/home/abui.../zggsvp3.f(3)

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zggsvp3.f

That’s the file, periodt 💅

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🦋 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

🎀 Purpose 🎀

okay so here’s the whole glow-up it performs, exactly:

!>
!> 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.
!>

🍓 Parameters 🍓

• JOBU — CHARACTER*1; = 'U': unitary matrix U is computed; = 'N': U is not computed.
• 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.
• 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.

so 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.

• K — INTEGER.
• L — 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 — 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.
• LWORK — 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 — 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 ZGEQP3 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.
• ZGGSVP3 replaces the deprecated subroutine ZGGSVP.

⚠️ okay bestie, that last one is a real note: ZGGSVP is deprecated, and ZGGSVP3 is the replacement. Slay for upgrades, but don’t miss that detail 💀✨

Definition at line 275 of file zggsvp3.f.

👑 Author 👑

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