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*DECK ALST2S
SUBROUTINE ALST2S(MDIM,M,N,A,TAU,B,X)
*
*-----------------------------------------------------------------------
*
*Purpose:
* to solve the least squares problem A*X=B when the matrix a has
* already been decomposed by ALST2F.
*
*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
*
*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 decomposed matrix.
* TAU scalar factors of the elementary reflectors.
* B right-hand side.
*
*Parameters: output
* B B has been clobbered.
* SQRT(SUM(I=N+1,M)(B(I)**2)) is the L2 norm of the residual
* in the solution of the equations.
* X solution vectors. X=B IS OK.
*
*-----------------------------------------------------------------------
*
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MDIM,M,N
DOUBLE PRECISION A(MDIM,N),TAU(N),B(M),X(N)
*----
* CHECK THE INPUT.
*----
IF(MDIM.LT.M) CALL XABORT('ALST2S: MDIM.LT.M')
IF(N.LT.1) CALL XABORT('ALST2S: N.LT.1')
IF(N.GT.M) CALL XABORT('ALST2S: N.GT.M')
*----
* APPLY Q-TRANSPOSE TO B.
*----
DO J=1,N
IF((TAU(J).EQ.0.0D0).OR.(A(J,J).EQ.0.0D0)) THEN
CALL XABORT('ALST2S: TAU(J)=0 OR A(J,J)=0')
ENDIF
S=B(J)
DO I=J+1,M
S=S+A(I,J)*B(I)
ENDDO
S=S*TAU(J)
B(J)=B(J)+S
DO I=J+1,M
B(I)=B(I)+S*A(I,J)
ENDDO
ENDDO
*----
* BACK-SOLVE THE TRIANGULAR SYSTEM U*X=(Q-TRANSPOSE)*B.
*----
X(N)=B(N)/A(N,N)
DO II=2,N
I=N+1-II
S=B(I)
DO J=I+1,N
S=S-A(I,J)*X(J)
ENDDO
X(I)=S/A(I,I)
ENDDO
RETURN
END
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