/home/abui.../dggsvp3.f(3)

💖 DGGSVP3 💖

Okay bestie, this one is straight from the LAPACK Library Functions Manual — and it's giving major orthogonal-matrix main character energy. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dggsvp3.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DGGSVP3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola,
     tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, lwork, info)

Yup, that's DGGSVP3 — say it with me, bestie. 💅

🦋 Function/Subroutine Documentation 🦋

subroutine DGGSVP3 (character jobu, character jobv, character jobq, integer
     m, integer p, integer n, double precision, dimension( lda, * ) a,
     integer lda, double precision, dimension( ldb, * ) b, integer ldb,
     double precision tola, double precision tolb, integer k, integer l,
     double precision, dimension( ldu, * ) u, integer ldu, double precision,
     dimension( ldv, * ) v, integer ldv, double precision, dimension( ldq, *
     ) q, integer ldq, integer, dimension( * ) iwork, double precision,
     dimension( * ) tau, double precision, dimension( * ) work, integer
     lwork, integer info)

DGGSVP3 💖

Purpose:

!>
!> DGGSVP3 computes orthogonal matrices U, V and Q such that
!>
!>                    N-K-L  K    L
!>  U**T*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**T*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**T,B**T)**T.
!>
!> This decomposition is the preprocessing step for computing the
!> Generalized Singular Value Decomposition (GSVD), see subroutine
!> DGGSVD3.
!>

So cute, so triangular. 🎀

Parameters

• JOBU (CHARACTER*1) — = 'U': orthogonal matrix U is computed; = 'N': U is not computed.
• JOBV (CHARACTER*1) — = 'V': orthogonal matrix V is computed; = 'N': V is not computed.
• JOBQ (CHARACTER*1) — = 'Q': orthogonal matrix Q is computed; = 'N': Q is not computed.
• M (INTEGER) — the number of rows of matrix A. M >= 0.
• P (INTEGER) — the number of rows of matrix B. P >= 0.
• N (INTEGER) — the number of columns of matrices A and B. N >= 0.
• A (DOUBLE PRECISION 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 array A. LDA >= max(1,M).
• B (DOUBLE PRECISION 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 array B. LDB >= max(1,P).
• TOLA (DOUBLE PRECISION) — threshold bestie, described together with TOLB right below.
• 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)*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) — K is 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**T,B**T)**T.
• U (DOUBLE PRECISION array, dimension (LDU,M)) — if JOBU = 'U', U contains the orthogonal matrix U. If JOBU = 'N', U is not referenced.
• LDU (INTEGER) — the leading dimension of array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
• V (DOUBLE PRECISION array, dimension (LDV,P)) — if JOBV = 'V', V contains the orthogonal matrix V. If JOBV = 'N', V is not referenced.
• LDV (INTEGER) — the leading dimension of array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
• Q (DOUBLE PRECISION array, dimension (LDQ,N)) — if JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ = 'N', Q is not referenced.
• LDQ (INTEGER) — the leading dimension of array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
• IWORK (INTEGER array, dimension (N)) — that's the whole spec, bestie.
• TAU (DOUBLE PRECISION array, dimension (N)) — also exactly that.
• WORK (DOUBLE PRECISION 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 DGEQP3 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.

Deprecated alert, bestie: DGGSVP3 replaces the deprecated subroutine DGGSVP.

Definition at line 269 of file dggsvp3.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. LAPACK Version 3.12.0, from <code>/home/abui.../dggsvp3.f(3)</code> — slay and stay orthogonal. 💅✨