---
name: "dlasda"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlasda/3lapack"
---

# dlasda(3lapack)

a divide and conquer approach, DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE

## NAME

DLASDA - a divide and conquer approach, DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE

## SYNOPSIS

- SUBROUTINE DLASDA(

  ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO )

- INTEGER

  ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE

- INTEGER

  GIVCOL( LDGCOL, \* ), GIVPTR( \* ), IWORK( \* ), K( \* ), PERM( LDGCOL, \* )

- DOUBLE

  PRECISION C( \* ), D( \* ), DIFL( LDU, \* ), DIFR( LDU, \* ), E( \* ), GIVNUM( LDU, \* ), POLES( LDU, \* ), S( \* ), U( LDU, \* ), VT( LDU, \* ), WORK( \* ), Z( LDU, \* )

## PURPOSE

Using a divide and conquer approach, DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes the singular values in the SVD B = U \* S \* VT. The orthogonal matrices U and VT are optionally computed in compact form.\
 A related subroutine, DLASD0, computes the singular values and the singular vectors in explicit form.\

## ARGUMENTS

ICOMPQ (input) INTEGER Specifies whether singular vectors are to be computed in compact form, as follows = 0: Compute singular values only.\
 \= 1: Compute singular vectors of upper bidiagonal matrix in compact form. SMLSIZ (input) INTEGER The maximum size of the subproblems at the bottom of the computation tree.

- N (input) INTEGER

  The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.

- SQRE (input) INTEGER

  Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N;\
   \= 1: The bidiagonal matrix has column dimension M = N + 1.

- D (input/output) DOUBLE PRECISION array, dimension ( N )

  On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values.

- E (input) DOUBLE PRECISION array, dimension ( M-1 )

  Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.

- U (output) DOUBLE PRECISION array,

  dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left singular vector matrices of all subproblems at the bottom level.

- LDU (input) INTEGER, LDU = \> N.

  The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.

- VT (output) DOUBLE PRECISION array,

  dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right singular vector matrices of all subproblems at the bottom level.

- K (output) INTEGER array,

  dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th secular equation on the computation tree.

- DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),

  where NLVL = floor(log\_2 (N/SMLSIZ))).

- DIFR (output) DOUBLE PRECISION array,

  dimension ( LDU, 2 \* NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 \* I - 1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(1:N, 2 \* I ) contains the normalizing factors for the right singular vector matrix. See DLASD8 for details.

- Z (output) DOUBLE PRECISION array,

  dimension ( LDU, NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. The first K elements of Z(1, I) contain the components of the deflation-adjusted updating row vector for subproblems on the I-th level.

- POLES (output) DOUBLE PRECISION array,

  dimension ( LDU, 2 \* NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2\*I - 1) and POLES(1, 2\*I) contain  the new and old singular values involved in the secular equations on the I-th level. GIVPTR (output) INTEGER array, dimension ( N ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree. GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 \* NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVCOL(1, 2 \*I - 1) and GIVCOL(1, 2 \*I) record the locations of Givens rotations performed on the I-th level on the computation tree. LDGCOL (input) INTEGER, LDGCOL = \> N. The leading dimension of arrays GIVCOL and PERM.

- PERM (output) INTEGER array,

  dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records permutations done on the I-th level of the computation tree. GIVNUM (output) DOUBLE PRECISION array, dimension ( LDU,  2 \* NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVNUM(1, 2 \*I - 1) and GIVNUM(1, 2 \*I) record the C- and S- values of Givens rotations performed on the I-th level on the computation tree.

- C (output) DOUBLE PRECISION array,

  dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the I-th subproblem is not square, on exit, C( I ) contains the C-value of a Givens rotation related to the right null space of the I-th subproblem.

- S (output) DOUBLE PRECISION array, dimension ( N ) if

  ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the I-th subproblem is not square, on exit, S( I ) contains the S-value of a Givens rotation related to the right null space of the I-th subproblem.

- WORK (workspace) DOUBLE PRECISION array, dimension

  (6 \* N + (SMLSIZ + 1)\*(SMLSIZ + 1)).

- IWORK (workspace) INTEGER array.

  Dimension must be at least (7 \* N).

- INFO (output) INTEGER

  \= 0:  successful exit.\
   \< 0:  if INFO = -i, the i-th argument had an illegal value.\
   \> 0:  if INFO = 1, an singular value did not converge

## FURTHER DETAILS

Based on contributions by\
\
    Ming Gu and Huan Ren, Computer Science Division, University of\
    California at Berkeley, USA\