dsyevx
dsyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABTOL, NFOUND, W, Z, LDZ, WORK, LDWORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION A(LDA,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSYEVX_64( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
* ABTOL, NFOUND, W, Z, LDZ, WORK, LDWORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER*8 IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION A(LDA,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SYEVX( JOBZ, RANGE, UPLO, N, A, [LDA], VL, VU, IL, IU,
* ABTOL, NFOUND, W, Z, [LDZ], [WORK], [LDWORK], [IWORK2], IFAIL,
* [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER, DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, Z
SUBROUTINE SYEVX_64( JOBZ, RANGE, UPLO, N, A, [LDA], VL, VU, IL, IU,
* ABTOL, NFOUND, W, Z, [LDZ], [WORK], [LDWORK], [IWORK2], IFAIL,
* [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: N, LDA, IL, IU, NFOUND, LDZ, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, Z
#include <sunperf.h>
void dsyevx(char jobz, char range, char uplo, int n, double *a, int lda, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, double *z, int ldz, int *ifail, int *info);
void dsyevx_64(char jobz, char range, char uplo, long n, double *a, long lda, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, double *z, long ldz, long *ifail, long *info);
dsyevx computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
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* JOBZ (input)
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* RANGE (input)
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* UPLO (input)
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* N (input)
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The order of the matrix A. N >= 0.
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* A (input/output)
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On entry, the symmetric matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO='L') or the upper
triangle (if UPLO='U') of A, including the diagonal, is
destroyed.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,N).
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* VL (input)
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If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
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* VU (input)
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See the description of VL.
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* IL (input)
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If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
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* IU (input)
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See the description of IL.
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* ABTOL (input)
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The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABTOL to
2*SLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
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* NFOUND (output)
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The total number of eigenvalues found. 0 <= NFOUND <= N.
If RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU-IL+1.
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* W (output)
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On normal exit, the first NFOUND elements contain the selected
eigenvalues in ascending order.
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* Z (input)
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If JOBZ = 'V', then if INFO = 0, the first NFOUND columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
If JOBZ = 'N', then Z is not referenced.
Note: the user must ensure that at least max(1,NFOUND) columns are
supplied in the array Z; if RANGE = 'V', the exact value of NFOUND
is not known in advance and an upper bound must be used.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
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* WORK (workspace)
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On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
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* LDWORK (input)
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The length of the array WORK. LDWORK >= max(1,8*N).
For optimal efficiency, LDWORK >= (NB+3)*N,
where NB is the max of the blocksize for SSYTRD and SORMTR
returned by ILAENV.
If LDWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LDWORK is issued by XERBLA.
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* IWORK2 (workspace)
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* IFAIL (output)
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If JOBZ = 'V', then if INFO = 0, the first NFOUND elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = 'N', then IFAIL is not referenced.
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* INFO (output)
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