SLASDQ computes the singular value decomposition (SVD) of a real


 (upper or lower) bidiagonal matrix with diagonal D and offdiagonal


 E, accumulating the transformations if desired. Letting B denote


 the input bidiagonal matrix, the algorithm computes orthogonal


 matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose


 of P). The singular values S are overwritten on D.


 The input matrix U  is changed to U  * Q  if desired.


 The input matrix VT is changed to P**T * VT if desired.


 The input matrix C  is changed to Q**T * C  if desired.


 See "Computing  Small Singular Values of Bidiagonal Matrices With


 Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,


 LAPACK Working Note #3, for a detailed description of the algorithm.

UPLO

          UPLO is CHARACTER*1


        On entry, UPLO specifies whether the input bidiagonal matrix


        is upper or lower bidiagonal, and whether it is square are


        not.


           UPLO = 'U' or 'u'   B is upper bidiagonal.


           UPLO = 'L' or 'l'   B is lower bidiagonal.

SQRE

          SQRE is INTEGER


        = 0: then the input matrix is N-by-N.


        = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and


             (N+1)-by-N if UPLU = 'L'.


        The bidiagonal matrix has


        N = NL + NR + 1 rows and


        M = N + SQRE >= N columns.

N

          N is INTEGER


        On entry, N specifies the number of rows and columns


        in the matrix. N must be at least 0.

NCVT

          NCVT is INTEGER


        On entry, NCVT specifies the number of columns of


        the matrix VT. NCVT must be at least 0.

NRU

          NRU is INTEGER


        On entry, NRU specifies the number of rows of


        the matrix U. NRU must be at least 0.

NCC

          NCC is INTEGER


        On entry, NCC specifies the number of columns of


        the matrix C. NCC must be at least 0.

D

          D is REAL array, dimension (N)


        On entry, D contains the diagonal entries of the


        bidiagonal matrix whose SVD is desired. On normal exit,


        D contains the singular values in ascending order.

E

          E is REAL array.


        dimension is (N-1) if SQRE = 0 and N if SQRE = 1.


        On entry, the entries of E contain the offdiagonal entries


        of the bidiagonal matrix whose SVD is desired. On normal


        exit, E will contain 0. If the algorithm does not converge,


        D and E will contain the diagonal and superdiagonal entries


        of a bidiagonal matrix orthogonally equivalent to the one


        given as input.

VT

          VT is REAL array, dimension (LDVT, NCVT)


        On entry, contains a matrix which on exit has been


        premultiplied by P**T, dimension N-by-NCVT if SQRE = 0


        and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).

LDVT

          LDVT is INTEGER


        On entry, LDVT specifies the leading dimension of VT as


        declared in the calling (sub) program. LDVT must be at


        least 1. If NCVT is nonzero LDVT must also be at least N.

U

          U is REAL array, dimension (LDU, N)


        On entry, contains a  matrix which on exit has been


        postmultiplied by Q, dimension NRU-by-N if SQRE = 0


        and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).

LDU

          LDU is INTEGER


        On entry, LDU  specifies the leading dimension of U as


        declared in the calling (sub) program. LDU must be at


        least max( 1, NRU ) .

C

          C is REAL array, dimension (LDC, NCC)


        On entry, contains an N-by-NCC matrix which on exit


        has been premultiplied by Q**T  dimension N-by-NCC if SQRE = 0


        and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).

LDC

          LDC is INTEGER


        On entry, LDC  specifies the leading dimension of C as


        declared in the calling (sub) program. LDC must be at


        least 1. If NCC is nonzero, LDC must also be at least N.

WORK

          WORK is REAL array, dimension (4*N)


        Workspace. Only referenced if one of NCVT, NRU, or NCC is


        nonzero, and if N is at least 2.

INFO

          INFO is INTEGER


        On exit, a value of 0 indicates a successful exit.


        If INFO < 0, argument number -INFO is illegal.


        If INFO > 0, the algorithm did not converge, and INFO


        specifies how many superdiagonals did not converge.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2016

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA