/home/abui...D/zggsvp.f(3)

💖 NAME 💖

Manual name: Library Functions Manual. Page: /home/abui...D/zggsvp.f(3).

The actual file this page is serving is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/DEPRECATED/zggsvp.f

✨ SYNOPSIS ✨

Functions/Subroutines

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

That's ZGGSVP, the subroutine in question. 💅

🦋 Function/Subroutine Documentation 🦋

subroutine ZGGSVP (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 info)

ZGGSVP is the main character here. 🫶

Purpose 💅

⚠️ Deprecated alert: this routine is deprecated and has been replaced by routine ZGGSVP3.

ZGGSVP 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 ZGGSVD.

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(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 ZGEQPF 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 262 of file zggsvp.f.

Author 🫖

Generated automatically by Doxygen for LAPACK from the source code.

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