cstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation
SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, * W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, RANGE COMPLEX Z(LDZ,*) INTEGER N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER ISUPPZ(*), IWORK(*) REAL VL, VU, ABSTOL REAL D(*), E(*), W(*), WORK(*)
SUBROUTINE CSTEGR_64( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, * M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, RANGE COMPLEX Z(LDZ,*) INTEGER*8 N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER*8 ISUPPZ(*), IWORK(*) REAL VL, VU, ABSTOL REAL D(*), E(*), W(*), WORK(*)
SUBROUTINE STEGR( JOBZ, RANGE, [N], D, E, VL, VU, IL, IU, ABSTOL, M, * W, Z, [LDZ], ISUPPZ, [WORK], [LWORK], [IWORK], [LIWORK], [INFO]) CHARACTER(LEN=1) :: JOBZ, RANGE COMPLEX, DIMENSION(:,:) :: Z INTEGER :: N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: ISUPPZ, IWORK REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: D, E, W, WORK
SUBROUTINE STEGR_64( JOBZ, RANGE, [N], D, E, VL, VU, IL, IU, ABSTOL, * M, W, Z, [LDZ], ISUPPZ, [WORK], [LWORK], [IWORK], [LIWORK], [INFO]) CHARACTER(LEN=1) :: JOBZ, RANGE COMPLEX, DIMENSION(:,:) :: Z INTEGER(8) :: N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: ISUPPZ, IWORK REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: D, E, W, WORK
#include <sunperf.h>
void cstegr(char jobz, char range, int n, float *d, float *e, float vl, float vu, int il, int iu, float abstol, int *m, float *w, complex *z, int ldz, int *isuppz, int *info);
void cstegr_64(char jobz, char range, long n, float *d, float *e, float vl, float vu, long il, long iu, float abstol, long *m, float *w, complex *z, long ldz, long *isuppz, long *info);
cstegr b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high relative accuracy by the dqds algorithm,
(c) If there is a cluster of close eigenvalues, "choose" sigma_i close to the cluster, and go to step (a),
(d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, compute the corresponding eigenvector by forming a rank-revealing twisted factorization.
The desired accuracy of the output can be specified by the input parameter ABSTOL.
For more details, see ``A new O(n^2)
algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem'', by Inderjit Dhillon,
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Note 1 : Currently CSTEGR is only set up to find ALL the n
eigenvalues and eigenvectors of T in O(n^2)
time
Note 2 : Currently the routine CSTEIN is called when an appropriate sigma_i cannot be chosen in step (c) above. CSTEIN invokes modified Gram-Schmidt when eigenvalues are close.
Note 3 : CSTEGR works only on machines which follow ieee-754 floating-point standard in their handling of infinities and NaNs. Normal execution of CSTEGR may create NaNs and infinities and hence may abort due to a floating point exception in environments which do not conform to the ieee standard.
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU] will be found. = 'I': the IL-th through IU-th eigenvalues will be found.
E(N)
need not be set.
On exit, E is overwritten.
max(1,M)
columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
WORK(1)
returns the optimal
(and minimal) LWORK.
max(1,18*N)
If LWORK = -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 LWORK is issued by XERBLA.
IWORK(1)
returns the optimal LIWORK.
max(1,10*N)
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = 1, internal error in SLARRE, if INFO = 2, internal error in CLARRV.
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Ken Stanley, Computer Science Division, University of California at Berkeley, USA