfix had been set to true) tries to improve on it by two ways:

• It queries also the QR routine (p?heev) for workspace size and takes this, if bigger than returned by p?heevd. That should ensure that the pzunmtr() routine does not encounter any difficulties.

• It additionally enlarges the real workspace size by the amount of memory needed by the pdlasrt() routine, to make sure this would not fail either.

Those fixes are empirical, may lead to oversized workspace allocations and probably would not even fix the allocation problem, but are the best we could find so far.

See Also

SCALAPACK documentation (routine p?heevd).

subroutine scalapackfx_module::scalafx_phegst_complex ( integer, intent(in)  ibtype, complex(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, complex(sp), dimension(:,:), intent(in)  bb, integer, dimension(dlen_), intent(in)  descb, real(sp), intent(out)  scale, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(out), optional  info  )

private

Reduces Hermitian-definite generalized eigenvalue problem to standard form.

Parameters

ibtype	Type of the problem (1, 2, 3).
aa	Matrix A.
desca	Descriptor of matrix A.
bb	Right hand side of the eigenvalue equation (B).
desb	Descriptor of matrix B.
scale	Scaling factors on return.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?sygst/p?hegst).

subroutine scalapackfx_module::scalafx_phegst_dcomplex ( integer, intent(in)  ibtype, complex(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, complex(dp), dimension(:,:), intent(in)  bb, integer, dimension(dlen_), intent(in)  descb, real(dp), intent(out)  scale, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(out), optional  info  )

private

Reduces Hermitian-definite generalized eigenvalue problem to standard form.

Parameters

ibtype	Type of the problem (1, 2, 3).
aa	Matrix A.
desca	Descriptor of matrix A.
bb	Right hand side of the eigenvalue equation (B).
desb	Descriptor of matrix B.
scale	Scaling factors on return.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?sygst/p?hegst).

subroutine scalapackfx_module::scalafx_phegv_complex ( complex(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, complex(sp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(sp), dimension(:), intent(out)  ww, complex(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(sp), dimension(:), intent(inout), optional, allocatable  work, real(sp), dimension(:), intent(inout), optional, allocatable  rwork, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves Hermitian generalized eigenvalue problem by the QR algorithm.

Invokes SCALAPACK routines p?potrf, p?hegst, p?heev, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated (automatically)
rwork	Real working array (if not specified, allocated automatically)
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?hegst, p?heev, p?trsm).

subroutine scalapackfx_module::scalafx_phegv_dcomplex ( complex(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, complex(dp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(dp), dimension(:), intent(out)  ww, complex(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(dp), dimension(:), intent(inout), optional, allocatable  work, real(dp), dimension(:), intent(inout), optional, allocatable  rwork, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves Hermitian generalized eigenvalue problem by the QR algorithm.

Invokes SCALAPACK routines p?potrf, p?hegst, p?heev, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated (automatically)
rwork	Real working array (if not specified, allocated automatically)
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?hegst, p?heev, p?trsm).

subroutine scalapackfx_module::scalafx_phegvd_complex ( complex(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, complex(sp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(sp), dimension(:), intent(out)  ww, complex(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(sp), dimension(:), intent(inout), optional, allocatable  work, real(sp), dimension(:), intent(inout), optional, allocatable  rwork, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves Hermitian eigenvalue problem by the divide and conquer algorithm.

Invokes SCALAPACK routines p?potrf, p?hegst, p?heevd, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated automatically)
rwork	Real working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values. See the scalafx_pheevd_complex() routine for details.
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?hegst, p?heevd, p?trsm).

subroutine scalapackfx_module::scalafx_phegvd_dcomplex ( complex(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, complex(dp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(dp), dimension(:), intent(out)  ww, complex(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, complex(dp), dimension(:), intent(inout), optional, allocatable  work, real(dp), dimension(:), intent(inout), optional, allocatable  rwork, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves Hermitian eigenvalue problem by the divide and conquer algorithm.

Invokes SCALAPACK routines p?potrf, p?hegst, p?heevd, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Complex working array (if not specified, allocated automatically)
rwork	Real working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values. See the scalafx_pheevd_dcomplex() routine for details.
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?hegst, p?heevd, p?trsm).

subroutine scalapackfx_module::scalafx_ppotrf_complex ( complex(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(out), optional  info  )

private

Computes the Cholesky factorization of a Hermitian positive definite matrix.

Parameters

desca	Descriptor of the matrix.
aa	Matrix.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix (default: 1)
ja	First column of the submatrix (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?potrf).

subroutine scalapackfx_module::scalafx_ppotrf_dcomplex ( complex(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(out), optional  info  )

private

Computes the Cholesky factorization of a Hermitian positive definite matrix.

Parameters

desca	Descriptor of the matrix.
aa	Matrix.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix (default: 1)
ja	First column of the submatrix (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?potrf).

subroutine scalapackfx_module::scalafx_ppotrf_dreal ( real(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(out), optional  info  )

private

Computes the Cholesky factorization of a Hermitian positive definite matrix.

Parameters

desca	Descriptor of the matrix.
aa	Matrix.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix (default: 1)
ja	First column of the submatrix (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?potrf).

subroutine scalapackfx_module::scalafx_ppotrf_real ( real(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(out), optional  info  )

private

Computes the Cholesky factorization of a Hermitian positive definite matrix.

Parameters

desca	Descriptor of the matrix.
aa	Matrix.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix (default: 1)
ja	First column of the submatrix (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?potrf).

subroutine scalapackfx_module::scalafx_psyev_dreal ( real(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:), intent(out)  ww, real(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(dp), dimension(:), intent(inout), optional, allocatable  work, integer, intent(out), optional  info  )

private

Solves real eigenvalue problem.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?syev).

subroutine scalapackfx_module::scalafx_psyev_real ( real(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:), intent(out)  ww, real(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(sp), dimension(:), intent(inout), optional, allocatable  work, integer, intent(out), optional  info  )

private

Solves real eigenvalue problem.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routine p?syev).

subroutine scalapackfx_module::scalafx_psyevd_dreal ( real(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:), intent(out)  ww, real(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(dp), dimension(:), intent(inout), optional, allocatable  work, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, integer, intent(out), optional  info  )

private

Solves symmetric eigenvalue problem by the divide and conquer algorithm.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

Note

Unfortunately, SCALAPACK seems to return the wrong real work space sizes for many cases. This routine (when allocfix had been set to true) tries to improve on it by two ways:

• It queries also the QR routine (p?syev) for workspace size and takes this, if bigger than returned by p?syevd. That should ensure that the pdormtr() routine does not encounter any difficulties.

• It additionally enlarges the real workspace size by the amount of memory needed by the pdlasrt() routine, to make sure this would not fail either.

Those fixes are empirical, may lead to oversized workspace allocations and probably would not even fix the allocation problem, but are the best we could find so far.

See Also

SCALAPACK documentation (routine p?syevd).

subroutine scalapackfx_module::scalafx_psyevd_real ( real(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:), intent(out)  ww, real(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(sp), dimension(:), intent(inout), optional, allocatable  work, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, integer, intent(out), optional  info  )

private

Solves symmetric eigenvalue problem by the divide and conquer algorithm.

Parameters

aa	Matrix to diagonalize (A).
desca	Descriptor of matrix A.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

Note

Unfortunately, SCALAPACK seems to return the wrong real work space sizes for many cases. This routine (when allocfix had been set to true) tries to improve on it by two ways:

• It queries also the QR routine (p?syev) for workspace size and takes this, if bigger than returned by p?syevd. That should ensure that the pdormtr() routine does not encounter any difficulties.

• It additionally enlarges the real workspace size by the amount of memory needed by the pdlasrt() routine, to make sure this would not fail either.

Those fixes are empirical, may lead to oversized workspace allocations and probably would not even fix the allocation problem, but are the best we could find so far.

See Also

SCALAPACK documentation (routine p?syevd).

subroutine scalapackfx_module::scalafx_psygst_dreal ( integer, intent(in)  ibtype, real(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:,:), intent(in)  bb, integer, dimension(dlen_), intent(in)  descb, real(dp), intent(out)  scale, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(out), optional  info  )

private

Reduces Hermitian-definite generalized eigenvalue problem to standard form.

Parameters

ibtype	Type of the problem (1, 2, 3).
aa	Matrix A.
desca	Descriptor of matrix A.
bb	Right hand side of the eigenvalue equation (B).
desb	Descriptor of matrix B.
scale	Scaling factors on return.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?sygst/p?hegst).

subroutine scalapackfx_module::scalafx_psygst_real ( integer, intent(in)  ibtype, real(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:,:), intent(in)  bb, integer, dimension(dlen_), intent(in)  descb, real(sp), intent(out)  scale, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(out), optional  info  )

private

Reduces Hermitian-definite generalized eigenvalue problem to standard form.

Parameters

ibtype	Type of the problem (1, 2, 3).
aa	Matrix A.
desca	Descriptor of matrix A.
bb	Right hand side of the eigenvalue equation (B).
desb	Descriptor of matrix B.
scale	Scaling factors on return.
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?sygst/p?hegst).

subroutine scalapackfx_module::scalafx_psygv_dreal ( real(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(dp), dimension(:), intent(out)  ww, real(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(dp), dimension(:), intent(inout), optional, allocatable  work, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves symmetric generalized eigenvalue problem by the QR algorithm.

Invokes SCALAPACK routines p?potrf, p?sygst, p?syev, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?hegst, p?heev, p?trsm).

subroutine scalapackfx_module::scalafx_psygv_real ( real(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(sp), dimension(:), intent(out)  ww, real(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(sp), dimension(:), intent(inout), optional, allocatable  work, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves symmetric generalized eigenvalue problem by the QR algorithm.

Invokes SCALAPACK routines p?potrf, p?sygst, p?syev, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?hegst, p?heev, p?trsm).

subroutine scalapackfx_module::scalafx_psygvd_dreal ( real(dp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(dp), dimension(:), intent(out)  ww, real(dp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(dp), dimension(:), intent(inout), optional, allocatable  work, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves real generalized eigenvalue problem by the divide and conquer algorithm.

Invokes SCALAPACK routines p?potrf, p?sygst, p?syevd, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values. See the scalafx_psyevd_dreal() routine for details.
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?sygst, p?syevd, p?trsm).

subroutine scalapackfx_module::scalafx_psygvd_real ( real(sp), dimension(:,:), intent(inout)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, real(sp), dimension(:), intent(out)  ww, real(sp), dimension(:,:), intent(out)  zz, integer, dimension(dlen_), intent(in)  descz, character, intent(in), optional  jobz, character, intent(in), optional  uplo, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb, integer, intent(in), optional  iz, integer, intent(in), optional  jz, real(sp), dimension(:), intent(inout), optional, allocatable  work, integer, dimension(:), intent(inout), optional, allocatable  iwork, logical, intent(in), optional  allocfix, logical, intent(in), optional  skipchol, integer, intent(out), optional  info  )

private

Solves real generalized eigenvalue problem by the divide and conquer algorithm.

Invokes SCALAPACK routines p?potrf, p?sygst, p?syevd, p?trsm in order to transform the general eigenvalue problem to the standard form and transform the eigenvectors back.

Parameters

aa	Matrix to diagonalize (A), transformed matrix on exit.
desca	Descriptor of matrix A.
bb	Matrix on the right hand side (B), transformed matrix on exit.
descb	Descriptor of matrix B.
ww	Eigenvalues on exit.
zz	Eigenvectors on exit (Z).
descz	Descriptor of the eigenvector matrix.
jobz	Job type (default: "V")
uplo	Upper or lower diagonal matrix (default: "L")
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)
iz	First row of the submatrix Z (default: 1)
jz	First column of the submatrix Z (default: 1)
work	Working array (if not specified, allocated automatically)
iwork	Integer working array (if not specified, allocated automatically)
allocfix	If yes, the routine tries to enlarge the workspace size as returned by the appropriate p?syevd() routine by some empirical values. See the scalafx_psyevd_real() routine for details.
skipchol	If true, the Cholesky transformation will be skipped. Array bb must have the Cholesky transformed form.
info	Info flag. If not specified and SCALAPACK calls returns nozero, subroutine stops.

See Also

SCALAPACK documentation (routines p?potrf, p?sygst, p?syevd, p?trsm).

subroutine scalapackfx_module::scalafx_ptrsm_complex ( complex(sp), dimension(:,:), intent(in)  aa, integer, dimension(dlen_), intent(in)  desca, complex(sp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, character, intent(in), optional  side, character, intent(in), optional  uplo, character, intent(in), optional  transa, character, intent(in), optional  diag, complex(sp), intent(in), optional  alpha, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb  )

private

Solves triangular matrix equation.

Parameters

aa	Left hand side of equation (A)
desca	Descriptor of matrix A.
bb	Right hand side (B).
descb	Descriptor of matrix B.
side	Side of A (default: "L")
uplo	Upper or lower diagonal matrix (default: "L")
transa	Transposition flag (default "N")
diag	Specifieds whether matrix A is unit triangular (default: "N")
alpha	Prefactor of B (default: 1.0)
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)

See Also

SCALAPACK documentation (routine p?trsm).

subroutine scalapackfx_module::scalafx_ptrsm_dcomplex ( complex(dp), dimension(:,:), intent(in)  aa, integer, dimension(dlen_), intent(in)  desca, complex(dp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, character, intent(in), optional  side, character, intent(in), optional  uplo, character, intent(in), optional  transa, character, intent(in), optional  diag, complex(dp), intent(in), optional  alpha, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb  )

private

Solves triangular matrix equation.

Parameters

aa	Left hand side of equation (A)
desca	Descriptor of matrix A.
bb	Right hand side (B).
descb	Descriptor of matrix B.
side	Side of A (default: "L")
uplo	Upper or lower diagonal matrix (default: "L")
transa	Transposition flag (default "N")
diag	Specifieds whether matrix A is unit triangular (default: "N")
alpha	Prefactor of B (default: 1.0)
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)

See Also

SCALAPACK documentation (routine p?trsm).

subroutine scalapackfx_module::scalafx_ptrsm_dreal ( real(dp), dimension(:,:), intent(in)  aa, integer, dimension(dlen_), intent(in)  desca, real(dp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, character, intent(in), optional  side, character, intent(in), optional  uplo, character, intent(in), optional  transa, character, intent(in), optional  diag, real(dp), intent(in), optional  alpha, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb  )

private

Solves triangular matrix equation.

Parameters

aa	Left hand side of equation (A)
desca	Descriptor of matrix A.
bb	Right hand side (B).
descb	Descriptor of matrix B.
side	Side of A (default: "L")
uplo	Upper or lower diagonal matrix (default: "L")
transa	Transposition flag (default "N")
diag	Specifieds whether matrix A is unit triangular (default: "N")
alpha	Prefactor of B (default: 1.0)
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)

See Also

SCALAPACK documentation (routine p?trsm).

subroutine scalapackfx_module::scalafx_ptrsm_real ( real(sp), dimension(:,:), intent(in)  aa, integer, dimension(dlen_), intent(in)  desca, real(sp), dimension(:,:), intent(inout)  bb, integer, dimension(dlen_), intent(in)  descb, character, intent(in), optional  side, character, intent(in), optional  uplo, character, intent(in), optional  transa, character, intent(in), optional  diag, real(sp), intent(in), optional  alpha, integer, intent(in), optional  ia, integer, intent(in), optional  ja, integer, intent(in), optional  ib, integer, intent(in), optional  jb  )

private

Solves triangular matrix equation.

Parameters

aa	Left hand side of equation (A)
desca	Descriptor of matrix A.
bb	Right hand side (B).
descb	Descriptor of matrix B.
side	Side of A (default: "L")
uplo	Upper or lower diagonal matrix (default: "L")
transa	Transposition flag (default "N")
diag	Specifieds whether matrix A is unit triangular (default: "N")
alpha	Prefactor of B (default: 1.0)
ia	First row of the submatrix A (default: 1)
ja	First column of the submatrix A (default: 1)
ib	First row of the submatrix B (default: 1)
jb	First column of the submatrix B (default: 1)

See Also

SCALAPACK documentation (routine p?trsm).

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The documentation for this module was generated from the following file:

• scalapackfx.F90