dstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
SUBROUTINE DSTEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE INTEGER N, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE DSTEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE STEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE INTEGER :: N, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: D, E, W, WORK REAL(8), DIMENSION(:,:) :: Z SUBROUTINE STEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: D, E, W, WORK REAL(8), DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void dstevx(char jobz, char range, int n, double *d, double *e, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, double *z, int ldz, int *ifail, int *info); void dstevx_64(char jobz, char range, long n, double *d, double *e, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, double *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library dstevx(3P) NAME dstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A SYNOPSIS SUBROUTINE DSTEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE INTEGER N, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE DSTEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE STEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE INTEGER :: N, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: D, E, W, WORK REAL(8), DIMENSION(:,:) :: Z SUBROUTINE STEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: D, E, W, WORK REAL(8), DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void dstevx(char jobz, char range, int n, double *d, double *e, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, double *z, int ldz, int *ifail, int *info); void dstevx_64(char jobz, char range, long n, double *d, double *e, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, double *z, long ldz, long *ifail, long *info); PURPOSE dstevx computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. ARGUMENTS JOBZ (input) = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. RANGE (input) = '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. N (input) The order of the matrix. N >= 0. D (input/output) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, D may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues. E (input/output) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A in elements 1 to N-1 of E; E(N) need not be set. On exit, E may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues. VL (input) 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'. VU (input) See the description of VL. IL (input) If RANGE='I', the indices (in ascending order) of the small- est 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'. IU (input) See the description of IL. ABTOL (input) The absolute error tolerance for the eigenvalues. An approx- imate eigenvalue is accepted as converged when it is deter- mined 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. Eigenvalues will be computed most accurately when ABTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABTOL to 2*DLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. NFOUND (output) The total number of eigenvalues found. 0 <= NFOUND <= N. If RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU- IL+1. W (output) The first NFOUND elements contain the selected eigenvalues in ascending order. Z (output) If JOBZ = 'V', then if INFO = 0, the first NFOUND columns of Z contain the orthonormal eigenvectors of the matrix A corre- sponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigen- vector fails to converge (INFO > 0), 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. LDZ (input) The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK (workspace) dimension(5*N) IWORK2 (workspace) INTEGER array, dimension (5*N) IFAIL (output) INTEGER array, dimension (N) 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. 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. Their indices are stored in array IFAIL. 7 Nov 2015 dstevx(3P)