LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
stpqrt2.f File Reference

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## Functions/Subroutines

subroutine stpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
STPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

## Function/Subroutine Documentation

 subroutine stpqrt2 ( integer M, integer N, integer L, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldt, * ) T, integer LDT, integer INFO )

STPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Purpose:
STPQRT2 computes a QR factorization of a real "triangular-pentagonal"
matrix C, which is composed of a triangular block A and pentagonal block B,
using the compact WY representation for Q.
Parameters:
 [in] M M is INTEGER The total number of rows of the matrix B. M >= 0. [in] N N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0. [in] L L is INTEGER The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details. [in,out] A A is REAL array, dimension (LDA,N) On entry, the upper triangular N-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the upper triangular matrix R. [in] LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). [in,out] B B is REAL array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B. The first M-L rows are rectangular, and the last L rows are upper trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details. [in] LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). [out] T T is REAL array, dimension (LDT,N) The N-by-N upper triangular factor T of the block reflector. See Further Details. [in] LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N) [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Date:
September 2012
Further Details:
The input matrix C is a (N+M)-by-N matrix

C = [ A ]
[ B ]

where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
upper trapezoidal matrix B2:

B = [ B1 ]  <- (M-L)-by-N rectangular
[ B2 ]  <-     L-by-N upper trapezoidal.

The upper trapezoidal matrix B2 consists of the first L rows of a
N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
B is rectangular M-by-N; if M=L=N, B is upper triangular.

The matrix W stores the elementary reflectors H(i) in the i-th column
below the diagonal (of A) in the (N+M)-by-N input matrix C

C = [ A ]  <- upper triangular N-by-N
[ B ]  <- M-by-N pentagonal

so that W can be represented as

W = [ I ]  <- identity, N-by-N
[ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which
we call V above.  Note that V has the same form as B; that is,

V = [ V1 ] <- (M-L)-by-N rectangular
[ V2 ] <-     L-by-N upper trapezoidal.

The columns of V represent the vectors which define the H(i)'s.
The (M+N)-by-(M+N) block reflector H is then given by

H = I - W * T * W^H

where W^H is the conjugate transpose of W and T is the upper triangular
factor of the block reflector.

Definition at line 174 of file stpqrt2.f.

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