DSPEVD(3F) DSPEVD(3F)
DSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
DSPEVD computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric 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) 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 + (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
first superdiagonal of the tridiagonal matrix T overwrite the
corresponding elements of A, and if UPLO = 'L', the diagonal and
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DSPEVD(3F) DSPEVD(3F)
first subdiagonal of T overwrite the corresponding elements of A.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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 (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK) On exit, if LWORK > 0, WORK(1) returns the
optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If N <= 1, LWORK
must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at
least 2*N. If JOBZ = 'V' and N > 1, LWORK must be at least ( 1 +
5*N + 2*N*lg N + 2*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 the 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.
DSPEVD(3F) DSPEVD(3F)
DSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage
SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
DSPEVD computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric 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) 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 + (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
first superdiagonal of the tridiagonal matrix T overwrite the
corresponding elements of A, and if UPLO = 'L', the diagonal and
Page 1
DSPEVD(3F) DSPEVD(3F)
first subdiagonal of T overwrite the corresponding elements of A.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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 (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK) On exit, if LWORK > 0, WORK(1) returns the
optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If N <= 1, LWORK
must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at
least 2*N. If JOBZ = 'V' and N > 1, LWORK must be at least ( 1 +
5*N + 2*N*lg N + 2*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 the 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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