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stpqrt.f(3) LAPACK stpqrt.f(3)

NAME

stpqrt.f

SYNOPSIS

Functions/Subroutines


subroutine stpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
STPQRT

Function/Subroutine Documentation

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

STPQRT

Purpose:


STPQRT computes a blocked 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:

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, and the order of the
triangular matrix A.
N >= 0.

L


L is INTEGER
The number of rows of the upper trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details.

NB


NB is INTEGER
The block size to be used in the blocked QR. N >= NB >= 1.

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.

LDA


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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.

LDB


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

T


T is REAL array, dimension (LDT,N)
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See Further Details.

LDT


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

WORK


WORK is REAL array, dimension (NB*N)

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 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 number of blocks is B = ceiling(N/NB), where each
block is of order NB except for the last block, which is of order
IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
for the last block) T's are stored in the NB-by-N matrix T as
T = [T1 T2 ... TB].

Definition at line 191 of file stpqrt.f.

Author

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