d8/dd8/dhels_8f_source.html

 C Work performed under the auspices of the U.S. Department of Energy

 C by Lawrence Livermore National Laboratory under contract number

 C W-7405-Eng-48.

 C

       SUBROUTINE dhels (A, LDA, N, Q, B)

 C

 C***BEGIN PROLOGUE  DHELS

 C***DATE WRITTEN   890101   (YYMMDD)

 C***REVISION DATE  900926   (YYMMDD)

 C

 C

 C-----------------------------------------------------------------------

 C***DESCRIPTION

 C

 C This is similar to the LINPACK routine DGESL except that

 C A is an upper Hessenberg matrix.

 C

 C     DHELS solves the least squares problem

 C

 C           MIN (B-A*X,B-A*X)

 C

 C     using the factors computed by DHEQR.

 C

 C     On entry

 C

 C        A       DOUBLE PRECISION (LDA, N)

 C                The output from DHEQR which contains the upper

 C                triangular factor R in the QR decomposition of A.

 C

 C        LDA     INTEGER

 C                The leading dimension of the array  A .

 C

 C        N       INTEGER

 C                A is originally an (N+1) by N matrix.

 C

 C        Q       DOUBLE PRECISION(2*N)

 C                The coefficients of the N givens rotations

 C                used in the QR factorization of A.

 C

 C        B       DOUBLE PRECISION(N+1)

 C                The right hand side vector.

 C

 C

 C     On return

 C

 C        B       The solution vector X.

 C

 C

 C     Modification of LINPACK.

 C     Peter Brown, Lawrence Livermore Natl. Lab.

 C

 C-----------------------------------------------------------------------

 C***ROUTINES CALLED

 C   DAXPY

 C

 C***END PROLOGUE  DHELS

 C

       INTEGER LDA, N

       DOUBLE PRECISION A(LDA,*), B(*), Q(*)

       INTEGER IQ, K, KB, KP1

       DOUBLE PRECISION C, S, T, T1, T2

 C

 C        Minimize (B-A*X,B-A*X).

 C        First form Q*B.

 C

          DO 20 k = 1, n

             kp1 = k + 1

             iq = 2*(k-1) + 1

             c = q(iq)

             s = q(iq+1)

             t1 = b(k)

             t2 = b(kp1)

             b(k) = c*t1 - s*t2

             b(kp1) = s*t1 + c*t2

    20    CONTINUE

 C

 C        Now solve R*X = Q*B.

 C

          DO 40 kb = 1, n

             k = n + 1 - kb

             b(k) = b(k)/a(k,k)

             t = -b(k)

             CALL daxpy (k-1, t, a(1,k), 1, b(1), 1)

    40    CONTINUE

       RETURN

 C

 C------END OF SUBROUTINE DHELS------------------------------------------

       END

dhels
subroutine dhels(A, LDA, N, Q, B)
Definition: dhels.f:6