zunbdb3 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns
SUBROUTINE ZUNBDB3(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) SUBROUTINE ZUNBDB3_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER*8 INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) F95 INTERFACE SUBROUTINE UNBDB3(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX21, LWORK, INFO COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 SUBROUTINE UNBDB3_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX21, LWORK, INFO COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 C INTERFACE #include <sunperf.h> void zunbdb3 (int m, int p, int q, doublecomplex *x11, int ldx11, dou- blecomplex *x21, int ldx21, double *theta, double *phi, dou- blecomplex *taup1, doublecomplex *taup2, doublecomplex *tauq1, int *info); void zunbdb3_64 (long m, long p, long q, doublecomplex *x11, long ldx11, doublecomplex *x21, long ldx21, double *theta, double *phi, doublecomplex *taup1, doublecomplex *taup2, doublecom- plex *tauq1, long *info);
Oracle Solaris Studio Performance Library zunbdb3(3P) NAME zunbdb3 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns SYNOPSIS SUBROUTINE ZUNBDB3(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) SUBROUTINE ZUNBDB3_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER*8 INFO, LWORK, M, P, Q, LDX11, LDX21 DOUBLE PRECISION PHI(*), THETA(*) DOUBLE COMPLEX TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), X11(LDX11,*), X21(LDX21,*) F95 INTERFACE SUBROUTINE UNBDB3(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER :: M, P, Q, LDX11, LDX21, LWORK, INFO COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 SUBROUTINE UNBDB3_64(M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO) INTEGER(8) :: M, P, Q, LDX11, LDX21, LWORK, INFO COMPLEX(8), DIMENSION(:) :: TAUP1, TAUP2, TAUQ1, WORK REAL(8), DIMENSION(:) :: THETA, PHI COMPLEX(8), DIMENSION(:,:) :: X11, X21 C INTERFACE #include <sunperf.h> void zunbdb3 (int m, int p, int q, doublecomplex *x11, int ldx11, dou- blecomplex *x21, int ldx21, double *theta, double *phi, dou- blecomplex *taup1, doublecomplex *taup2, doublecomplex *tauq1, int *info); void zunbdb3_64 (long m, long p, long q, doublecomplex *x11, long ldx11, doublecomplex *x21, long ldx21, double *theta, double *phi, doublecomplex *taup1, doublecomplex *taup2, doublecom- plex *tauq1, long *info); PURPOSE zunbdb3 simultaneously bidiagonalizes the blocks of a tall and skinny matrix X with orthonomal columns: [ B11 ] [ X11 ] [ P1 | ] [ 0 ] [-----] = [---------] [-----] Q1**T . [ X21 ] [ | P2 ] [ B21 ] [ 0 ] ARGUMENTS M (input) M is INTEGER The number of rows X11 plus the number of rows in X21. P (input) P is INTEGER The number of rows in X11. 0 <= P <= M. M-P <= min(P,Q,M-Q). Q (input) Q is INTEGER The number of columns in X11 and X21. 0 <= Q <= M. X11 (input/output) X11 is COMPLEX*16 array, dimension (LDX11,Q) On entry, the top block of the matrix X to be reduced. On exit, the columns of tril(X11) specify reflectors for P1 and the rows of triu(X11,1) specify reflectors for Q1. LDX11 (input) LDX11 is INTEGER The leading dimension of X11. LDX11 >= P. X21 (input/output) X21 is COMPLEX*16 array, dimension (LDX21,Q) On entry, the bottom block of the matrix X to be reduced. On exit, the columns of tril(X21) specify reflectors for P2. LDX21 (input) LDX21 is INTEGER The leading dimension of X21. LDX21 >= M-P. THETA (output) THETA is DOUBLE PRECISION array, dimension (Q) The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details. PHI (output) PHI is DOUBLE PRECISION array, dimension (Q-1) The entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. See Further Details. TAUP1 (output) TAUP1 is COMPLEX*16 array, dimension (P) The scalar factors of the elementary reflectors that define P1. TAUP2 (output) TAUP2 is COMPLEX*16 array, dimension (M-P) The scalar factors of the elementary reflectors that define P2. TAUQ1 (output) TAUQ1 is COMPLEX*16 array, dimension (Q) The scalar factors of the elementary reflectors that define Q1. WORK (output) WORK is COMPLEX*16 array, dimension (LWORK) LWORK (input) LWORK is INTEGER The dimension of the array WORK. LWORK >= M-Q. 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. INFO (output) INFO is INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. FURTHER DETAILS The upper-bidiagonal blocks B11, B21 are represented implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry in each bidiagonal band is a product of a sine or cosine of a THETA with a sine or cosine of a PHI. See [1] or ZUNCSD for details. P1, P2, and Q1 are represented as products of elementary reflectors. See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR and ZUNGLQ. 7 Nov 2015 zunbdb3(3P)