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📦 version 3.12.0, in opensuse-leap 16.0

💖 ZTPMLQT — Library Functions Manual 💖

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🌸 NAME 🌸

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

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

🧚 FUNCTION/SUBROUTINE DOCUMENTATION 🧚

subroutine ZTPMLQT (character side, character trans, integer m, integer n,
    integer k, integer l, integer mb, complex*16, dimension( ldv, * ) v,
    integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( * ) work, integer info)

ZTPMLQT

💖 PURPOSE 💖

ZTPMLQT applies a complex unitary matrix Q obtained from a complex block reflector H to a general complex matrix C, which consists of two blocks A and B. 🫶

🌸 PARAMETERS 🌸

SIDE

SIDE is CHARACTER*1.

  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.

TRANS

TRANS is CHARACTER*1.

  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.

M

M is INTEGER.

The number of rows of the matrix B. M >= 0. 💖

N

N is INTEGER.

The number of columns of the matrix B. N >= 0. 🌸

K

K is INTEGER.

The number of elementary reflectors whose product defines the matrix Q. ✨

L

L is INTEGER.

The order of the trapezoidal part of V. K >= L >= 0. See Further Details.

MB

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 ZTPLQT. 🔥

V

V is COMPLEX*16 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 ZTPLQT in B. See Further Details.

LDV

LDV is INTEGER.

The leading dimension of the array V. LDV >= K.

T

T is COMPLEX*16 array, dimension (LDT,K).

The upper triangular factors of the block reflectors as returned by ZTPLQT, stored as a MB-by-K matrix.

LDT

LDT is INTEGER.

The leading dimension of the array T. LDT >= MB.

A

A is COMPLEX*16 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**H*C or C*Q or C*Q**H. See Further Details. 👑

LDA

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

B is COMPLEX*16 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**H*C or C*Q or C*Q**H. See Further Details. 🦋

LDB

LDB is INTEGER.

The leading dimension of the array B. LDB >= max(1,M).

WORK

WORK is COMPLEX*16 array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. 🌈

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 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 complex unitary matrix Q is formed from V and T.

If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.

If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.

If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H. 💜

📍 Definition at line 212 of file ztpmlqt.f.

👑 AUTHOR (GENERATED EDITION) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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