zstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse itera- tion
SUBROUTINE ZSTEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) DOUBLE COMPLEX Z(LDZ,*) INTEGER N, M, LDZ, INFO INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*) DOUBLE PRECISION D(*), E(*), W(*), WORK(*) SUBROUTINE ZSTEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) DOUBLE COMPLEX Z(LDZ,*) INTEGER*8 N, M, LDZ, INFO INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*) DOUBLE PRECISION D(*), E(*), W(*), WORK(*) F95 INTERFACE SUBROUTINE STEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) COMPLEX(8), DIMENSION(:,:) :: Z INTEGER :: N, M, LDZ, INFO INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL REAL(8), DIMENSION(:) :: D, E, W, WORK SUBROUTINE STEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) COMPLEX(8), DIMENSION(:,:) :: Z INTEGER(8) :: N, M, LDZ, INFO INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL REAL(8), DIMENSION(:) :: D, E, W, WORK C INTERFACE #include <sunperf.h> void zstein(int n, double *d, double *e, int m, double *w, int *iblock, int *isplit, doublecomplex *z, int ldz, int *ifail, int *info); void zstein_64(long n, double *d, double *e, long m, double *w, long *iblock, long *isplit, doublecomplex *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library zstein(3P) NAME zstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse itera- tion SYNOPSIS SUBROUTINE ZSTEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) DOUBLE COMPLEX Z(LDZ,*) INTEGER N, M, LDZ, INFO INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*) DOUBLE PRECISION D(*), E(*), W(*), WORK(*) SUBROUTINE ZSTEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) DOUBLE COMPLEX Z(LDZ,*) INTEGER*8 N, M, LDZ, INFO INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*) DOUBLE PRECISION D(*), E(*), W(*), WORK(*) F95 INTERFACE SUBROUTINE STEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) COMPLEX(8), DIMENSION(:,:) :: Z INTEGER :: N, M, LDZ, INFO INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL REAL(8), DIMENSION(:) :: D, E, W, WORK SUBROUTINE STEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO) COMPLEX(8), DIMENSION(:,:) :: Z INTEGER(8) :: N, M, LDZ, INFO INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL REAL(8), DIMENSION(:) :: D, E, W, WORK C INTERFACE #include <sunperf.h> void zstein(int n, double *d, double *e, int m, double *w, int *iblock, int *isplit, doublecomplex *z, int ldz, int *ifail, int *info); void zstein_64(long n, double *d, double *e, long m, double *w, long *iblock, long *isplit, doublecomplex *z, long ldz, long *ifail, long *info); PURPOSE zstein computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration. The maximum number of iterations allowed for each eigenvector is speci- fied by an internal parameter MAXITS (currently set to 5). Although the eigenvectors are real, they are stored in a complex array, which may be passed to ZUNMTR or ZUPMTR for back transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form. ARGUMENTS N (input) The order of the matrix. N >= 0. D (input) The n diagonal elements of the tridiagonal matrix T. E (input) The (n-1) subdiagonal elements of the tridiagonal matrix T, stored in elements 1 to N-1; E(N) need not be set. M (input) The number of eigenvectors to be found. 0 <= M <= N. W (input) The first M elements of W contain the eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. ( The output array W from SSTEBZ with ORDER = 'B' is expected here. ) IBLOCK (input) The submatrix indices associated with the corresponding ei- genvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the first submatrix from the top, =2 if W(i) belongs to the sec- ond submatrix, etc. ( The output array IBLOCK from SSTEBZ is expected here. ) ISPLIT (input) The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc. ( The output array ISPLIT from SSTEBZ is expected here. ) Z (output) The computed eigenvectors. The eigenvector associated with the eigenvalue W(i) is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations. The imaginary parts of the eigen- vectors are set to zero. LDZ (input) The leading dimension of the array Z. LDZ >= max(1,N). WORK (workspace) dimension(5*N) IWORK (workspace) dimension(N) IFAIL (output) INTEGER array, dimension (M) On normal exit, all elements of IFAIL are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array IFAIL. INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, then i eigenvectors failed to converge in MAXITS iterations. Their indices are stored in array IFAIL. 7 Nov 2015 zstein(3P)