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*DECK ALST2F
SUBROUTINE ALST2F(MDIM,M,N,A,TAU)
*
*-----------------------------------------------------------------------
*
*Purpose:
* to obtain the QR factorization of the matrix a using Householder
* transformations. Use LAPACK's DGEQRF routine storage. Douple precision
* routine.
*
*Copyright:
* Copyright (C) 1993 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Reference:
* P.A. BUSINGER, Num. Math. 7, 269-276 (1965).
*
*Parameters: input
* MDIM dimensioned column length of A.
* M number of rows of A
* N number of columns of A. N.le.M is assumed.
* A matrix A.
*
*Parameters: output
* A decomposed matrix. On exit, the elements on and above the
* diagonal of the array contain the m by n upper trapezoidal
* matrix R (R is upper triangular if m >= n); the elements
* below the diagonal, with the array TAU, represent the
* orthogonal matrix Q as a product of elementary reflectors.
* TAU scalar factors of the elementary reflectors.
*
*-----------------------------------------------------------------------
*
IMPLICIT REAL(KIND=8)(A-H,O-Z)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MDIM,M,N
REAL(KIND=8) A(MDIM,N),TAU(N)
*----
* LOCAL VARIABLES
*----
CHARACTER HSMG*131
*----
* ALLOCATABLE ARRAYS
*----
REAL(KIND=8), ALLOCATABLE, DIMENSION(:,:) :: W
*----
* CHECK THE INPUT
*----
IF(MDIM.LT.M) CALL XABORT('ALST2F: MDIM.LT.M')
IF(N.LT.1) CALL XABORT('ALST2F: N.LT.1')
IF(N.GT.M) THEN
WRITE(HSMG,'(18HALST2F: N.GT.M (N=,I3,3H M=,I3,2H).)') N,M
CALL XABORT(HSMG)
ENDIF
*----
* PERFORM QR FACTORIZATION.
*----
ALLOCATE(W(M,1))
DO J=1,N
M1 = M-J+1; W(:M1,1) = A(J:M,J); X1 = W(1,1);
AX = SQRT(DOT_PRODUCT(W(:M1,1),W(:M1,1)))
A1 = ABS(X1); S = SIGN(1.0D0,W(1,1));
SSSS = -AX*S; A1 = A1+AX;
W(1,1) = A1*S
DD2 = A1*AX
IF(DD2 == 0.0D0) CALL XABORT('ALST2F: SINGULAR REFLECTION')
W(:M1,1) = W(:M1,1)/SQRT(DD2)
A(J:M,J) = W(:M1,1)
IF(J < N) THEN
A(J:M,J+1:N) = A(J:M,J+1:N)
1 -MATMUL(W(:M1,:),(MATMUL(TRANSPOSE(W(:M1,:)),A(J:M,J+1:N))))
ENDIF
DIAG = A(J,J)
A(J:M,J) = A(J:M,J)/DIAG
A(J,J) = SSSS
TAU(J) = -DIAG*DIAG
ENDDO
DEALLOCATE(W)
RETURN
END
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