Man page - hpgvd(3)

Packages contains this manual

Manual

hpgvd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpgvd (integer itype, character jobz, character uplo, integern, complex, dimension( * ) ap, complex, dimension( * ) bp, real,dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex,dimension( * ) work, integer lwork, real, dimension( * ) rwork, integerlrwork, integer, dimension( * ) iwork, integer liwork, integer info)
subroutine dspgvd (integer itype, character jobz, character uplo, integern, double precision, dimension( * ) ap, double precision, dimension( *) bp, double precision, dimension( * ) w, double precision, dimension(ldz, * ) z, integer ldz, double precision, dimension( * ) work, integerlwork, integer, dimension( * ) iwork, integer liwork, integer info)
subroutine sspgvd (integer itype, character jobz, character uplo, integern, real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( *) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * )work, integer lwork, integer, dimension( * ) iwork, integer liwork,integer info)
subroutine zhpgvd (integer itype, character jobz, character uplo, integern, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, doubleprecision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integerldz, complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,integer liwork, integer info)
Author

NAME

hpgvd - {hp,sp}gvd: eig, divide and conquer

SYNOPSIS

Functions

subroutine chpgvd (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CHPGVD
subroutine dspgvd (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, iwork, liwork, info)
DSPGVD
subroutine sspgvd (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, iwork, liwork, info)
SSPGVD
subroutine zhpgvd (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHPGVD

Detailed Description

Function Documentation

subroutine chpgvd (integer itype, character jobz, character uplo, integern, complex, dimension( * ) ap, complex, dimension( * ) bp, real,dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex,dimension( * ) work, integer lwork, real, dimension( * ) rwork, integerlrwork, integer, dimension( * ) iwork, integer liwork, integer info)

CHPGVD

Purpose:

CHPGVD computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, the contents of AP are destroyed.

BP

BP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = ā€™Uā€™, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H, in the same storage
format as B.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is COMPLEX array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the matrix Z of
eigenvectors. The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.

LWORK

LWORK is INTEGER
The dimension of array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 2*N.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is REAL array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the required LRWORK.

LRWORK

LRWORK is INTEGER
The dimension of array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK >= N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPPTRF or CHPEVD returned an error code:
<= N: if INFO = i, CHPEVD failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not convergeto zero;
> N: if INFO = N + i, for 1 <= i <= n, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

subroutine dspgvd (integer itype, character jobz, character uplo, integern, double precision, dimension( * ) ap, double precision, dimension( *) bp, double precision, dimension( * ) w, double precision, dimension(ldz, * ) z, integer ldz, double precision, dimension( * ) work, integerlwork, integer, dimension( * ) iwork, integer liwork, integer info)

DSPGVD

Purpose:

DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, the contents of AP are destroyed.

BP

BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = ā€™Uā€™, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T, in the same storage
format as B.

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the matrix Z of
eigenvectors. The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= 2*N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEVD returned an error code:
<= N: if INFO = i, DSPEVD failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

subroutine sspgvd (integer itype, character jobz, character uplo, integern, real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( *) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * )work, integer lwork, integer, dimension( * ) iwork, integer liwork,integer info)

SSPGVD

Purpose:

SSPGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

AP

AP is REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, the contents of AP are destroyed.

BP

BP is REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = ā€™Uā€™, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T, in the same storage
format as B.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is REAL array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the matrix Z of
eigenvectors. The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= 2*N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPPTRF or SSPEVD returned an error code:
<= N: if INFO = i, SSPEVD failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

subroutine zhpgvd (integer itype, character jobz, character uplo, integern, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, doubleprecision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integerldz, complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,integer liwork, integer info)

ZHPGVD

Purpose:

ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, the contents of AP are destroyed.

BP

BP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = ā€™Uā€™, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

On exit, the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H, in the same storage
format as B.

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the matrix Z of
eigenvectors. The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= N.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 2*N.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the required LRWORK.

LRWORK

LRWORK is INTEGER
The dimension of array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK >= N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of array IWORK.
If JOBZ = ā€™Nā€™ or N <= 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the required sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPPTRF or ZHPEVD returned an error code:
<= N: if INFO = i, ZHPEVD failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not convergeto zero;
> N: if INFO = N + i, for 1 <= i <= n, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Author

Generated automatically by Doxygen for LAPACK from the source code.