# slasda.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **slasda** (ICOMPQ, SMLSIZ, **N**, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)**SLASDA** computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

## Function/Subroutine Documentation

### subroutine slasda (integer ICOMPQ, integer SMLSIZ, integer N, integer SQRE, real, dimension( * ) D, real, dimension( * ) E, real, dimension( ldu, * ) U, integer LDU, real, dimension( ldu, * ) VT, integer, dimension( * ) K, real, dimension( ldu, * ) DIFL, real, dimension( ldu, * ) DIFR, real, dimension( ldu, * ) Z, real, dimension( ldu, * ) POLES, integer, dimension( * ) GIVPTR, integer, dimension( ldgcol, * ) GIVCOL, integer LDGCOL, integer, dimension( ldgcol, * ) PERM, real, dimension( ldu, * ) GIVNUM, real, dimension( * ) C, real, dimension( * ) S, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

**SLASDA** computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

**Purpose:**

Using a divide and conquer approach, SLASDA 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, SLASD0, computes the singular values and the singular vectors in explicit form.

**Parameters:***ICOMPQ*ICOMPQ is 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*SMLSIZ is INTEGER The maximum size of the subproblems at the bottom of the computation tree.

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

*SQRE*SQRE is 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*D is REAL 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*E is REAL array, dimension ( M-1 ) Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.

*U*U is REAL 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*LDU is INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.

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

*K*K is 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*DIFL is REAL array, dimension ( LDU, NLVL ), where NLVL = floor(log_2 (N/SMLSIZ))).

*DIFR*DIFR is REAL 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 SLASD8 for details.

*Z*Z is REAL 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*POLES is REAL 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*GIVPTR is 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*GIVCOL is 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*LDGCOL is INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM.

*PERM*PERM is 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*GIVNUM is REAL 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*C is REAL 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*S is REAL 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*WORK is REAL array, dimension (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

*IWORK*IWORK is INTEGER array, dimension (7*N).

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

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

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

Definition at line 275 of file slasda.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasda(3) is an alias of slasda.f(3).