mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2025-01-01 06:23:39 +01:00
149 lines
4.5 KiB
Fortran
149 lines
4.5 KiB
Fortran
*DECK DGBSL
|
|
SUBROUTINE DGBSL (ABD, LDA, N, ML, MU, IPVT, B, JOB)
|
|
C***BEGIN PROLOGUE DGBSL
|
|
C***PURPOSE Solve the real band system A*X=B or TRANS(A)*X=B using
|
|
C the factors computed by DGBCO or DGBFA.
|
|
C***LIBRARY SLATEC (LINPACK)
|
|
C***CATEGORY D2A2
|
|
C***TYPE DOUBLE PRECISION (SGBSL-S, DGBSL-D, CGBSL-C)
|
|
C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE
|
|
C***AUTHOR Moler, C. B., (U. of New Mexico)
|
|
C***DESCRIPTION
|
|
C
|
|
C DGBSL solves the double precision band system
|
|
C A * X = B or TRANS(A) * X = B
|
|
C using the factors computed by DGBCO or DGBFA.
|
|
C
|
|
C On Entry
|
|
C
|
|
C ABD DOUBLE PRECISION(LDA, N)
|
|
C the output from DGBCO or DGBFA.
|
|
C
|
|
C LDA INTEGER
|
|
C the leading dimension of the array ABD .
|
|
C
|
|
C N INTEGER
|
|
C the order of the original matrix.
|
|
C
|
|
C ML INTEGER
|
|
C number of diagonals below the main diagonal.
|
|
C
|
|
C MU INTEGER
|
|
C number of diagonals above the main diagonal.
|
|
C
|
|
C IPVT INTEGER(N)
|
|
C the pivot vector from DGBCO or DGBFA.
|
|
C
|
|
C B DOUBLE PRECISION(N)
|
|
C the right hand side vector.
|
|
C
|
|
C JOB INTEGER
|
|
C = 0 to solve A*X = B ,
|
|
C = nonzero to solve TRANS(A)*X = B , where
|
|
C TRANS(A) is the transpose.
|
|
C
|
|
C On Return
|
|
C
|
|
C B the solution vector X .
|
|
C
|
|
C Error Condition
|
|
C
|
|
C A division by zero will occur if the input factor contains a
|
|
C zero on the diagonal. Technically this indicates singularity
|
|
C but it is often caused by improper arguments or improper
|
|
C setting of LDA . It will not occur if the subroutines are
|
|
C called correctly and if DGBCO has set RCOND .GT. 0.0
|
|
C or DGBFA has set INFO .EQ. 0 .
|
|
C
|
|
C To compute INVERSE(A) * C where C is a matrix
|
|
C with P columns
|
|
C CALL DGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z)
|
|
C IF (RCOND is too small) GO TO ...
|
|
C DO 10 J = 1, P
|
|
C CALL DGBSL(ABD,LDA,N,ML,MU,IPVT,C(1,J),0)
|
|
C 10 CONTINUE
|
|
C
|
|
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
|
|
C Stewart, LINPACK Users' Guide, SIAM, 1979.
|
|
C***ROUTINES CALLED DAXPY, DDOT
|
|
C***REVISION HISTORY (YYMMDD)
|
|
C 780814 DATE WRITTEN
|
|
C 890531 Changed all specific intrinsics to generic. (WRB)
|
|
C 890831 Modified array declarations. (WRB)
|
|
C 890831 REVISION DATE from Version 3.2
|
|
C 891214 Prologue converted to Version 4.0 format. (BAB)
|
|
C 900326 Removed duplicate information from DESCRIPTION section.
|
|
C (WRB)
|
|
C 920501 Reformatted the REFERENCES section. (WRB)
|
|
C***END PROLOGUE DGBSL
|
|
INTEGER LDA,N,ML,MU,IPVT(*),JOB
|
|
DOUBLE PRECISION ABD(LDA,*),B(*)
|
|
C
|
|
DOUBLE PRECISION DDOT,T
|
|
INTEGER K,KB,L,LA,LB,LM,M,NM1
|
|
C***FIRST EXECUTABLE STATEMENT DGBSL
|
|
M = MU + ML + 1
|
|
NM1 = N - 1
|
|
IF (JOB .NE. 0) GO TO 50
|
|
C
|
|
C JOB = 0 , SOLVE A * X = B
|
|
C FIRST SOLVE L*Y = B
|
|
C
|
|
IF (ML .EQ. 0) GO TO 30
|
|
IF (NM1 .LT. 1) GO TO 30
|
|
DO 20 K = 1, NM1
|
|
LM = MIN(ML,N-K)
|
|
L = IPVT(K)
|
|
T = B(L)
|
|
IF (L .EQ. K) GO TO 10
|
|
B(L) = B(K)
|
|
B(K) = T
|
|
10 CONTINUE
|
|
CALL DAXPY(LM,T,ABD(M+1,K),1,B(K+1),1)
|
|
20 CONTINUE
|
|
30 CONTINUE
|
|
C
|
|
C NOW SOLVE U*X = Y
|
|
C
|
|
DO 40 KB = 1, N
|
|
K = N + 1 - KB
|
|
B(K) = B(K)/ABD(M,K)
|
|
LM = MIN(K,M) - 1
|
|
LA = M - LM
|
|
LB = K - LM
|
|
T = -B(K)
|
|
CALL DAXPY(LM,T,ABD(LA,K),1,B(LB),1)
|
|
40 CONTINUE
|
|
GO TO 100
|
|
50 CONTINUE
|
|
C
|
|
C JOB = NONZERO, SOLVE TRANS(A) * X = B
|
|
C FIRST SOLVE TRANS(U)*Y = B
|
|
C
|
|
DO 60 K = 1, N
|
|
LM = MIN(K,M) - 1
|
|
LA = M - LM
|
|
LB = K - LM
|
|
T = DDOT(LM,ABD(LA,K),1,B(LB),1)
|
|
B(K) = (B(K) - T)/ABD(M,K)
|
|
60 CONTINUE
|
|
C
|
|
C NOW SOLVE TRANS(L)*X = Y
|
|
C
|
|
IF (ML .EQ. 0) GO TO 90
|
|
IF (NM1 .LT. 1) GO TO 90
|
|
DO 80 KB = 1, NM1
|
|
K = N - KB
|
|
LM = MIN(ML,N-K)
|
|
B(K) = B(K) + DDOT(LM,ABD(M+1,K),1,B(K+1),1)
|
|
L = IPVT(K)
|
|
IF (L .EQ. K) GO TO 70
|
|
T = B(L)
|
|
B(L) = B(K)
|
|
B(K) = T
|
|
70 CONTINUE
|
|
80 CONTINUE
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
RETURN
|
|
END
|