• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

zbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B.

SYNOPSIS

  SUBROUTINE ZBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, 
 *      C, LDC, WORK, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX VT(LDVT,*), U(LDU,*), C(LDC,*)
  INTEGER N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
  DOUBLE PRECISION D(*), E(*), WORK(*)

  SUBROUTINE ZBDSQR_64( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, 
 *      LDU, C, LDC, WORK, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX VT(LDVT,*), U(LDU,*), C(LDC,*)
  INTEGER*8 N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
  DOUBLE PRECISION D(*), E(*), WORK(*)

F95 INTERFACE

  SUBROUTINE BDSQR( UPLO, [N], [NCVT], [NRU], [NCC], D, E, VT, [LDVT], 
 *       U, [LDU], C, [LDC], [WORK], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:,:) :: VT, U, C
  INTEGER :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
  REAL(8), DIMENSION(:) :: D, E, WORK

  SUBROUTINE BDSQR_64( UPLO, [N], [NCVT], [NRU], [NCC], D, E, VT, 
 *       [LDVT], U, [LDU], C, [LDC], [WORK], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:,:) :: VT, U, C
  INTEGER(8) :: N, NCVT, NRU, NCC, LDVT, LDU, LDC, INFO
  REAL(8), DIMENSION(:) :: D, E, WORK

C INTERFACE

#include <sunperf.h>

void zbdsqr(char uplo, int n, int ncvt, int nru, int ncc, double *d, double *e, doublecomplex *vt, int ldvt, doublecomplex *u, int ldu, doublecomplex *c, int ldc, int *info);

void zbdsqr_64(char uplo, long n, long ncvt, long nru, long ncc, double *d, double *e, doublecomplex *vt, long ldvt, doublecomplex *u, long ldu, doublecomplex *c, long ldc, long *info);

PURPOSE

zbdsqr computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B: B = Q * S * P' (P' denotes the transpose of P), where S is a diagonal matrix with non-negative diagonal elements (the singular values of B), and Q and P are orthogonal matrices.

The routine computes S, and optionally computes U * Q, P' * VT, or Q' * C, for given complex input matrices U, VT, and C.

See ``Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy,'' by J. Demmel and W. Kahan, LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, no. 5, pp. 873-912, Sept 1990) and

``Accurate singular values and differential qd algorithms,'' by B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics Department, University of California at Berkeley, July 1992 for a detailed description of the algorithm.

ARGUMENTS

• UPLO (input)
  

   = 'U':  B is upper bidiagonal;

   = 'L':  B is lower bidiagonal.

• N (input)
  The order of the matrix B. N > = 0.

• NCVT (input)
  The number of columns of the matrix VT. NCVT > = 0.

• NRU (input)
  The number of rows of the matrix U. NRU > = 0.

• NCC (input)
  The number of columns of the matrix C. NCC > = 0.

• D (input/output)
  On entry, the n diagonal elements of the bidiagonal matrix B. On exit, if INFO =0, the singular values of B in decreasing order.

• E (input/output)
  On entry, the elements of E contain the offdiagonal elements of of the bidiagonal matrix whose SVD is desired. On normal exit (INFO = 0), E is destroyed. If the algorithm does not converge (INFO > 0), D and E will contain the diagonal and superdiagonal elements of a bidiagonal matrix orthogonally equivalent to the one given as input. E(N) is used for workspace.

• VT (input/output)
  On entry, an N-by-NCVT matrix VT. On exit, VT is overwritten by P' * VT. VT is not referenced if NCVT = 0.

• LDVT (input)
  The leading dimension of the array VT. LDVT > = max(1,N) if NCVT > 0; LDVT > = 1 if NCVT = 0.

• U (input/output)
  On entry, an NRU-by-N matrix U. On exit, U is overwritten by U * Q. U is not referenced if NRU = 0.

• LDU (input)
  The leading dimension of the array U. LDU > = max(1,NRU).

• C (input/output)
  On entry, an N-by-NCC matrix C. On exit, C is overwritten by Q' * C. C is not referenced if NCC = 0.

• LDC (input)
  The leading dimension of the array C. LDC > = max(1,N) if NCC > 0; LDC > =1 if NCC = 0.

• WORK (workspace)
  dimension (4*N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  If INFO  = -i, the i-th argument had an illegal value

   > 0:  the algorithm did not converge; D and E contain the
  elements of a bidiagonal matrix which is orthogonally
  similar to the input matrix B;  if INFO  = i, i
  elements of E have not converged to zero.