SRC/ztpmlqt.f(3)

💖 NAME 💖

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📜 SYNOPSIS 📜

🧚 Functions/Subroutines 🧚

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

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🧚 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

ZTPMLQT is the main character here, no cap. 👑

🌈 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 — CHARACTER*1
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — CHARACTER*1
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• M — INTEGER
  • The number of rows of the matrix B. M >= 0.
• N — INTEGER
  • The number of columns of the matrix B. N >= 0.
• K — INTEGER
  • The number of elementary reflectors whose product defines the matrix Q.
• L — INTEGER
  • The order of the trapezoidal part of V.
  • K >= L >= 0. See Further Details.
• MB — 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 — 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 — INTEGER
  • The leading dimension of the array V. LDV >= K.
• T — 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 — INTEGER
  • The leading dimension of the array T. LDT >= MB.
• A — 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 — INTEGER
  • The leading dimension of the array A.
  • If SIDE = 'L', LDA >= max(1,K);
  • If SIDE = 'R', LDA >= max(1,M).
• B — 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 — INTEGER
  • The leading dimension of the array B.
  • LDB >= max(1,M).
• WORK — COMPLEX*16 array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
• INFO — 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.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 💅

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