---
name: "dlasd7.f"
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/dlasd7.f"
---

# dlasd7.f(3)

## NAME

SRC/dlasd7.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlasd7** (icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info)\
 **DLASD7** merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

## Function/Subroutine Documentation

### subroutine dlasd7 (integer icompq, integer nl, integer nr, integer sqre, integer k, double precision, dimension( \* ) d, double precision, dimension( \* ) z, double precision, dimension( \* ) zw, double precision, dimension( \* ) vf, double precision, dimension( \* ) vfw, double precision, dimension( \* ) vl, double precision, dimension( \* ) vlw, double precision alpha, double precision beta, double precision, dimension( \* ) dsigma, integer, dimension( \* ) idx, integer, dimension( \* ) idxp, integer, dimension( \* ) idxq, integer, dimension( \* ) perm, integer givptr, integer, dimension( ldgcol, \* ) givcol, integer ldgcol, double precision, dimension( ldgnum, \* ) givnum, integer ldgnum, double precision c, double precision s, integer info)

**DLASD7** merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

**Purpose:**

```
!>
!> DLASD7 merges the two sets of singular values together into a single
!> sorted set. Then it tries to deflate the size of the problem. There
!> are two ways in which deflation can occur:  when two or more singular
!> values are close together or if there is a tiny entry in the Z
!> vector. For each such occurrence the order of the related
!> secular equation problem is reduced by one.
!>
!> DLASD7 is called from DLASD6.
!>
```

**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.
!>
```

*NL*

```
!>          NL is INTEGER
!>         The row dimension of the upper block. NL >= 1.
!>
```

*NR*

```
!>          NR is INTEGER
!>         The row dimension of the lower block. NR >= 1.
!>
```

*SQRE*

```
!>          SQRE is INTEGER
!>         = 0: the lower block is an NR-by-NR square matrix.
!>         = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
!>
!>         The bidiagonal matrix has
!>         N = NL + NR + 1 rows and
!>         M = N + SQRE >= N columns.
!>
```

*K*

```
!>          K is INTEGER
!>         Contains the dimension of the non-deflated matrix, this is
!>         the order of the related secular equation. 1 <= K <=N.
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension ( N )
!>         On entry D contains the singular values of the two submatrices
!>         to be combined. On exit D contains the trailing (N-K) updated
!>         singular values (those which were deflated) sorted into
!>         increasing order.
!>
```

*Z*

```
!>          Z is DOUBLE PRECISION array, dimension ( M )
!>         On exit Z contains the updating row vector in the secular
!>         equation.
!>
```

*ZW*

```
!>          ZW is DOUBLE PRECISION array, dimension ( M )
!>         Workspace for Z.
!>
```

*VF*

```
!>          VF is DOUBLE PRECISION array, dimension ( M )
!>         On entry, VF(1:NL+1) contains the first components of all
!>         right singular vectors of the upper block; and VF(NL+2:M)
!>         contains the first components of all right singular vectors
!>         of the lower block. On exit, VF contains the first components
!>         of all right singular vectors of the bidiagonal matrix.
!>
```

*VFW*

```
!>          VFW is DOUBLE PRECISION array, dimension ( M )
!>         Workspace for VF.
!>
```

*VL*

```
!>          VL is DOUBLE PRECISION array, dimension ( M )
!>         On entry, VL(1:NL+1) contains the  last components of all
!>         right singular vectors of the upper block; and VL(NL+2:M)
!>         contains the last components of all right singular vectors
!>         of the lower block. On exit, VL contains the last components
!>         of all right singular vectors of the bidiagonal matrix.
!>
```

*VLW*

```
!>          VLW is DOUBLE PRECISION array, dimension ( M )
!>         Workspace for VL.
!>
```

*ALPHA*

```
!>          ALPHA is DOUBLE PRECISION
!>         Contains the diagonal element associated with the added row.
!>
```

*BETA*

```
!>          BETA is DOUBLE PRECISION
!>         Contains the off-diagonal element associated with the added
!>         row.
!>
```

*DSIGMA*

```
!>          DSIGMA is DOUBLE PRECISION array, dimension ( N )
!>         Contains a copy of the diagonal elements (K-1 singular values
!>         and one zero) in the secular equation.
!>
```

*IDX*

```
!>          IDX is INTEGER array, dimension ( N )
!>         This will contain the permutation used to sort the contents of
!>         D into ascending order.
!>
```

*IDXP*

```
!>          IDXP is INTEGER array, dimension ( N )
!>         This will contain the permutation used to place deflated
!>         values of D at the end of the array. On output IDXP(2:K)
!>         points to the nondeflated D-values and IDXP(K+1:N)
!>         points to the deflated singular values.
!>
```

*IDXQ*

```
!>          IDXQ is INTEGER array, dimension ( N )
!>         This contains the permutation which separately sorts the two
!>         sub-problems in D into ascending order.  Note that entries in
!>         the first half of this permutation must first be moved one
!>         position backward; and entries in the second half
!>         must first have NL+1 added to their values.
!>
```

*PERM*

```
!>          PERM is INTEGER array, dimension ( N )
!>         The permutations (from deflation and sorting) to be applied
!>         to each singular block. Not referenced if ICOMPQ = 0.
!>
```

*GIVPTR*

```
!>          GIVPTR is INTEGER
!>         The number of Givens rotations which took place in this
!>         subproblem. Not referenced if ICOMPQ = 0.
!>
```

*GIVCOL*

```
!>          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
!>         Each pair of numbers indicates a pair of columns to take place
!>         in a Givens rotation. Not referenced if ICOMPQ = 0.
!>
```

*LDGCOL*

```
!>          LDGCOL is INTEGER
!>         The leading dimension of GIVCOL, must be at least N.
!>
```

*GIVNUM*

```
!>          GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
!>         Each number indicates the C or S value to be used in the
!>         corresponding Givens rotation. Not referenced if ICOMPQ = 0.
!>
```

*LDGNUM*

```
!>          LDGNUM is INTEGER
!>         The leading dimension of GIVNUM, must be at least N.
!>
```

*C*

```
!>          C is DOUBLE PRECISION
!>         C contains garbage if SQRE =0 and the C-value of a Givens
!>         rotation related to the right null space if SQRE = 1.
!>
```

*S*

```
!>          S is DOUBLE PRECISION
!>         S contains garbage if SQRE =0 and the S-value of a Givens
!>         rotation related to the right null space if SQRE = 1.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>         = 0:  successful exit.
!>         < 0:  if INFO = -i, the i-th argument had an illegal value.
!>
```

**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 **276** of file **dlasd7.f**.

## Author

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