# dggsvp.f - Man Page

SRC/DEPRECATED/dggsvp.f

## Synopsis

### Functions/Subroutines

subroutine **dggsvp** (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, info)**DGGSVP**

## Function/Subroutine Documentation

### subroutine dggsvp (character jobu, character jobv, character jobq, integer m, integer p, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision tola, double precision tolb, integer k, integer l, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) iwork, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

**DGGSVP**

**Purpose:**

This routine is deprecated and has been replaced by routine DGGSVP3. DGGSVP 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 DGGSVD.

**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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION

*TOLB*TOLB is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)

*WORK*WORK is DOUBLE PRECISION 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.

**Further Details:**The subroutine uses LAPACK subroutine DGEQPF 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 **dggsvp.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK