ZSTEQR(3F) ZSTEQR(3F)
ZSTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method
SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
DOUBLE PRECISION D( * ), E( * ), WORK( * )
COMPLEX*16 Z( LDZ, * )
ZSTEQR 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 complex Hermitian matrix can also be found
if ZHETRD or ZHPTRD or ZHBTRD 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
Hermitian matrix. On entry, Z must contain the unitary 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix. On exit, E has been destroyed.
Z (input/output) COMPLEX*16 array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the unitary 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 Hermitian matrix, and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix. If
COMPZ = 'N', then Z is not referenced.
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ZSTEQR(3F) ZSTEQR(3F)
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
eigenvectors are desired, then LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION 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 unitarily similar to the
original matrix.
ZSTEQR(3F) ZSTEQR(3F)
ZSTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method
SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
DOUBLE PRECISION D( * ), E( * ), WORK( * )
COMPLEX*16 Z( LDZ, * )
ZSTEQR 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 complex Hermitian matrix can also be found
if ZHETRD or ZHPTRD or ZHBTRD 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
Hermitian matrix. On entry, Z must contain the unitary 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix. On exit, E has been destroyed.
Z (input/output) COMPLEX*16 array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the unitary 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 Hermitian matrix, and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix. If
COMPZ = 'N', then Z is not referenced.
Page 1
ZSTEQR(3F) ZSTEQR(3F)
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
eigenvectors are desired, then LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION 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 unitarily similar to the
original matrix.
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