ztpqrt2.f man page

ztpqrt2.f —

Synopsis

Functions/Subroutines

subroutine ztpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
ZTPQRT2 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 ztpqrt2 (integerM, integerN, integerL, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldt, * )T, integerLDT, integerINFO)

ZTPQRT2 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:

ZTPQRT2 computes a QR factorization of a complex "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 total 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.

A

A is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDT,N)
The N-by-N upper triangular factor T of the block reflector.
See Further Details.

LDT

LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,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:

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 ztpqrt2.f.

Author

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Referenced By

ztpqrt2(3) is an alias of ztpqrt2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK