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196 lines
5 KiB
Fortran
196 lines
5 KiB
Fortran
*DECK SSPSL
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SUBROUTINE SSPSL (AP, N, KPVT, B)
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C***BEGIN PROLOGUE SSPSL
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C***PURPOSE Solve a real symmetric system using the factors obtained
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C from SSPFA.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2B1A
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C***TYPE SINGLE PRECISION (SSPSL-S, DSPSL-D, CHPSL-C, CSPSL-C)
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C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, PACKED, SOLVE, SYMMETRIC
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C***AUTHOR Bunch, J., (UCSD)
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C***DESCRIPTION
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C
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C SSISL solves the real symmetric system
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C A * X = B
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C using the factors computed by SSPFA.
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C
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C On Entry
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C
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C AP REAL(N*(N+1)/2)
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C the output from SSPFA.
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C
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C N INTEGER
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C the order of the matrix A .
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C
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C KPVT INTEGER(N)
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C the pivot vector from SSPFA.
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C
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C B REAL(N)
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C the right hand side vector.
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C
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C On Return
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C
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C B the solution vector X .
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C
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C Error Condition
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C
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C A division by zero may occur if SSPCO has set RCOND .EQ. 0.0
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C or SSPFA has set INFO .NE. 0 .
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C
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C To compute INVERSE(A) * C where C is a matrix
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C with P columns
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C CALL SSPFA(AP,N,KPVT,INFO)
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C IF (INFO .NE. 0) GO TO ...
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C DO 10 J = 1, P
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C CALL SSPSL(AP,N,KPVT,C(1,J))
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C 10 CONTINUE
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C
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C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
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C Stewart, LINPACK Users' Guide, SIAM, 1979.
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C***ROUTINES CALLED SAXPY, SDOT
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C***REVISION HISTORY (YYMMDD)
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C 780814 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890831 Modified array declarations. (WRB)
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C 891107 Modified routine equivalence list. (WRB)
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C 891107 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE SSPSL
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INTEGER N,KPVT(*)
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REAL AP(*),B(*)
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C
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REAL AK,AKM1,BK,BKM1,SDOT,DENOM,TEMP
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INTEGER IK,IKM1,IKP1,K,KK,KM1K,KM1KM1,KP
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C
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C LOOP BACKWARD APPLYING THE TRANSFORMATIONS AND
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C D INVERSE TO B.
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C
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C***FIRST EXECUTABLE STATEMENT SSPSL
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K = N
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IK = (N*(N - 1))/2
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10 IF (K .EQ. 0) GO TO 80
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KK = IK + K
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IF (KPVT(K) .LT. 0) GO TO 40
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C
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C 1 X 1 PIVOT BLOCK.
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C
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IF (K .EQ. 1) GO TO 30
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KP = KPVT(K)
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IF (KP .EQ. K) GO TO 20
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C
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C INTERCHANGE.
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C
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TEMP = B(K)
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B(K) = B(KP)
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B(KP) = TEMP
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20 CONTINUE
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C
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C APPLY THE TRANSFORMATION.
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C
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CALL SAXPY(K-1,B(K),AP(IK+1),1,B(1),1)
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30 CONTINUE
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C
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C APPLY D INVERSE.
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C
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B(K) = B(K)/AP(KK)
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K = K - 1
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IK = IK - K
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GO TO 70
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40 CONTINUE
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C
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C 2 X 2 PIVOT BLOCK.
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C
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IKM1 = IK - (K - 1)
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IF (K .EQ. 2) GO TO 60
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KP = ABS(KPVT(K))
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IF (KP .EQ. K - 1) GO TO 50
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C
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C INTERCHANGE.
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C
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TEMP = B(K-1)
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B(K-1) = B(KP)
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B(KP) = TEMP
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50 CONTINUE
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C
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C APPLY THE TRANSFORMATION.
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C
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CALL SAXPY(K-2,B(K),AP(IK+1),1,B(1),1)
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CALL SAXPY(K-2,B(K-1),AP(IKM1+1),1,B(1),1)
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60 CONTINUE
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C
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C APPLY D INVERSE.
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C
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KM1K = IK + K - 1
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KK = IK + K
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AK = AP(KK)/AP(KM1K)
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KM1KM1 = IKM1 + K - 1
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AKM1 = AP(KM1KM1)/AP(KM1K)
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BK = B(K)/AP(KM1K)
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BKM1 = B(K-1)/AP(KM1K)
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DENOM = AK*AKM1 - 1.0E0
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B(K) = (AKM1*BK - BKM1)/DENOM
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B(K-1) = (AK*BKM1 - BK)/DENOM
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K = K - 2
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IK = IK - (K + 1) - K
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70 CONTINUE
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GO TO 10
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80 CONTINUE
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C
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C LOOP FORWARD APPLYING THE TRANSFORMATIONS.
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C
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K = 1
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IK = 0
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90 IF (K .GT. N) GO TO 160
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IF (KPVT(K) .LT. 0) GO TO 120
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C
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C 1 X 1 PIVOT BLOCK.
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C
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IF (K .EQ. 1) GO TO 110
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C
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C APPLY THE TRANSFORMATION.
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C
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B(K) = B(K) + SDOT(K-1,AP(IK+1),1,B(1),1)
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KP = KPVT(K)
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IF (KP .EQ. K) GO TO 100
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C
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C INTERCHANGE.
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C
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TEMP = B(K)
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B(K) = B(KP)
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B(KP) = TEMP
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100 CONTINUE
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110 CONTINUE
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IK = IK + K
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K = K + 1
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GO TO 150
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120 CONTINUE
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C
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C 2 X 2 PIVOT BLOCK.
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C
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IF (K .EQ. 1) GO TO 140
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C
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C APPLY THE TRANSFORMATION.
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C
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B(K) = B(K) + SDOT(K-1,AP(IK+1),1,B(1),1)
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IKP1 = IK + K
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B(K+1) = B(K+1) + SDOT(K-1,AP(IKP1+1),1,B(1),1)
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KP = ABS(KPVT(K))
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IF (KP .EQ. K) GO TO 130
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C
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C INTERCHANGE.
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C
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TEMP = B(K)
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B(K) = B(KP)
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B(KP) = TEMP
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130 CONTINUE
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140 CONTINUE
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IK = IK + K + K + 1
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K = K + 2
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150 CONTINUE
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GO TO 90
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160 CONTINUE
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RETURN
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END
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