# sggsvp.f man page

sggsvp.f —

## Synopsis

### Functions/Subroutines

subroutinesggsvp(JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO)SGGSVP

## Function/Subroutine Documentation

### subroutine sggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, realTOLA, realTOLB, integerK, integerL, real, dimension( ldu, * )U, integerLDU, real, dimension( ldv, * )V, integerLDV, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )IWORK, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)

**SGGSVP**

**Purpose:**

```
SGGSVP computes orthogonal matrices U, V and Q such that
N-K-L K L
U**T*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )
N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )
N-K-L K L
V**T*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )
where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T.
This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
SGGSVD.
```

**Parameters:**

*JOBU*

```
JOBU is CHARACTER*1
= 'U': Orthogonal matrix U is computed;
= 'N': U is not computed.
```

*JOBV*

```
JOBV is CHARACTER*1
= 'V': Orthogonal matrix V is computed;
= 'N': V is not computed.
```

*JOBQ*

```
JOBQ is CHARACTER*1
= 'Q': Orthogonal matrix Q is computed;
= 'N': Q is not computed.
```

*M*

```
M is INTEGER
The number of rows of the matrix A. M >= 0.
```

*P*

```
P is INTEGER
The number of rows of the matrix B. P >= 0.
```

*N*

```
N is INTEGER
The number of columns of the matrices A and B. N >= 0.
```

*A*

```
A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.
```

*LDA*

```
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
```

*B*

```
B is REAL array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.
```

*LDB*

```
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).
```

*TOLA*

`TOLA is REAL`

*TOLB*

```
TOLB is REAL
TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.
```

*K*

`K is INTEGER`

*L*

```
L is INTEGER
On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A**T,B**T)**T.
```

*U*

```
U is REAL array, dimension (LDU,M)
If JOBU = 'U', U contains the orthogonal matrix U.
If JOBU = 'N', U is not referenced.
```

*LDU*

```
LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = 'U'; LDU >= 1 otherwise.
```

*V*

```
V is REAL array, dimension (LDV,P)
If JOBV = 'V', V contains the orthogonal matrix V.
If JOBV = 'N', V is not referenced.
```

*LDV*

```
LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = 'V'; LDV >= 1 otherwise.
```

*Q*

```
Q is REAL array, dimension (LDQ,N)
If JOBQ = 'Q', Q contains the orthogonal matrix Q.
If JOBQ = 'N', Q is not referenced.
```

*LDQ*

```
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = 'Q'; LDQ >= 1 otherwise.
```

*IWORK*

`IWORK is INTEGER array, dimension (N)`

*TAU*

`TAU is REAL array, dimension (N)`

*WORK*

`WORK is REAL array, dimension (max(3*N,M,P))`

*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.

**Date:**

November 2011

**Further Details:**

The subroutine uses LAPACK subroutine SGEQPF for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix. It may be replaced by a better rank determination strategy.

Definition at line 253 of file sggsvp.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

sggsvp(3) is an alias of sggsvp.f(3).