---
name: "lasda"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/lasda"
---

# lasda(3)

lasda: D&C step: top level solver

## NAME

lasda - lasda: D&C step: top level solver

## SYNOPSIS

### Functions

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

## Detailed Description

## Function Documentation

### subroutine dlasda (integer icompq, integer smlsiz, integer n, integer sqre, double precision, dimension( \* ) d, double precision, dimension( \* ) e, double precision, dimension( ldu, \* ) u, integer ldu, double precision, dimension( ldu, \* ) vt, integer, dimension( \* ) k, double precision, dimension( ldu, \* ) difl, double precision, dimension( ldu, \* ) difr, double precision, dimension( ldu, \* ) z, double precision, dimension( ldu, \* ) poles, integer, dimension( \* ) givptr, integer, dimension( ldgcol, \* ) givcol, integer ldgcol, integer, dimension( ldgcol, \* ) perm, double precision, dimension( ldu, \* ) givnum, double precision, dimension( \* ) c, double precision, dimension( \* ) s, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**DLASDA** 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, 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.
!>
```

**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 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*

```
!>          E is DOUBLE PRECISION array, dimension ( M-1 )
!>         Contains the subdiagonal entries of the bidiagonal matrix.
!>         On exit, E has been destroyed.
!>
```

*U*

```
!>          U is 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*

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

*VT*

```
!>          VT is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( LDU, NLVL ),
!>         where NLVL = floor(log_2 (N/SMLSIZ))).
!>
```

*DIFR*

```
!>          DIFR is 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*

```
!>          Z is 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*

```
!>          POLES is 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*

```
!>          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 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*

```
!>          C is 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*

```
!>          S is 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*

```
!>          WORK is DOUBLE PRECISION 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.

**Contributors:**

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

Definition at line **270** of file **dlasda.f**.

### 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.

**Contributors:**

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

Definition at line **270** of file **slasda.f**.

## Author

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