ctpqrt-f(3)

ctpqrt.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine ctpqrt (integerM, integerN, integerL, integerNB, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldt, * )T, integerLDT, complex, dimension( * )WORK, integerINFO)

CTPQRT

Purpose:

 CTPQRT computes a blocked 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 is INTEGER
 The number of rows of the matrix B. 
 M >= 0.

 N is INTEGER
 The number of columns of the matrix B, and the order of the
 triangular matrix A.
 N >= 0.

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

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

 A is COMPLEX 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 is COMPLEX 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 is COMPLEX 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 COMPLEX 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:

April 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 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 189 of file ctpqrt.f.

Author

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