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CCCCCCCCCCCCCCCCCC MATHEMATICAL PACKAGE CCCCCCCCCCCCCCCCCCCCCCC
CCCCCCC MOST OF THESE ROUTINE ARE FULLY VECTORIZED ON CRAY-1 CCCCCC
CCCCCCC THEY ARE ROUGHLY RESPONSIBLE OF 70% OF THE CPU TIME CCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
DOUBLE PRECISION FUNCTION SDOT (N,X,IX,Y,IY)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION X(*),Y(*)
C SDOT=DOT PRODUCT OF VECTOR X, STEP IX, BY VECTOR Y, STEP IY,
C N ELEMENTS.
C SIMULATE ROUTINE ON CRAY (SAME NAME AND CALLING SEQUENCE).
J=1
SDOT=0.D0
DO 10 I=1,(N-1)*IX+1,IX
SDOT=SDOT+X(I)*Y(J)
10 J=J+IY
RETURN
END
SUBROUTINE SCOPY (N,X,IX,Y,IY)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C COPY VECTOR X, STEP IX ONTO VECTOR Y, STEP IY, N ELEMENTS.
C SIMULATE ROUTINE ON CRAY (SAME NAME AND CALLING SEQUENCE).
DIMENSION X(*),Y(*)
I=1
DO 10 J=1,IY*(N-1)+1,IY
Y(J)=X(I)
10 I=I+IX
RETURN
END
SUBROUTINE SAXPY(N,A,X,IX,Y,IY)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C VECTOR INCREMENT Y=Y+A*X WITH X & Y VECTORS OF LENGTH N, A SCALAR.
C IX STEP OF X, IY STEP OF Y.
C SIMULATE ROUTINE ON CRAY (SAME NAME AND CALLING SEQUENCE).
DIMENSION X(*),Y(*)
I=1
DO 10 J=1,IY*(N-1)+1,IY
Y(J)=Y(J)+A*X(I)
10 I=I+IX
RETURN
END
SUBROUTINE MXM(A,NAR,B,NBR,C,NCC)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C RECTANGULAR MATRIX PRODUCT C=A*B.
C EACH MATRIX IS ENTIRELY FULLFILLED AND PACKED.
C SIMULATE ROUTINE ON CRAY (SAME NAME AND CALLING SEQUENCE).
DIMENSION A(NAR,NBR),B(NBR,NCC),C(NAR,NCC)
DO 20 J=1,NCC
DO 10 I=1,NAR
10 C(I,J)=0.D0
DO 20 K=1,NBR
DO 20 I=1,NAR
20 C(I,J)=C(I,J)+A(I,K)*B(K,J)
RETURN
END
SUBROUTINE MXMT (A,NAR,B,NBR,C,NCC)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C MATRIX PRODUCT C(NAR,NCC) = A(NAR,NBR) * (B(NCC,NBR))'
C ALL MATRICES RECTANGULAR , PACKED.
DIMENSION A(NAR,NBR),B(NCC,NBR),C(NAR,NCC)
DO 20 J=1,NCC
DO 10 I=1,NAR
10 C(I,J)=0.D0
DO 20 K=1,NBR
DO 20 I=1,NAR
20 C(I,J)=C(I,J)+A(I,K)*B(J,K)
RETURN
END
SUBROUTINE MTXM (A,NAR,B,NBR,C,NCC)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C MATRIX PRODUCT C(NAR,NCC) = (A(NBR,NAR))' * B(NBR,NCC)
C ALL MATRICES RECTANGULAR , PACKED.
DIMENSION A(NBR,NAR),B(NBR,NCC),C(NAR,NCC)
DO 20 J=1,NCC
DO 10 I=1,NAR
10 C(I,J)=0.D0
DO 20 K=1,NBR
DO 20 I=1,NAR
20 C(I,J)=C(I,J)+A(K,I)*B(K,J)
RETURN
END
SUBROUTINE MTXMC (A,NAR,B,NBR,C)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C MATRIX PRODUCT C(NAR,NAR) = (A(NBR,NAR))' * B(NBR,NAR)
C A AND B RECTANGULAR , PACKED,
C C LOWER LEFT TRIANGLE ONLY, PACKED IN CANONICAL ORDER.
DIMENSION A(NBR,NAR),B(NBR,NAR),C(*)
C NOTE ... THIS IS THE BEST VERSION ON CRAY 1.
L=1
DO 10 I=1,NAR
CALL MXM (A(1,I),1,B,NBR,C(L),I)
10 L=L+I
RETURN
END
SUBROUTINE SUPDOT(S,H,G,N,IG)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C (S)=(H)*(G) WITH H IN PACKED FORM (CANONICAL ORDER).
C IG IS THE INCREMENT FOR THE VECTOR G.
DIMENSION S(*),H(*),G(*)
C CRAY-1 VERSION
CCC K=1
CCC L=1
CCC DO 10 I=1,N
CCC S(I)=SDOT(I,H(K),1,G,IG,I)
CCC IF(I.GT.1) THEN
CCC L=L+IG
CCC CALL SAXPY(I-1,G(L),H(K),1,S,1)
CCC ENDIF
CCC 10 K=K+I
CCC RETURN
CCC END
C SCALAR VERSION OK WITH IG=1 ONLY.
K=0
DO 20 I=1,N
SUM=0.D0
DO 10 J=1,I
10 SUM=SUM+G(J)*H(K+J)
S(I)=SUM
20 K=K+I
IF (N.EQ.1) RETURN
K=1
DO 40 I=2,N
GI=G(I)
DO 30 J=1,I-1
30 S(J)=S(J)+H(K+J)*GI
40 K=K+I
RETURN
END
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