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

💖 NAME 💖

Bestie, welcome to the manual page for /home/abui...D/sggsvp.f(3) — it lives in the Library Functions Manual. The source file is this whole iconic path:

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

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here’s the callable tea ☕ — the subroutine signature exactly as it appears:

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)

And the name itself: SGGSVP.

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🫶 Function/Subroutine Documentation 🫶

Okay so here’s the full signature again, no cap:

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 💅

Gather round, bestie — the source has a whole vibe check at the top. It says, loud and clear:

!>
!> This routine is deprecated and has been replaced by routine SGGSVP3.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.
!>

🚨 Deprecated alert: this routine is deprecated and has been replaced by routine SGGSVP3. It computes orthogonal matrices U, V and Q, and it’s 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. It’s the number of rows of the matrix A. Requirement: M >= 0.

🔹 P

P is INTEGER. It’s the number of rows of the matrix B. Requirement: P >= 0.

🔹 N

N is INTEGER. It’s the number of columns of the matrices A and B. Requirement: N >= 0.

🔹 A

A is a REAL array, dimension (LDA,N).

On entry, it’s the M-by-N matrix A.

On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section. 💅

🔹 LDA

LDA is INTEGER. It’s the leading dimension of the array A. Requirement: LDA >= max(1,M).

🔹 B

B is a REAL array, dimension (LDB,N).

On entry, it’s the P-by-N matrix B.

On exit, B contains the triangular matrix described in the Purpose section.

🔹 LDB

LDB is INTEGER. It’s the leading dimension of the array B. Requirement: 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 the Purpose section. K + L = effective numerical rank of (A**T,B**T)**T.

🔹 U

U is a 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. It’s the leading dimension of the array U.

LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.

🔹 V

V is a 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. It’s the leading dimension of the array V.

LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.

🔹 Q

Q is a 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. It’s the leading dimension of the array Q.

LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.

🔹 IWORK

IWORK is an INTEGER array, dimension (N).

🔹 TAU

TAU is a REAL array, dimension (N).

🔹 WORK

WORK is a 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 automatically by Doxygen for LAPACK from the source code.

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