SRC/zggsvp3.f(3)

Welcome to SRC/zggsvp3.f(3), brought to you by the Library Functions Manual — yes, that's the header, and we're folding it in like a cute little intro. 💅 This page is all about zggsvp3, and she is lowkey iconic.

✨ NAME ✨

SRC/zggsvp3.f — that's the file, periodt. 🎀

🌸 SYNOPSIS 🌸

Functions/Subroutines

       subroutine zggsvp3 (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)
           ZGGSVP3

🦋 Function/Subroutine Documentation 🦋

subroutine zggsvp3

subroutine zggsvp3 (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 lwork, integer info)
    ZGGSVP3

ZGGSVP3 — main character energy, no cap. 👑

Purpose:

Okay so bestie, here's the whole slay: ZGGSVP3 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 ZGGSVD3. It's giving "prep work before the main event" and honestly? Obsessed. 💖

Parameters

• JOBU — CHARACTER*1. 'U': Unitary matrix U is computed; 'N': U is not computed. Choose your fighter. 🦋
• JOBV — CHARACTER*1. 'V': Unitary matrix V is computed; 'N': V is not computed.
• JOBQ — CHARACTER*1. '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*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. She goes in one way and comes out iconic. ✨
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,P).
• TOLA — DOUBLE PRECISION.
• TOLB — 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. So like, choose your tolerance wisely, bestie. 🎀
• 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*16 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*16 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*16 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 — DOUBLE PRECISION array, dimension (2*N).
• TAU — COMPLEX*16 array, dimension (N).
• WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. She's the workspace queen. 👑
• LWORK — INTEGER. The dimension of the array WORK. LWORK >= 1.

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. It's giving "just asking for the vibe check, not the whole fit." 💅

• 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.

Academic icons only. 🎓✨

Further Details:

Real talk: the subroutine uses LAPACK subroutine ZGEQP3 for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix — yes, "the a matrix", that's the original tea, bestie 😭. It may be replaced by a better rank determination strategy.

🚨 Warning, bestie: ZGGSVP3 replaces the deprecated subroutine ZGGSVP. Deprecated means don't start new stuff with it unless you have a time machine. 💀

Definition at line 275 of file zggsvp3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. Yes, the robots wrote the footer, and they ate. 🫶

---

Okay that's the whole page, bestie — LAPACK Version 3.12.0, source file SRC/zggsvp3.f(3), and the footer is serving source-code realness. 💖✨