SRC/DEPRECATED/sggsvp.f(3)

🌸 NAME 🌸

SRC/DEPRECATED/sggsvp.f(3) — okay so this is the Library Functions Manual page for SRC/DEPRECATED/sggsvp.f. It’s the deprecated LAPACK sggsvp routine, and we are keeping every single detail because that’s the whole vibe. 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

💖 Function/Subroutine Documentation 💖

🎀 subroutine sggsvp 🎀

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

SGGSVP

🎯 Purpose 🎯

Bestie, important: this routine is deprecated and has been replaced by routine SGGSVP3.

SGGSVP 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 SGGSVD.

🌈 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 REAL 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 REAL 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 REAL.
• TOLB — TOLB is REAL.

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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N).
• WORK — WORK is REAL 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 SGEQPF 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 sggsvp.f.

💀 Author (generated) 💀

Generated automatically by Doxygen for LAPACK from the source code.

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💖 LAPACK Version 3.12.0 · source: SRC/DEPRECATED/sggsvp.f(3) · that’s the whole page, bestie, and every flag, formula, and warning stayed in the chat. 🫶💅