/home/abui.../cggsvp3.f(3)

🦋 /home/abui.../cggsvp3.f(3) — Library Functions Manual 🦋

okay so bestie, welcome to the Library Functions Manual page for /home/abui.../cggsvp3.f(3). We're in LAPACK 3.12.0 land, file cggsvp3.f, and this subroutine is lowkey main character energy. Buckle up. 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cggsvp3.f

🦋 SYNOPSIS 🦋

🧁 Functions/Subroutines 🧁

subroutine CGGSVP3 (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)

CGGSVP3

👑 Function/Subroutine Documentation 👑

🌈 subroutine CGGSVP3 🌈

subroutine CGGSVP3 (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 lwork, integer info)

CGGSVP3

💖 Purpose 💖

Okay so here's the whole point, bestie: CGGSVP3 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 CGGSVD3. 🫶

🌟 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(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 CGEQP3 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.

🚨 CGGSVP3 replaces the deprecated subroutine CGGSVP. Not me being dramatic, it literally says deprecated.

Definition at line 275 of file cggsvp3.f.

🧚 Author 🧚

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