DGEQRT (3) Linux Manual Page

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

 M is INTEGER

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

N

 N is INTEGER

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

NB

 NB is INTEGER

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

A

 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

 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 2013

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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