SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, * W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, RANGE DOUBLE COMPLEX Z(LDZ,*) INTEGER N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER ISUPPZ(*), IWORK(*) DOUBLE PRECISION VL, VU, ABSTOL DOUBLE PRECISION D(*), E(*), W(*), WORK(*) SUBROUTINE ZSTEGR_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 DOUBLE COMPLEX Z(LDZ,*) INTEGER*8 N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER*8 ISUPPZ(*), IWORK(*) DOUBLE PRECISION VL, VU, ABSTOL DOUBLE PRECISION 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(8), DIMENSION(:,:) :: Z INTEGER :: N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: ISUPPZ, IWORK REAL(8) :: VL, VU, ABSTOL REAL(8), 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(8), DIMENSION(:,:) :: Z INTEGER(8) :: N, IL, IU, M, LDZ, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: ISUPPZ, IWORK REAL(8) :: VL, VU, ABSTOL REAL(8), DIMENSION(:) :: D, E, W, WORK
void zstegr(char jobz, char range, int n, double *d, double *e, double vl, double vu, int il, int iu, double abstol, int *m, double *w, doublecomplex *z, int ldz, int *isuppz, int *info);
void zstegr_64(char jobz, char range, long n, double *d, double *e, double vl, double vu, long il, long iu, double abstol, long *m, double *w, doublecomplex *z, long ldz, long *isuppz, long *info);
(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.
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.
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.