SRC/DEPRECATED/cggsvp.f(3)

🌸 SRC/DEPRECATED/cggsvp.f(3) 🌸

okay bestie, welcome to the Library Functions Manual page for SRC/DEPRECATED/cggsvp.f. This is the deprecated LAPACK corner of the universe, and we are keeping every single detail intact. 💅

🌸 NAME 🌸

SRC/DEPRECATED/cggsvp.f — that's the file, bestie. No cap.

✨ SYNOPSIS ✨

Functions/Subroutines

There is literally one subroutine here and it is giving main character energy:

subroutine cggsvp (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)
    CGGSVP

🫶 Function/Subroutine Documentation 🫶

cggsvp

subroutine cggsvp (character jobu, character jobv, character jobq, integer
    m, integer p, integer n, complex, dimension( lda, * ) a, integer lda,
    complex, dimension( ldb, * ) b, integer ldb, real tola, real tolb,
    integer k, integer l, complex, dimension( ldu, * ) u, integer ldu,
    complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldq, *
    ) q, integer ldq, integer, dimension( * ) iwork, real, dimension( * )
    rwork, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer info)
    CGGSVP

Purpose 🎯

The page says it directly: this routine is deprecated and has been replaced by routine CGGSVP3. Not me being dramatic, that is literally the situation. 💀

CGGSVP 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 CGGSVD. 💖

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 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 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**H,B**H)**H.
• U — U is COMPLEX 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 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 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 REAL array, dimension (2*N).
• TAU — TAU is COMPLEX array, dimension (N).
• WORK — WORK is COMPLEX 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 👑

The author list is literally:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🔥 Further Details 🔥

The subroutine uses LAPACK subroutine CGEQPF 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 259 of file cggsvp.f.

💅 Author (generated version) 💅

Generated automatically by Doxygen for LAPACK from the source code.

✨ that's the whole page, bestie. Sign-off vibe: LAPACK Version 3.12.0, source SRC/DEPRECATED/cggsvp.f(3), and no date listed in the footer — love that for us. 💖🎀