SRC/dggsvp3.f(3)

💅 SRC/dggsvp3.f(3)

okay so bestie, this page is SRC/dggsvp3.f(3) from the Library Functions Manual, and it’s all about DGGSVP3 — the LAPACK routine that does the preprocessing step for the Generalized Singular Value Decomposition (GSVD). no cap, we’re keeping every single argument, threshold, and rank tea. let’s go ✨

🌸 NAME

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)
• DGGSVP3

💖 Function/Subroutine Documentation

okay here’s the full signature, character-for-character, bestie — do not lose a comma:

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.

🎀 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 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 — 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 the 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 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)*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 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 the 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 the 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 the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
• IWORK — INTEGER array, dimension (N).
• TAU — DOUBLE PRECISION array, dimension (N).
• 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. 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.
• 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.

🚨 tea: 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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k bye bestie 💖 this iconic little page is LAPACK, version 3.12.0, from SRC/dggsvp3.f(3) — and yes, she ate. periodt. 🌈