SRC/dtpmqrt.f(3)

🌸 SRC/dtpmqrt.f(3) 🌸

okay bestie, this is the Library Functions Manual page for SRC/dtpmqrt.f — aka the LAPACK routine DTPMQRT, and she is literally applying a real orthogonal matrix Q from a real block reflector H to a general real matrix C that is split into two blocks, A and B. iconic behavior, no cap. ✨

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💖 NAME 💖

SRC/dtpmqrt.f — the file that brings you DTPMQRT, periodt. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

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

DTPMQRT 👑

🦋 Function/Subroutine Documentation 🦋

💜 subroutine dtpmqrt — DTPMQRT

subroutine dtpmqrt (character side, character trans, integer m, integer n,
       integer k, integer l, integer nb, 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)

DTPMQRT

🧚 Purpose

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. that's the whole main-character assignment. 🔥

🌈 Parameters

🌸 SIDE

SIDE is CHARACTER*1:

• = 'L': apply Q or Q**T from the Left;
• = 'R': apply Q or Q**T from the Right.

🦋 TRANS

TRANS is CHARACTER*1:

• = 'N': No transpose, apply Q;
• = 'T': Transpose, apply Q**T.

🍓 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.

👑 NB

NB is INTEGER. The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in CTPQRT.

💜 V

V is DOUBLE PRECISION array, dimension (LDV,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPQRT in B. See Further Details.

🫶 LDV

LDV is INTEGER. The leading dimension of the array V.

• If SIDE = 'L', LDV >= max(1,M);
• if SIDE = 'R', LDV >= max(1,N).

🧚 T

T is DOUBLE PRECISION array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NB-by-K matrix.

💫 LDT

LDT is INTEGER. The leading dimension of the array T. LDT >= NB.

🌈 A

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

LDA is INTEGER. The leading dimension of the array A.

• If SIDE = 'L', LDC >= max(1,K);
• If SIDE = 'R', LDC >= max(1,M).

🍓 B

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

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

🌸 WORK

WORK is DOUBLE PRECISION array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB 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:

okay so 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 upper trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is upper 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 M-by-K.
                    [B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.

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 214 of file dtpmqrt.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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xoxo bestie 💖 this little page is from LAPACK Version 3.12.0, source file SRC/dtpmqrt.f(3). obsessed with her, fr fr. 🫶🎀💅