You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
454 lines
17 KiB
FortranFixed
454 lines
17 KiB
FortranFixed
19 years ago
|
***********************************************************************
|
||
|
|
* ZCOOMV. Prolog to be updated. *
|
||
|
|
* *
|
||
|
|
* FUNCTION: Driver for routines performing one of the sparse *
|
||
|
|
* matrix vector operations *
|
||
|
|
* *
|
||
|
|
* y = alpha*op(A)*x + beta*y *
|
||
|
|
* *
|
||
|
|
* where op(A) is one of: *
|
||
|
|
* *
|
||
|
|
* op(A) = A or op(A) = A' or *
|
||
|
|
* op(A) = lower or upper part of A *
|
||
|
|
* *
|
||
|
|
* alpha and beta are scalars. *
|
||
|
|
* The data structure of the matrix is related *
|
||
|
|
* to the scalar computer. *
|
||
|
|
* This is an internal routine called by: *
|
||
|
|
* DSMMV *
|
||
|
|
* *
|
||
|
|
* ENTRY-POINT = DSRMV *
|
||
|
|
* INPUT = *
|
||
|
|
* *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: TRANS *
|
||
|
|
* POSITION: PARAMETER NO 1. *
|
||
|
|
* ATTRIBUTES: CHARACTER*1 *
|
||
|
|
* VALUES: 'N' 'T' 'L' 'U' *
|
||
|
|
* DESCRIPTION: Specifies the form of op(A) to be used in the *
|
||
|
|
* matrix vector multiplications as follows: *
|
||
|
|
* *
|
||
|
|
* TRANS = 'N' , op( A ) = A. *
|
||
|
|
* *
|
||
|
|
* TRANS = 'T' , op( A ) = A'. *
|
||
|
|
* *
|
||
|
|
* TRANS = 'L' or 'U', op( A ) = lower or *
|
||
|
|
* upper part of A *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: DIAG *
|
||
|
|
* POSITION: PARAMETER NO 2. *
|
||
|
|
* ATTRIBUTES: CHARACTER*1 *
|
||
|
|
* VALUES: 'N' 'U' *
|
||
|
|
* DESCRIPTION: *
|
||
|
|
* Specifies whether or not the matrix A has *
|
||
|
|
* unit diagonal as follows: *
|
||
|
|
* *
|
||
|
|
* DIAG = 'N' A is not assumed *
|
||
|
|
* to have unit diagonal *
|
||
|
|
* *
|
||
|
|
* DIAG = 'U' A is assumed *
|
||
|
|
* to have unit diagonal. *
|
||
|
|
* *
|
||
|
|
* WARNING: it is the caller's responsibility *
|
||
|
|
* to ensure that if the matrix has unit *
|
||
|
|
* diagonal, there are no elements of the *
|
||
|
|
* diagonal are stored in the arrays AS and JA. *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: M *
|
||
|
|
* POSITION: PARAMETER NO 3. *
|
||
|
|
* ATTRIBUTES: INTEGER*4. *
|
||
|
|
* VALUES: M >= 0 *
|
||
|
|
* DESCRIPTION: Number of rows of the matrix op(A). *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: N *
|
||
|
|
* POSITION: PARAMETER NO 4. *
|
||
|
|
* ATTRIBUTES: INTEGER*4. *
|
||
|
|
* VALUES: N >= 0 *
|
||
|
|
* DESCRIPTION: Number of columns of the matrix op(A) *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: ALPHA *
|
||
|
|
* POSITION: PARAMETER NO 5. *
|
||
|
|
* ATTRIBUTES: REAL*8. *
|
||
|
|
* VALUES: any. *
|
||
|
|
* DESCRIPTION: Specifies the scalar alpha. *
|
||
|
|
* *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: AS *
|
||
|
|
* POSITION: PARAMETER NO 6. *
|
||
|
|
* ATTRIBUTES: REAL*8: ARRAY(IA(M+1)-1) *
|
||
|
|
* VALUES: ANY *
|
||
|
|
* DESCRIPTION: Array containing the non zero coefficients of *
|
||
|
|
* the sparse matrix op(A). *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: JA *
|
||
|
|
* POSITION: PARAMETER NO 7. *
|
||
|
|
* ATTRIBUTES: INTEGER*4: ARRAY(IA(M+1)-1) *
|
||
|
|
* VALUES: 0 < JA(I) <= M *
|
||
|
|
* DESCRIPTION: Array containing the column number of the *
|
||
|
|
* nonzero coefficients stored in array AS. *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: IA *
|
||
|
|
* POSITION: PARAMETER NO 8. *
|
||
|
|
* ATTRIBUTES: INTEGER*4: ARRAY(*) *
|
||
|
|
* VALUES: IA(I) > 0 *
|
||
|
|
* DESCRIPTION: Contains the pointers for the beginning of *
|
||
|
|
* each rows. *
|
||
|
|
* *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: X *
|
||
|
|
* POSITION: PARAMETER NO 9. *
|
||
|
|
* ATTRIBUTES: REAL*8 ARRAY(N) (or ARRAY(M) when op(A) = A') *
|
||
|
|
* VALUES: any. *
|
||
|
|
* DESCRIPTION: Contains the values of the vector to be *
|
||
|
|
* multiplied by the matrix A. *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: BETA *
|
||
|
|
* POSITION: PARAMETER NO 10. *
|
||
|
|
* ATTRIBUTES: REAL*8. *
|
||
|
|
* VALUES: any. *
|
||
|
|
* DESCRIPTION: Specifies the scalar beta. *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: Y *
|
||
|
|
* POSITION: PARAMETER NO 11. *
|
||
|
|
* ATTRIBUTES: REAL*8 ARRAY(M) (or ARRAY(N) when op(A) = A') *
|
||
|
|
* VALUES: any. *
|
||
|
|
* DESCRIPTION: Contains the values of the vector to be *
|
||
|
|
* updated by the matrix-vector multiplication. *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: WORK *
|
||
|
|
* POSITION: PARAMETER NO 12. *
|
||
|
|
* ATTRIBUTES: REAL*8 ARRAY(M) (or ARRAY(N) when op(A) = A') *
|
||
|
|
* VALUES: any. *
|
||
|
|
* DESCRIPTION: Work area available to the program. It is used *
|
||
|
|
* only when TRANS = 'T'. *
|
||
|
|
* *
|
||
|
|
* OUTPUT = *
|
||
|
|
* *
|
||
|
|
* *
|
||
|
|
* SYMBOLIC NAME: Y *
|
||
|
|
* POSITION: PARAMETER NO 11. *
|
||
|
|
* ATTRIBUTES: REAL*8 ARRAY(M) (or ARRAY(N) when op(A) = A') *
|
||
|
|
* VALUES: any. *
|
||
|
|
* DESCRIPTION: Contains the values of the vector *
|
||
|
|
* updated by the matrix-vector multiplication. *
|
||
|
|
* *
|
||
|
|
* *
|
||
|
|
***********************************************************************
|
||
|
|
SUBROUTINE ZCOOMV (TRANS,DIAG,M,N,ALPHA,AS,IA,JA,INFOA,X,
|
||
|
|
+ BETA,Y,WORK)
|
||
|
|
C .. Parameters ..
|
||
|
|
COMPLEX*16 ONE, ZERO
|
||
|
|
PARAMETER (ONE=(1.0D0,0.0D0),ZERO=(0.0D0,0.0D0))
|
||
|
|
C .. Scalar Arguments ..
|
||
|
|
COMPLEX*16 ALPHA, BETA
|
||
|
|
INTEGER M, N
|
||
|
|
CHARACTER DIAG, TRANS
|
||
|
|
C .. Array Arguments ..
|
||
|
|
COMPLEX*16 AS(*), WORK(*), X(*), Y(*)
|
||
|
|
INTEGER IA(*), JA(*),infoa(*)
|
||
|
|
C .. Local Scalars ..
|
||
|
|
COMPLEX*16 ACC, TX
|
||
|
|
INTEGER I, J, K, NCOLA, NROWA,DUM, NNZ, IR, JC
|
||
|
|
LOGICAL SYM, TRA, UNI
|
||
|
|
C .. Executable Statements ..
|
||
|
|
C
|
||
|
|
UNI = (DIAG.EQ.'U')
|
||
|
|
TRA = (TRANS.EQ.'T')
|
||
|
|
|
||
|
|
C Symmetric matrix upper or lower
|
||
|
|
SYM = ((TRANS.EQ.'L').OR.(TRANS.EQ.'U'))
|
||
|
|
C
|
||
|
|
IF ( .NOT. TRA) THEN
|
||
|
|
NROWA = M
|
||
|
|
NCOLA = N
|
||
|
|
ELSE IF (TRA) THEN
|
||
|
|
NROWA = N
|
||
|
|
NCOLA = M
|
||
|
|
END IF !(....TRA)
|
||
|
|
|
||
|
|
IF (ALPHA.EQ.ZERO) THEN
|
||
|
|
IF (BETA.EQ.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ZERO
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO 20 I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)
|
||
|
|
20 CONTINUE
|
||
|
|
ENDIF
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
|
||
|
|
NNZ = INFOA(1)
|
||
|
|
C
|
||
|
|
IF (SYM) THEN
|
||
|
|
IF (UNI) THEN
|
||
|
|
C
|
||
|
|
C ......Symmetric with unitary diagonal.......
|
||
|
|
C ....OK!!
|
||
|
|
C To be optimized
|
||
|
|
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
C
|
||
|
|
C Product for diagonal elements
|
||
|
|
C
|
||
|
|
Y(I) = BETA*Y(I) + ALPHA*X(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ALPHA*X(I)
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
|
||
|
|
C Product for other elements
|
||
|
|
|
||
|
|
|
||
|
|
I = 1
|
||
|
|
J = I
|
||
|
|
DO WHILE (I.LE.NNZ)
|
||
|
|
|
||
|
|
DO WHILE ((IA(J).EQ.IA(I)).AND.
|
||
|
|
+ (J.LE.NNZ))
|
||
|
|
J = J+1
|
||
|
|
ENDDO
|
||
|
|
|
||
|
|
ACC = ZERO
|
||
|
|
IR = IA(I)
|
||
|
|
TX = X(IR)
|
||
|
|
DO K = I, J-1
|
||
|
|
JC = JA(K)
|
||
|
|
ACC = ACC + AS(K)*X(JC)
|
||
|
|
Y(JC) = Y(JC) + ALPHA * AS(K)*TX
|
||
|
|
ENDDO
|
||
|
|
Y(IR) = Y(IR) + ALPHA * ACC
|
||
|
|
I = J
|
||
|
|
ENDDO
|
||
|
|
C
|
||
|
|
ELSE IF ( .NOT. UNI) THEN
|
||
|
|
C
|
||
|
|
C Check if matrix is lower or upper
|
||
|
|
C
|
||
|
|
IF (TRANS.EQ.'L') THEN
|
||
|
|
C
|
||
|
|
C LOWER CASE: diagonal element is the last element of row
|
||
|
|
C ....OK!
|
||
|
|
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ZERO
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
|
||
|
|
I = 1
|
||
|
|
J = I
|
||
|
|
DO WHILE (I.LE.NNZ)
|
||
|
|
DO WHILE ((IA(J).EQ.IA(I)).AND.
|
||
|
|
+ (J.LE.NNZ))
|
||
|
|
J = J+1
|
||
|
|
ENDDO
|
||
|
|
ACC = ZERO
|
||
|
|
IR = IA(I)
|
||
|
|
TX = X(IR)
|
||
|
|
DO K = I, J-1
|
||
|
|
JC = JA(K)
|
||
|
|
ACC = ACC + AS(K)*X(JC)
|
||
|
|
IF (IR.NE.JC) THEN
|
||
|
|
Y(JC) = Y(JC) + ALPHA * AS(K)*TX
|
||
|
|
ENDIF
|
||
|
|
ENDDO
|
||
|
|
Y(IR) = Y(IR) + ALPHA * ACC
|
||
|
|
I = J
|
||
|
|
ENDDO
|
||
|
|
|
||
|
|
|
||
|
|
ELSE ! ....Trans<>L
|
||
|
|
C
|
||
|
|
C UPPER CASE
|
||
|
|
C ....OK!! (Actually it's just the same as above!)
|
||
|
|
C
|
||
|
|
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ZERO
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
|
||
|
|
I = 1
|
||
|
|
J = I
|
||
|
|
DO WHILE (I.LE.NNZ)
|
||
|
|
DO WHILE ((IA(J).EQ.IA(I)).AND.
|
||
|
|
+ (J.LE.NNZ))
|
||
|
|
J = J+1
|
||
|
|
ENDDO
|
||
|
|
ACC = ZERO
|
||
|
|
IR = IA(I)
|
||
|
|
TX = X(IR)
|
||
|
|
DO K = I, J-1
|
||
|
|
JC = JA(K)
|
||
|
|
ACC = ACC + AS(K)*X(JC)
|
||
|
|
IF (IR.NE.JC) THEN
|
||
|
|
Y(JC) = Y(JC) + ALPHA * AS(K)*TX
|
||
|
|
ENDIF
|
||
|
|
ENDDO
|
||
|
|
Y(IR) = Y(IR) + ALPHA * ACC
|
||
|
|
I = J
|
||
|
|
ENDDO
|
||
|
|
|
||
|
|
END IF ! ......TRANS=='L'
|
||
|
|
|
||
|
|
END IF ! ......Not UNI
|
||
|
|
C
|
||
|
|
ELSE IF ( .NOT. TRA) THEN !......NOT SYM
|
||
|
|
|
||
|
|
IF ( .NOT. UNI) THEN
|
||
|
|
C
|
||
|
|
C .......General Not Unit, No Traspose
|
||
|
|
C
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ZERO
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
|
||
|
|
I = 1
|
||
|
|
J = I
|
||
|
|
DO WHILE (I.LE.NNZ)
|
||
|
|
DO WHILE ((IA(J).EQ.IA(I)).AND.
|
||
|
|
+ (J.LE.NNZ))
|
||
|
|
J = J+1
|
||
|
|
ENDDO
|
||
|
|
ACC = ZERO
|
||
|
|
IR = IA(I)
|
||
|
|
DO K = I, J-1
|
||
|
|
JC = JA(K)
|
||
|
|
ACC = ACC + AS(K)*X(JC)
|
||
|
|
ENDDO
|
||
|
|
Y(IR) = Y(IR) + ALPHA * ACC
|
||
|
|
I = J
|
||
|
|
ENDDO
|
||
|
|
C
|
||
|
|
ELSE IF (UNI) THEN
|
||
|
|
C
|
||
|
|
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)+ALPHA*X(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ALPHA*X(I)
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
|
||
|
|
I = 1
|
||
|
|
J = I
|
||
|
|
DO WHILE (I.LE.NNZ)
|
||
|
|
DO WHILE ((IA(J).EQ.IA(I)).AND.
|
||
|
|
+ (J.LE.NNZ))
|
||
|
|
J = J+1
|
||
|
|
ENDDO
|
||
|
|
ACC = ZERO
|
||
|
|
IR = IA(I)
|
||
|
|
DO K = I, J-1
|
||
|
|
JC = JA(K)
|
||
|
|
ACC = ACC + AS(K)*X(JC)
|
||
|
|
ENDDO
|
||
|
|
Y(IR) = Y(IR) + ALPHA * ACC
|
||
|
|
I = J
|
||
|
|
ENDDO
|
||
|
|
|
||
|
|
END IF !....End Testing on UNI
|
||
|
|
C
|
||
|
|
ELSE IF (TRA) THEN !....Else on SYM (swapped M and N)
|
||
|
|
C
|
||
|
|
IF ( .NOT. UNI) THEN
|
||
|
|
C
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ZERO
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
C
|
||
|
|
ELSE IF (UNI) THEN
|
||
|
|
C
|
||
|
|
|
||
|
|
IF (BETA.NE.ZERO) THEN
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = BETA*Y(I)+ALPHA*X(I)
|
||
|
|
ENDDO
|
||
|
|
ELSE
|
||
|
|
DO I = 1, M
|
||
|
|
Y(I) = ALPHA*X(I)
|
||
|
|
ENDDO
|
||
|
|
ENDIF
|
||
|
|
C
|
||
|
|
END IF !....UNI
|
||
|
|
C
|
||
|
|
IF (ALPHA.EQ.ONE) THEN
|
||
|
|
C
|
||
|
|
I = 1
|
||
|
|
DO I=1,NNZ
|
||
|
|
IR = JA(I)
|
||
|
|
JC = IA(I)
|
||
|
|
Y(IR) = Y(IR) + AS(I)*X(JC)
|
||
|
|
ENDDO
|
||
|
|
C
|
||
|
|
ELSE IF (ALPHA.EQ.-ONE) THEN
|
||
|
|
C
|
||
|
|
I = 1
|
||
|
|
DO I=1,NNZ
|
||
|
|
IR = JA(I)
|
||
|
|
JC = IA(I)
|
||
|
|
Y(IR) = Y(IR) - AS(I)*X(JC)
|
||
|
|
ENDDO
|
||
|
|
C
|
||
|
|
ELSE !.....Else on TRA
|
||
|
|
I = 1
|
||
|
|
DO I=1,NNZ
|
||
|
|
IR = JA(I)
|
||
|
|
JC = IA(I)
|
||
|
|
Y(IR) = Y(IR) + ALPHA*AS(I)*X(JC)
|
||
|
|
ENDDO
|
||
|
|
|
||
|
|
c$$$C
|
||
|
|
c$$$C This work array is used for efficiency
|
||
|
|
c$$$C
|
||
|
|
c$$$ DO 420 I = 1, N
|
||
|
|
c$$$ WORK(I) = ALPHA*X(I)
|
||
|
|
c$$$ 420 CONTINUE
|
||
|
|
c$$$C
|
||
|
|
c$$$ DO 460 I = 1, n
|
||
|
|
c$$$ DO 440 J = IA(I), IA(I+1) - 1
|
||
|
|
c$$$ K = JA(J)
|
||
|
|
c$$$ Y(K) = Y(K) + AS(J)*WORK(I)
|
||
|
|
c$$$ 440 CONTINUE
|
||
|
|
c$$$ 460 CONTINUE
|
||
|
|
c$$$C
|
||
|
|
END IF !.....End testing on ALPHA
|
||
|
|
|
||
|
|
END IF !.....End testing on SYM
|
||
|
|
C
|
||
|
|
RETURN
|
||
|
|
C
|
||
|
|
C END OF DSRMV
|
||
|
|
C
|
||
|
|
END
|
||
|
|
|