sstebz - compute the eigenvalues of a symmetric tridiagonal matrix T
SUBROUTINE SSTEBZ(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER*1 RANGE, ORDER INTEGER N, IL, IU, M, NSPLIT, INFO INTEGER IBLOCK(*), ISPLIT(*), IWORK(*) REAL VL, VU, ABSTOL REAL D(*), E(*), W(*), WORK(*) SUBROUTINE SSTEBZ_64(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER*1 RANGE, ORDER INTEGER*8 N, IL, IU, M, NSPLIT, INFO INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*) REAL VL, VU, ABSTOL REAL D(*), E(*), W(*), WORK(*) F95 INTERFACE SUBROUTINE STEBZ(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER(LEN=1) :: RANGE, ORDER INTEGER :: N, IL, IU, M, NSPLIT, INFO INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: D, E, W, WORK SUBROUTINE STEBZ_64(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER(LEN=1) :: RANGE, ORDER INTEGER(8) :: N, IL, IU, M, NSPLIT, INFO INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: D, E, W, WORK C INTERFACE #include <sunperf.h> void sstebz(char range, char order, int n, float vl, float vu, int il, int iu, float abstol, float *d, float *e, int *m, int *nsplit, float *w, int *iblock, int *isplit, int *info); void sstebz_64(char range, char order, long n, float vl, float vu, long il, long iu, float abstol, float *d, float *e, long *m, long *nsplit, float *w, long *iblock, long *isplit, long *info);
Oracle Solaris Studio Performance Library sstebz(3P) NAME sstebz - compute the eigenvalues of a symmetric tridiagonal matrix T SYNOPSIS SUBROUTINE SSTEBZ(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER*1 RANGE, ORDER INTEGER N, IL, IU, M, NSPLIT, INFO INTEGER IBLOCK(*), ISPLIT(*), IWORK(*) REAL VL, VU, ABSTOL REAL D(*), E(*), W(*), WORK(*) SUBROUTINE SSTEBZ_64(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER*1 RANGE, ORDER INTEGER*8 N, IL, IU, M, NSPLIT, INFO INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*) REAL VL, VU, ABSTOL REAL D(*), E(*), W(*), WORK(*) F95 INTERFACE SUBROUTINE STEBZ(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER(LEN=1) :: RANGE, ORDER INTEGER :: N, IL, IU, M, NSPLIT, INFO INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: D, E, W, WORK SUBROUTINE STEBZ_64(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) CHARACTER(LEN=1) :: RANGE, ORDER INTEGER(8) :: N, IL, IU, M, NSPLIT, INFO INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: D, E, W, WORK C INTERFACE #include <sunperf.h> void sstebz(char range, char order, int n, float vl, float vu, int il, int iu, float abstol, float *d, float *e, int *m, int *nsplit, float *w, int *iblock, int *isplit, int *info); void sstebz_64(char range, char order, long n, float vl, float vu, long il, long iu, float abstol, float *d, float *e, long *m, long *nsplit, float *w, long *iblock, long *isplit, long *info); PURPOSE sstebz computes the eigenvalues of a symmetric tridiagonal matrix T. The user may ask for all eigenvalues, all eigenvalues in the half-open interval (VL, VU], or the IL-th through IU-th eigenvalues. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that. See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix", Report CS41, Computer Science Dept., Stanford University, July 21, 1966. ARGUMENTS RANGE (input) = 'A': ("All") all eigenvalues will be found. = 'V': ("Value") all eigenvalues in the half-open interval (VL, VU] will be found. = 'I': ("Index") the IL-th through IU-th eigenvalues (of the entire matrix) will be found. ORDER (input) = 'B': ("By Block") the eigenvalues will be grouped by split- off block (see IBLOCK, ISPLIT) and ordered from smallest to largest within the block. = 'E': ("Entire matrix") the ei- genvalues for the entire matrix will be ordered from smallest to largest. N (input) The order of the tridiagonal matrix T. N >= 0. VL (input) If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. Eigenvalues less than or equal to VL, or greater than VU, will not be returned. 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. ABSTOL (input) The absolute tolerance for the eigenvalues. An eigenvalue (or cluster) is considered to be located if it has been determined to lie in an interval whose width is ABSTOL or less. If ABSTOL is less than or equal to zero, then ULP*|T| will be used, where |T| means the 1-norm of T. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. D (input) The n diagonal elements of the tridiagonal matrix T. E (input) The (n-1) off-diagonal elements of the tridiagonal matrix T. M (output) The actual number of eigenvalues found. 0 <= M <= N. (See also the description of INFO=2,3.) NSPLIT (output) The number of diagonal blocks in the matrix T. 1 <= NSPLIT <= N. W (output) On exit, the first M elements of W will contain the eigenval- ues. (SSTEBZ may use the remaining N-M elements as workspace.) IBLOCK (output) At each row/column j where E(j) is zero or small, the matrix T is considered to split into a block diagonal matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which block (from 1 to the number of blocks) the eigenvalue W(i) belongs. (SSTEBZ may use the remaining N-M elements as workspace.) ISPLIT (output) 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., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. (Only the first NSPLIT elements will actually be used, but since the user cannot know a priori what value NSPLIT will have, N words must be reserved for ISPLIT.) WORK (workspace) dimension(4*N) IWORK (workspace) dimension(3*N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: some or all of the eigenvalues failed to converge or were not computed: =1 or 3: Bisection failed to converge for some eigenvalues; these eigenvalues are flagged by a negative block number. The effect is that the eigenvalues may not be as accurate as the absolute and relative tolerances. This is generally caused by unexpectedly inaccurate arithmetic. =2 or 3: RANGE='I' only: Not all of the eigenvalues IL:IU were found. Effect: M < IU+1-IL Cause: non-monotonic arithmetic, causing the Sturm sequence to be non-monotonic. Cure: recalculate, using RANGE='A', and pick out eigenvalues IL:IU. = 4: RANGE='I', and the Gershgorin interval initially used was too small. No eigenvalues were computed. 7 Nov 2015 sstebz(3P)