SRC/dtpmlqt.f(3)

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🎀 NAME 🎀

SRC/dtpmlqt.f

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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👑 Function/Subroutine Documentation 👑

subroutine dtpmlqt

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

Purpose

okay so DTPMQRT 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. yes, that’s the exact name in the Purpose text — we’re not editing it, bestie 💅

Parameters

• SIDE — is CHARACTER*1:
  • = 'L': apply Q or Q**T from the Left;
  • = 'R': apply Q or Q**T from the Right.
• TRANS — is CHARACTER*1:
  • = 'N': No transpose, apply Q;
  • = 'T': Transpose, apply Q**T.
• M — is INTEGER. The number of rows of the matrix B. M >= 0.
• N — is INTEGER. The number of columns of the matrix B. N >= 0.
• K — is INTEGER. The number of elementary reflectors whose product defines the matrix Q.
• L — is INTEGER. The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
• MB — is INTEGER. The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DTPLQT.
• V — is DOUBLE PRECISION 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 DTPLQT in B. See Further Details.
• LDV — is INTEGER. The leading dimension of the array V. LDV >= K.
• T — is DOUBLE PRECISION array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by DTPLQT, stored as a MB-by-K matrix.
• LDT — is INTEGER. The leading dimension of the array T. LDT >= MB.
• A — is DOUBLE PRECISION 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 — is INTEGER. The leading dimension of the array A.
  • If SIDE = 'L', LDA >= max(1,K);
  • If SIDE = 'R', LDA >= max(1,M).
• B — is DOUBLE PRECISION 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 — is INTEGER. The leading dimension of the array B. LDB >= max(1,M).
• WORK — is DOUBLE PRECISION array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
• 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

okay bestie, here’s the lore ✨

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 dtpmlqt.f.

Author

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