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

💅 STPMLQT 💅

Okay bestie, this is the /home/abui.../stpmlqt.f(3) page from the LAPACK Library Functions Manual. The actual source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stpmlqt.f, and this whole page is about one very specific Fortran subroutine. Let’s get into it. 🫶

NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stpmlqt.f — that’s the file, that’s the name, no cap. ✨

SYNOPSIS

Functions/Subroutines

• subroutine STPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info) — STPMLQT

subroutine STPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda,
    b, ldb, work, info)

Function/Subroutine Documentation

subroutine STPMLQT (...)

subroutine STPMLQT (character side, character trans, integer m, integer n,
     integer k, integer l, integer mb, real, dimension( ldv, * ) v, integer
     ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, * )
     a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
     dimension( * ) work, integer info)

STPMLQT — that’s the subroutine, and yes she’s the main character here. 👑

Purpose

Okay so STPMLQT applies a real orthogonal matrix Q obtained from a real block reflector H to a general real matrix C, which consists of two blocks A and B. That’s the whole purpose, periodt. 💅

Parameters

• SIDE — SIDE is CHARACTER*1. It controls where Q or Q**T gets applied from:
  • = 'L': apply Q or Q**T from the Left.
  • = 'R': apply Q or Q**T from the Right.
• TRANS — TRANS is CHARACTER*1. It says whether we’re transposing or not:
  • = 'N': No transpose, apply Q.
  • = 'T': Transpose, apply Q**T.
• M — M is INTEGER. It’s the number of rows of the matrix B. Constraint: M >= 0.
• N — N is INTEGER. It’s the number of columns of the matrix B. Constraint: N >= 0.
• K — K is INTEGER. It’s the number of elementary reflectors whose product defines the matrix Q.
• L — L is INTEGER. It’s the order of the trapezoidal part of V. Constraint: K >= L >= 0. See Further Details for the full tea.
• MB — MB is INTEGER. It’s the block size used for the storage of T. Constraint: K >= MB >= 1. This must be the same value of MB used to generate T in STPLQT.
• V — V is REAL array, dimension (LDV,K). The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STPLQT in B. See Further Details.
• LDV — LDV is INTEGER. It’s the leading dimension of the array V. Constraint: LDV >= K.
• T — T is REAL array, dimension (LDT,K). These are the upper triangular factors of the block reflectors as returned by STPLQT, stored as a MB-by-K matrix.
• LDT — LDT is INTEGER. It’s the leading dimension of the array T. Constraint: LDT >= MB.
• A — A is REAL array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'. On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.
• LDA — LDA is INTEGER. It’s the leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); if SIDE = 'R', LDA >= max(1,M).
• B — B is REAL array, dimension (LDB,N). On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.
• LDB — LDB is INTEGER. It’s the leading dimension of the array B. Constraint: LDB >= max(1,M).
• WORK — WORK is REAL array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
• INFO — INFO is INTEGER. Exit status tea:
  • = 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 columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2:

V = [V1] [V2].

The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
                    [B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.

The real orthogonal matrix Q is formed from V and T.

• If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
• If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
• If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
• If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

Definition at line 212 of file stpmlqt.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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