SRC/ctpmlqt.f(3)

🌸 NAME 🌸

SRC/ctpmlqt.f

okay bestie, this page is SRC/ctpmlqt.f(3) from the Library Functions Manual, and it’s giving serious LAPACK subroutine energy. 💅

✨ SYNOPSIS ✨

💅 Functions/Subroutines

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

🧚 Function/Subroutine Documentation 🧚

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

🎀 Purpose 🎀

No cap, here’s the whole point: CTPMLQT 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. Periodt. ✨

🔥 Parameters 🔥

• SIDE — SIDE is CHARACTER*1; = 'L': apply Q or QH from the Left; = 'R': apply Q or QH 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 CTPLQT.
• V — V is COMPLEX 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 CTPLQT in B. See Further Details.
• LDV — LDV is INTEGER; the leading dimension of the array V. LDV >= K.
• T — T is COMPLEX array, dimension (LDT,K); the upper triangular factors of the block reflectors as returned by CTPLQT, stored as a MB-by-K matrix.
• LDT — LDT is INTEGER; the leading dimension of the array T. LDT >= MB.
• A — A is COMPLEX 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 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 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 197 of file ctpmlqt.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💖 this was SRC/ctpmlqt.f(3) from LAPACK Version 3.12.0, and yes bestie, that’s the whole iconic page. 🫶✨