/home/abui...D/dggsvp.f(3)

💅 NAME

okay bestie, this is the page for /home/abui...D/dggsvp.f(3) from the LAPACK Library Functions Manual — and it's all about DGGSVP, the deprecated-but-still-doing-her-thing preprocessing routine. 💖

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✨ SYNOPSIS

🧚 Functions/Subroutines

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

DGGSVP — yes ma'am, that's the name. 💅

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🔥 Function/Subroutine Documentation

subroutine DGGSVP (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 info)

DGGSVP

🎀 Purpose

Deprecated alert 🚨 This routine is deprecated and has been replaced by routine DGGSVP3.

DGGSVP 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 DGGSVD. ✨

🦋 Parameters

• JOBU — JOBU is CHARACTER*1; = 'U': orthogonal matrix U is computed; = 'N': U is not computed.
• JOBV — JOBV is CHARACTER*1; = 'V': orthogonal matrix V is computed; = 'N': V is not computed.
• JOBQ — JOBQ is CHARACTER*1; = 'Q': orthogonal 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 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 — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• B — B is 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 — 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)*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 — K is INTEGER.
• L — L is 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 — U is DOUBLE PRECISION array, dimension (LDU,M). If JOBU = 'U', U contains the orthogonal 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 DOUBLE PRECISION array, dimension (LDV,P). If JOBV = 'V', V contains the orthogonal 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 DOUBLE PRECISION array, dimension (LDQ,N). If JOBQ = 'Q', Q contains the orthogonal 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).
• TAU — TAU is DOUBLE PRECISION array, dimension (N).
• WORK — WORK is DOUBLE PRECISION 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 DGEQPF 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 253 of file dggsvp.f.

💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 LAPACK, Version 3.12.0 — page path /home/abui...D/dggsvp.f(3). That's the whole tea, bestie — stay slay! 💅✨