SRC/DEPRECATED/dggsvp.f(3)

✨ NAME ✨

SRC/DEPRECATED/dggsvp.f — this is the manual page for the deprecated DGGSVP routine, from the Library Functions Manual (section 3). She’s retired, bestie, but the lore is still here. 💅

🌸 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

💖 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 🎀

Okay so real talk: this routine is deprecated and has been replaced by routine DGGSVP3. Not me being dramatic — that’s literally in the source. 😭

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 — 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(3*N,M,P))
• 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 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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Bye bestie! That’s the whole page — from LAPACK Version 3.12.0, source SRC/DEPRECATED/dggsvp.f(3). Stay linear, stay orthogonal. 💖✨