SRC/stpmlqt.f(3)

💅 NAME 💅

Okay bestie, welcome to the SRC/stpmlqt.f(3) page from the Library Functions Manual — it’s giving “SRC/stpmlqt.f” and it’s all about the STPMLQT subroutine. 🫶

---

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

---

💖 Function/Subroutine Documentation 💖

🎀 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

🦋 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 vibe. 💫

🎀 Parameters 🎀

• SIDE — CHARACTER*1. It tells you which side 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 — CHARACTER*1. This is the transpose switch:
  • = 'N': No transpose, apply Q;
  • = 'T': Transpose, apply Q**T.
• M — INTEGER. The number of rows of the matrix B. M >= 0. slay.
• N — INTEGER. The number of columns of the matrix B. N >= 0. periodt.
• K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. iconic.
• 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 STPLQT. bestie, do not mix those up. 🫶
• V — 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 — INTEGER. The leading dimension of the array V. LDV >= K.
• T — REAL array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by STPLQT, stored as a MB-by-K matrix.
• LDT — INTEGER. The leading dimension of the array T. LDT >= MB.
• A — 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 — INTEGER. The leading dimension of the array A.
  • If SIDE = 'L', LDA >= max(1,K);
  • If SIDE = 'R', LDA >= max(1,M).
• B — 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,M).
• WORK — REAL array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. no cap.
• INFO — INTEGER. The exit-status bestie:
  • = 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. 🤖✨

💖 okay that’s the whole page, bestie — it’s LAPACK, Version 3.12.0, and the file is SRC/stpmlqt.f(3). mwah 💅✨