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149 lines
4.4 KiB
Fortran
149 lines
4.4 KiB
Fortran
*DECK SGBSL
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SUBROUTINE SGBSL (ABD, LDA, N, ML, MU, IPVT, B, JOB)
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C***BEGIN PROLOGUE SGBSL
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C***PURPOSE Solve the real band system A*X=B or TRANS(A)*X=B using
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C the factors computed by SGBCO or SGBFA.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2A2
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C***TYPE SINGLE PRECISION (SGBSL-S, DGBSL-D, CGBSL-C)
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C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE
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C***AUTHOR Moler, C. B., (U. of New Mexico)
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C***DESCRIPTION
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C
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C SGBSL solves the real band system
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C A * X = B or TRANS(A) * X = B
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C using the factors computed by SBGCO or SGBFA.
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C
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C On Entry
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C
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C ABD REAL(LDA, N)
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C the output from SBGCO or SGBFA.
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C
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C LDA INTEGER
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C the leading dimension of the array ABD .
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C
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C N INTEGER
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C the order of the original matrix.
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C
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C ML INTEGER
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C number of diagonals below the main diagonal.
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C
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C MU INTEGER
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C number of diagonals above the main diagonal.
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C
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C IPVT INTEGER(N)
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C the pivot vector from SBGCO or SGBFA.
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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 JOB INTEGER
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C = 0 to solve A*X = B ,
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C = nonzero to solve TRANS(A)*X = B , where
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C TRANS(A) is the transpose.
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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 will occur if the input factor contains a
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C zero on the diagonal. Technically, this indicates singularity,
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C but it is often caused by improper arguments or improper
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C setting of LDA . It will not occur if the subroutines are
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C called correctly and if SBGCO has set RCOND .GT. 0.0
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C or SGBFA has set INFO .EQ. 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 SBGCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z)
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C If (RCOND is too small) GO TO ...
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C DO 10 J = 1, P
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C CALL SGBSL(ABD,LDA,N,ML,MU,IPVT,C(1,J),0)
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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 890831 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 SGBSL
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INTEGER LDA,N,ML,MU,IPVT(*),JOB
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REAL ABD(LDA,*),B(*)
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C
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REAL SDOT,T
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INTEGER K,KB,L,LA,LB,LM,M,NM1
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C***FIRST EXECUTABLE STATEMENT SGBSL
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M = MU + ML + 1
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NM1 = N - 1
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IF (JOB .NE. 0) GO TO 50
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C
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C JOB = 0 , SOLVE A * X = B
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C FIRST SOLVE L*Y = B
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C
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IF (ML .EQ. 0) GO TO 30
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IF (NM1 .LT. 1) GO TO 30
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DO 20 K = 1, NM1
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LM = MIN(ML,N-K)
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L = IPVT(K)
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T = B(L)
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IF (L .EQ. K) GO TO 10
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B(L) = B(K)
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B(K) = T
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10 CONTINUE
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CALL SAXPY(LM,T,ABD(M+1,K),1,B(K+1),1)
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20 CONTINUE
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30 CONTINUE
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C
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C NOW SOLVE U*X = Y
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C
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DO 40 KB = 1, N
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K = N + 1 - KB
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B(K) = B(K)/ABD(M,K)
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LM = MIN(K,M) - 1
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LA = M - LM
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LB = K - LM
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T = -B(K)
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CALL SAXPY(LM,T,ABD(LA,K),1,B(LB),1)
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40 CONTINUE
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GO TO 100
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50 CONTINUE
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C
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C JOB = NONZERO, SOLVE TRANS(A) * X = B
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C FIRST SOLVE TRANS(U)*Y = B
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C
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DO 60 K = 1, N
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LM = MIN(K,M) - 1
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LA = M - LM
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LB = K - LM
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T = SDOT(LM,ABD(LA,K),1,B(LB),1)
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B(K) = (B(K) - T)/ABD(M,K)
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60 CONTINUE
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C
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C NOW SOLVE TRANS(L)*X = Y
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C
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IF (ML .EQ. 0) GO TO 90
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IF (NM1 .LT. 1) GO TO 90
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DO 80 KB = 1, NM1
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K = N - KB
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LM = MIN(ML,N-K)
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B(K) = B(K) + SDOT(LM,ABD(M+1,K),1,B(K+1),1)
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L = IPVT(K)
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IF (L .EQ. K) GO TO 70
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T = B(L)
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B(L) = B(K)
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B(K) = T
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70 CONTINUE
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80 CONTINUE
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90 CONTINUE
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100 CONTINUE
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RETURN
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END
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