CHPEVD(3F) CHPEVD(3F)
CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage
SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) 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 + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*nj)/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
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CHPEVD(3F) CHPEVD(3F)
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 (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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 (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of array WORK. If N <= 1, LWORK must
be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least
N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
RWORK (workspace/output) REAL array,
dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
optimal LRWORK.
LRWORK (input) INTEGER
The dimension of array RWORK. If N <= 1, LRWORK
must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at
least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
4*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k such
that 2**k >= N.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK
must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at
least 2 + 5*N.
INFO (output) 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 offdiagonal
elements of an intermediate tridiagonal form did not
converge to zero.
CHPEVD(3F) CHPEVD(3F)
CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage
SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
LRWORK, IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) 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 + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*nj)/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
Page 1
CHPEVD(3F) CHPEVD(3F)
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 (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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 (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of array WORK. If N <= 1, LWORK must
be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least
N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
RWORK (workspace/output) REAL array,
dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
optimal LRWORK.
LRWORK (input) INTEGER
The dimension of array RWORK. If N <= 1, LRWORK
must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at
least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
4*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k such
that 2**k >= N.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK
must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at
least 2 + 5*N.
INFO (output) 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 offdiagonal
elements of an intermediate tridiagonal form did not
converge to zero.
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