# stpmqrt.f man page

stpmqrt.f —

## Synopsis

### Functions/Subroutines

subroutine **stpmqrt** (SIDE, TRANS, M, **N**, K, L, NB, V, LDV, T, LDT, A, **LDA**, B, **LDB**, WORK, INFO)**STPMQRT**

## Function/Subroutine Documentation

### subroutine stpmqrt (character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer NB, 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)

**STPMQRT**

**Purpose:**

STPMQRT applies a real orthogonal matrix Q obtained from a "triangular-pentagonal" real block reflector H to a general real matrix C, which consists of two blocks A and B.

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

*WORK*WORK is REAL 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.

**Date:**December 2016

**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 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 218 of file stpmqrt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page stpmqrt(3) is an alias of stpmqrt.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK