dgeqrt-f(3)

dgeqrt.f –

Synopsis

Functions/Subroutines

subroutine dgeqrt (M, N, NB, A, LDA, T, LDT, WORK, INFO)
DGEQRT

Function/Subroutine Documentation

subroutine dgeqrt (integerM, integerN, integerNB, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( * )WORK, integerINFO)

DGEQRT

Purpose:

 DGEQRT computes a blocked QR factorization of a real M-by-N matrix A
 using the compact WY representation of Q.

Parameters:

 M is INTEGER
 The number of rows of the matrix A. M >= 0.

 N is INTEGER
 The number of columns of the matrix A. N >= 0.

 NB is INTEGER
 The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.

 A is DOUBLE PRECISION array, dimension (LDA,N)
 On entry, the M-by-N matrix A.
 On exit, the elements on and above the diagonal of the array
 contain the min(M,N)-by-N upper trapezoidal matrix R (R is
 upper triangular if M >= N); the elements below the diagonal
 are the columns of V.

LDA

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

 T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
 The upper triangular block reflectors stored in compact form
 as a sequence of upper triangular blocks. See below
 for further details.

LDT

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

WORK

 WORK is DOUBLE PRECISION 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:

November 2011

Further Details:

 The matrix V stores the elementary reflectors H(i) in the i-th column
 below the diagonal. For example, if M=5 and N=3, the matrix V is
 V = ( 1 )
 ( v1 1 )
 ( v1 v2 1 )
 ( v1 v2 v3 )
 ( v1 v2 v3 )
 where the vi's represent the vectors which define H(i), which are returned
 in the matrix A. The 1's along the diagonal of V are not stored in A.
 Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each
 block is of order NB except for the last block, which is of order 
 IB = K - (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 142 of file dgeqrt.f.

Author

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