/home/abui.../sggsvp3.f(3)

💖 NAME 💖

okay so you're looking at sggsvp3.f(3) from the Library Functions Manual, and this is the LAPACK source page for the file below. Slay, bestie, you found it 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sggsvp3.f

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🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

subroutine SGGSVP3 (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)

SGGSVP3 👑

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🦋 FUNCTION/SUBROUTINE DOCUMENTATION 🦋

subroutine SGGSVP3 (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 lwork, integer info)

SGGSVP3

🎀 Purpose 🎀

bestie, the whole point is this: SGGSVP3 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 SGGSVD3. iconic behavior, honestly 💫

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🧚 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. no cap, thresholds matter 🫶

• 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(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is 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 — INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🔥 Further Details: 🔥

The subroutine uses LAPACK subroutine SGEQP3 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.

SGGSVP3 replaces the deprecated subroutine SGGSVP. 💀 important deprecated lore, bestie

Definition at line 269 of file sggsvp3.f.

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🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💖 — it's LAPACK, Version 3.12.0, and the footer path is /home/abui.../sggsvp3.f(3). periodt 💅✨