SRC/DEPRECATED/zggsvp.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

💖 NAME 💖

Bestie, this is SRC/DEPRECATED/zggsvp.f, straight out of the Library Functions Manual. Buckle up — it’s giving deprecated-but-iconic linear algebra energy. 💅

✨ 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)

ZGGSVP

🎀 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

💫 Purpose 💫

Okay so first thing, no cap: this routine is deprecated and has been replaced by routine ZGGSVP3. Not me being dramatic — that’s literally the docs. 🫶

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. Slay. 🔥

🦋 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. Important vibe check. 🫶

K

K is INTEGER.

L

L is 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

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 👑

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