Man page - hpgv(3)

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Manual

hpgv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpgv (integer itype, character jobz, character uplo, integer n,complex, dimension( * ) ap, complex, dimension( * ) bp, real,dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex,dimension( * ) work, real, dimension( * ) rwork, integer info)
subroutine dspgv (integer itype, character jobz, character uplo, integer n,double precision, dimension( * ) ap, double precision, dimension( * )bp, double precision, dimension( * ) w, double precision, dimension(ldz, * ) z, integer ldz, double precision, dimension( * ) work, integerinfo)
subroutine sspgv (integer itype, character jobz, character uplo, integer n,real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * )w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,integer info)
subroutine zhpgv (integer itype, character jobz, character uplo, integer n,complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, doubleprecision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integerldz, complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)
Author

NAME

hpgv - {hp,sp}gv: eig, QR iteration

SYNOPSIS

Functions

subroutine chpgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork, info)
CHPGV
subroutine dspgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)
DSPGV
subroutine sspgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)
SSPGV
subroutine zhpgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork, info)
ZHPGV

Detailed Description

Function Documentation

subroutine chpgv (integer itype, character jobz, character uplo, integer n,complex, dimension( * ) ap, complex, dimension( * ) bp, real,dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex,dimension( * ) work, real, dimension( * ) rwork, integer info)

CHPGV

Purpose:

CHPGV 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.

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, 2*N-1))

RWORK

RWORK is REAL array, dimension (max(1, 3*N-2))

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPPTRF or CHPEV returned an error code:
<= N: if INFO = i, CHPEV 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.

subroutine dspgv (integer itype, character jobz, character uplo, integer n,double precision, dimension( * ) ap, double precision, dimension( * )bp, double precision, dimension( * ) w, double precision, dimension(ldz, * ) z, integer ldz, double precision, dimension( * ) work, integerinfo)

DSPGV

Purpose:

DSPGV 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.

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 (3*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEV returned an error code:
<= N: if INFO = i, DSPEV 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.

subroutine sspgv (integer itype, character jobz, character uplo, integer n,real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * )w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,integer info)

SSPGV

Purpose:

SSPGV 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.

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 (3*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPPTRF or SSPEV returned an error code:
<= N: if INFO = i, SSPEV 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.

subroutine zhpgv (integer itype, character jobz, character uplo, integer n,complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, doubleprecision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integerldz, complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)

ZHPGV

Purpose:

ZHPGV 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.

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, 2*N-1))

RWORK

RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPPTRF or ZHPEV returned an error code:
<= N: if INFO = i, ZHPEV 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.

Author

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