table of contents
| hpev(3) | LAPACK | hpev(3) |
NAME¶
hpev - {hp,sp}ev: eig, QR iteration
SYNOPSIS¶
Functions¶
subroutine chpev (jobz, uplo, n, ap, w, z, ldz, work,
rwork, info)
CHPEV computes the eigenvalues and, optionally, the left and/or right
eigenvectors for OTHER matrices subroutine dspev (jobz, uplo, n,
ap, w, z, ldz, work, info)
DSPEV computes the eigenvalues and, optionally, the left and/or right
eigenvectors for OTHER matrices subroutine sspev (jobz, uplo, n,
ap, w, z, ldz, work, info)
SSPEV computes the eigenvalues and, optionally, the left and/or right
eigenvectors for OTHER matrices subroutine zhpev (jobz, uplo, n,
ap, w, z, ldz, work, rwork, info)
ZHPEV computes the eigenvalues and, optionally, the left and/or right
eigenvectors for OTHER matrices
Detailed Description¶
Function Documentation¶
subroutine chpev (character jobz, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)¶
CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Purpose:
CHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.
Parameters
JOBZ
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
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 = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dspev (character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)¶
DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Purpose:
DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage.
Parameters
JOBZ
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
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 = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sspev (character jobz, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)¶
SSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Purpose:
SSPEV computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage.
Parameters
JOBZ
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
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 = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zhpev (character jobz, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)¶
ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Purpose:
ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.
Parameters
JOBZ
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
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 = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |