SSTEQR(3F) SSTEQR(3F)
SSTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method
SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
SSTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method. The
eigenvectors of a full or band symmetric matrix can also be found if
SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to
tridiagonal form.
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'V': Compute eigenvalues and eigenvectors of the original
symmetric matrix. On entry, Z must contain the orthogonal matrix
used to reduce the original matrix to tridiagonal form. = 'I':
Compute eigenvalues and eigenvectors of the tridiagonal matrix.
Z is initialized to the identity matrix.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On
exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix. On exit, E has been destroyed.
Z (input/output) REAL array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the orthogonal matrix
used in the reduction to tridiagonal form. On exit, if INFO = 0,
then if COMPZ = 'V', Z contains the orthonormal eigenvectors of
the original symmetric matrix, and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix. If
COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
eigenvectors are desired, then LDZ >= max(1,N).
Page 1
SSTEQR(3F) SSTEQR(3F)
WORK (workspace) REAL array, dimension (max(1,2*N-2))
If COMPZ = 'N', then WORK is not referenced.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in a
total of 30*N iterations; if INFO = i, then i elements of E have
not converged to zero; on exit, D and E contain the elements of a
symmetric tridiagonal matrix which is orthogonally similar to the
original matrix.
SSTEQR(3F) SSTEQR(3F)
SSTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method
SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
SSTEQR computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method. The
eigenvectors of a full or band symmetric matrix can also be found if
SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to
tridiagonal form.
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'V': Compute eigenvalues and eigenvectors of the original
symmetric matrix. On entry, Z must contain the orthogonal matrix
used to reduce the original matrix to tridiagonal form. = 'I':
Compute eigenvalues and eigenvectors of the tridiagonal matrix.
Z is initialized to the identity matrix.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On
exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix. On exit, E has been destroyed.
Z (input/output) REAL array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the orthogonal matrix
used in the reduction to tridiagonal form. On exit, if INFO = 0,
then if COMPZ = 'V', Z contains the orthonormal eigenvectors of
the original symmetric matrix, and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix. If
COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
eigenvectors are desired, then LDZ >= max(1,N).
Page 1
SSTEQR(3F) SSTEQR(3F)
WORK (workspace) REAL array, dimension (max(1,2*N-2))
If COMPZ = 'N', then WORK is not referenced.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: the algorithm has failed to find all the eigenvalues in a
total of 30*N iterations; if INFO = i, then i elements of E have
not converged to zero; on exit, D and E contain the elements of a
symmetric tridiagonal matrix which is orthogonally similar to the
original matrix.
PPPPaaaaggggeeee 2222 [ Back ]
|
