# ?lasdq

Computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by ?bdsdc.

## Syntax

call slasdq( uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info )

call dlasdq( uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info )

## Description

The routine ?lasdq computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal d and off-diagonal e, accumulating the transformations if desired. If B is the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that `B = Q*S*PT`. 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 `PT*VT` if desired.

The input matrix C is changed to `QT*C` if desired.

## Input Parameters

uplo

  CHARACTER*1. On entry, uplo specifies whether the input bidiagonal matrix is upper or lower bidiagonal.

  If `uplo = 'U'` or 'u' , B is upper bidiagonal;

  If `uplo = 'L'` or 'l' , B is lower bidiagonal.

sqre

  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

  INTEGER. On entry, n specifies the number of rows and columns in the matrix. n must be at least 0.

ncvt

  INTEGER. On entry, ncvt specifies the number of columns of the matrix VT. ncvt must be at least 0.

nru

  INTEGER. On entry, nru specifies the number of rows of the matrix U. nru must be at least 0.

ncc

  INTEGER. On entry, ncc specifies the number of columns of the matrix C. ncc must be at least 0.

d

  REAL for slasdq

  DOUBLE PRECISION for dlasdq.

  Array, DIMENSION (n). On entry, d contains the diagonal entries of the bidiagonal matrix.

e

  REAL for slasdq

  DOUBLE PRECISION for dlasdq.

  Array, DIMENSION is (n-1) if `sqre = 0` and n if `sqre = 1`. On entry, the entries of e contain the off-diagonal entries of the bidiagonal matrix.

vt

  REAL for slasdq

  DOUBLE PRECISION for dlasdq.

  Array, DIMENSION (ldvt, ncvt). On entry, contains a matrix which on exit has been premultiplied by PT, dimension n-by-ncvt if `sqre = 0` and (n+1)-by-ncvt if `sqre = 1` (not referenced if ncvt=0).

ldvt

  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

  REAL for slasdq

  DOUBLE PRECISION for dlasdq.

  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

  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

  REAL for slasdq

  DOUBLE PRECISION for dlasdq.

  Array, DIMENSION (ldc, ncc). On entry, contains an n-by-ncc matrix which on exit has been premultiplied by Q', dimension n-by-ncc if `sqre = 0` and (n+1)-by-ncc if `sqre = 1` (not referenced if ncc=0).

ldc

  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 non-zero, ldc must also be at least n.

work

  REAL for slasdq

  DOUBLE PRECISION for dlasdq.

  Array, DIMENSION (4n). This is a workspace array. Only referenced if one of ncvt, nru, or ncc is nonzero, and if n is at least 2.

## Output Parameters

d

  On normal exit, d contains the singular values in ascending order.

e

  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

  On exit, the matrix has been premultiplied by P'.

u

  On exit, the matrix has been postmultiplied by Q.

c

  On exit, the matrix has been premultiplied by Q'.

info

  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.

Parent topic: Auxiliary Routines