dlasq1 - compute the singular values of a real square bidiagonal matrix. Used by sbdsqr
SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) INTEGER INFO, N DOUBLE PRECISION D(*), E(*), WORK(*) SUBROUTINE DLASQ1_64( N, D, E, WORK, INFO ) INTEGER*8 INFO, N DOUBLE PRECISION D(*), E(*), WORK(*) F95 INTERFACE SUBROUTINE LASQ1( N, D, E, WORK, INFO ) INTEGER :: N, INFO REAL(8), DIMENSION(:) :: D, E, WORK SUBROUTINE LASQ1_64( N, D, E, WORK, INFO ) INTEGER(8) :: N, INFO REAL(8), DIMENSION(:) :: D, E, WORK C INTERFACE #include <sunperf.h> void dlasq1 (int n, double *d, double *e, int *info); void dlasq1_64 (long n, double *d, double *e, long *info);
Oracle Solaris Studio Performance Library dlasq1(3P) NAME dlasq1 - compute the singular values of a real square bidiagonal matrix. Used by sbdsqr SYNOPSIS SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) INTEGER INFO, N DOUBLE PRECISION D(*), E(*), WORK(*) SUBROUTINE DLASQ1_64( N, D, E, WORK, INFO ) INTEGER*8 INFO, N DOUBLE PRECISION D(*), E(*), WORK(*) F95 INTERFACE SUBROUTINE LASQ1( N, D, E, WORK, INFO ) INTEGER :: N, INFO REAL(8), DIMENSION(:) :: D, E, WORK SUBROUTINE LASQ1_64( N, D, E, WORK, INFO ) INTEGER(8) :: N, INFO REAL(8), DIMENSION(:) :: D, E, WORK C INTERFACE #include <sunperf.h> void dlasq1 (int n, double *d, double *e, int *info); void dlasq1_64 (long n, double *d, double *e, long *info); PURPOSE dlasq1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. The algorithm was first presented in "Accurate singular values and differential qd algorithms" by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994, and the present implementation is described in "An implementation of the dqds Algorithm (Positive Case)", LAPACK Working Note. ARGUMENTS N (input) N is INTEGER The number of rows and columns in the matrix. N >= 0. D (input/output) D is DOUBLE PRECISION array, dimension (N) On entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in decreasing order. E (input/output) E is DOUBLE PRECISION array, dimension (N) On entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E is overwritten. WORK (output) WORK is DOUBLE PRECISION array, dimension (4*N) INFO (output) INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: the algorithm failed = 1, a split was marked by a positive value in E = 2, current block of Z not diagonalized after 100*N iterations (in inner while loop) On exit D and E represent a matrix with the same singular values which the calling subroutine could use to finish the computation, or even feed back into DLASQ1 = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks) 7 Nov 2015 dlasq1(3P)