# zggsvp3.f - Man Page

SRC/zggsvp3.f

## Synopsis

### Functions/Subroutines

subroutine **zggsvp3** (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)**ZGGSVP3**

## Function/Subroutine Documentation

### subroutine zggsvp3 (character jobu, character jobv, character jobq, integer m, integer p, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision tola, double precision tolb, integer k, integer l, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) iwork, double precision, dimension( * ) rwork, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

**ZGGSVP3**

**Purpose:**

ZGGSVP3 computes unitary matrices U, V and Q such that N-K-L K L U**H*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**H*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**H,B**H)**H. This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine ZGGSVD3.

**Parameters***JOBU*JOBU is CHARACTER*1 = 'U': Unitary matrix U is computed; = 'N': U is not computed.

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

*JOBQ*JOBQ is CHARACTER*1 = 'Q': Unitary 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 COMPLEX*16 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 COMPLEX*16 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)*MAZHEPS, TOLB = MAX(P,N)*norm(B)*MAZHEPS. 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**H,B**H)**H.

*U*U is COMPLEX*16 array, dimension (LDU,M) If JOBU = 'U', U contains the unitary 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 COMPLEX*16 array, dimension (LDV,P) If JOBV = 'V', V contains the unitary 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 COMPLEX*16 array, dimension (LDQ,N) If JOBQ = 'Q', Q contains the unitary 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)

*RWORK*RWORK is DOUBLE PRECISION array, dimension (2*N)

*TAU*TAU is COMPLEX*16 array, dimension (N)

*WORK*WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*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 ZGEQP3 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. ZGGSVP3 replaces the deprecated subroutine ZGGSVP.

Definition at line **275** of file **zggsvp3.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zggsvp3(3) is an alias of zggsvp3.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK