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

🌸 NAME 🌸

hey bestie 💖 you're reading the Library Functions Manual page for /home/abui...D/cggsvp.f(3), and the file it documents is:

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

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here's the synopsis, copy-paste exact:

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

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💅 Function/Subroutine Documentation 💅

The typed-out signature, exactly as written:

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 🦋

okay so first thing, bestie: this routine is deprecated and has been replaced by routine CGGSVP3. not me showing up late to the function party 💀 But here's the whole vibe:

!>
!> This routine is deprecated and has been replaced by routine CGGSVP3.
!>
!> 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 — CHARACTER*1; the "do we compute U?" switch.
  • = 'U': Unitary matrix U is computed.
  • = 'N': U is not computed.
• JOBV — CHARACTER*1; the "do we compute V?" switch.
  • = 'V': Unitary matrix V is computed.
  • = 'N': V is not computed.
• JOBQ — CHARACTER*1; the "do we compute Q?" switch.
  • = 'Q': Unitary matrix Q is computed.
  • = 'N': Q is not computed.
• M — INTEGER. The number of rows of the matrix A. M >= 0.
• P — INTEGER. The number of rows of the matrix B. P >= 0.
• N — INTEGER. The number of columns of the matrices A and B. N >= 0.
• A — 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,P).
• TOLA — REAL.
• TOLB — REAL.

TOLA and TOLB together 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 — INTEGER.
• L — INTEGER.

On exit, K and L specify the dimension of the subblocks described in the Purpose section. K + L = effective numerical rank of (A**H,B**H)**H.

• U — COMPLEX array, dimension (LDU,M). If JOBU = 'U', U contains the unitary matrix U. If JOBU = 'N', U is not referenced.
• LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
• V — COMPLEX array, dimension (LDV,P). If JOBV = 'V', V contains the unitary matrix V. If JOBV = 'N', V is not referenced.
• LDV — INTEGER. The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
• Q — COMPLEX array, dimension (LDQ,N). If JOBQ = 'Q', Q contains the unitary matrix Q. If JOBQ = 'N', Q is not referenced.
• LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
• IWORK — INTEGER array, dimension (N).
• RWORK — REAL array, dimension (2*N).
• TAU — COMPLEX array, dimension (N).
• WORK — COMPLEX array, dimension (max(3*N,M,P)).
• INFO — 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 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.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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