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OpenLibm/slatec/sdpst.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras. 
Replace amos with slatec
2012-12-31 16:37:05 -05:00

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*DECK SDPST
SUBROUTINE SDPST (EL, F, FA, H, IMPL, JACOBN, MATDIM, MITER, ML,
8 MU, N, NDE, NQ, SAVE2, T, USERS, Y, YH, YWT, UROUND, NFE, NJE,
8 A, DFDY, FAC, IER, IPVT, SAVE1, ISWFLG, BND, JSTATE)
C***BEGIN PROLOGUE SDPST
C***SUBSIDIARY
C***PURPOSE Subroutine SDPST evaluates the Jacobian matrix of the right
C hand side of the differential equations.
C***LIBRARY SLATEC (SDRIVE)
C***TYPE SINGLE PRECISION (SDPST-S, DDPST-D, CDPST-C)
C***AUTHOR Kahaner, D. K., (NIST)
C National Institute of Standards and Technology
C Gaithersburg, MD 20899
C Sutherland, C. D., (LANL)
C Mail Stop D466
C Los Alamos National Laboratory
C Los Alamos, NM 87545
C***DESCRIPTION
C
C If MITER is 1, 2, 4, or 5, the matrix
C P = I - L(0)*H*Jacobian is stored in DFDY and subjected to LU
C decomposition, with the results also stored in DFDY.
C***ROUTINES CALLED SGBFA, SGEFA, SNRM2
C***REVISION HISTORY (YYMMDD)
C 790601 DATE WRITTEN
C 900329 Initial submission to SLATEC.
C***END PROLOGUE SDPST
INTEGER I, IFLAG, IMAX, IMPL, INFO, ISWFLG, J, J2, JSTATE, K,
8 MATDIM, MITER, ML, MU, MW, N, NDE, NFE, NJE, NQ
REAL A(MATDIM,*), BL, BND, BP, BR, BU, DFDY(MATDIM,*),
8 DFDYMX, DIFF, DY, EL(13,12), FAC(*), FACMAX, FACMIN, FACTOR,
8 H, SAVE1(*), SAVE2(*), SCALE, SNRM2, T, UROUND, Y(*),
8 YH(N,*), YJ, YS, YWT(*)
INTEGER IPVT(*)
LOGICAL IER
PARAMETER(FACMAX = .5E0, BU = 0.5E0)
C***FIRST EXECUTABLE STATEMENT SDPST
NJE = NJE + 1
IER = .FALSE.
IF (MITER .EQ. 1 .OR. MITER .EQ. 2) THEN
IF (MITER .EQ. 1) THEN
CALL JACOBN (N, T, Y, DFDY, MATDIM, ML, MU)
IF (N .EQ. 0) THEN
JSTATE = 8
RETURN
END IF
IF (ISWFLG .EQ. 3) BND = SNRM2(N*N, DFDY, 1)
FACTOR = -EL(1,NQ)*H
DO 110 J = 1,N
DO 110 I = 1,N
110 DFDY(I,J) = FACTOR*DFDY(I,J)
ELSE IF (MITER .EQ. 2) THEN
BR = UROUND**(.875E0)
BL = UROUND**(.75E0)
BP = UROUND**(-.15E0)
FACMIN = UROUND**(.78E0)
DO 170 J = 1,N
YS = MAX(ABS(YWT(J)), ABS(Y(J)))
120 DY = FAC(J)*YS
IF (DY .EQ. 0.E0) THEN
IF (FAC(J) .LT. FACMAX) THEN
FAC(J) = MIN(100.E0*FAC(J), FACMAX)
GO TO 120
ELSE
DY = YS
END IF
END IF
IF (NQ .EQ. 1) THEN
DY = SIGN(DY, SAVE2(J))
ELSE
DY = SIGN(DY, YH(J,3))
END IF
DY = (Y(J) + DY) - Y(J)
YJ = Y(J)
Y(J) = Y(J) + DY
CALL F (N, T, Y, SAVE1)
IF (N .EQ. 0) THEN
JSTATE = 6
RETURN
END IF
Y(J) = YJ
FACTOR = -EL(1,NQ)*H/DY
DO 140 I = 1,N
140 DFDY(I,J) = (SAVE1(I) - SAVE2(I))*FACTOR
C Step 1
DIFF = ABS(SAVE2(1) - SAVE1(1))
IMAX = 1
DO 150 I = 2,N
IF (ABS(SAVE2(I) - SAVE1(I)) .GT. DIFF) THEN
IMAX = I
DIFF = ABS(SAVE2(I) - SAVE1(I))
END IF
150 CONTINUE
C Step 2
IF (MIN(ABS(SAVE2(IMAX)), ABS(SAVE1(IMAX))) .GT. 0.E0) THEN
SCALE = MAX(ABS(SAVE2(IMAX)), ABS(SAVE1(IMAX)))
C Step 3
IF (DIFF .GT. BU*SCALE) THEN
FAC(J) = MAX(FACMIN, FAC(J)*.5E0)
ELSE IF (BR*SCALE .LE. DIFF .AND. DIFF .LE. BL*SCALE) THEN
FAC(J) = MIN(FAC(J)*2.E0, FACMAX)
C Step 4
ELSE IF (DIFF .LT. BR*SCALE) THEN
FAC(J) = MIN(BP*FAC(J), FACMAX)
END IF
END IF
170 CONTINUE
IF (ISWFLG .EQ. 3) BND = SNRM2(N*N, DFDY, 1)/(-EL(1,NQ)*H)
NFE = NFE + N
END IF
IF (IMPL .EQ. 0) THEN
DO 190 I = 1,N
190 DFDY(I,I) = DFDY(I,I) + 1.E0
ELSE IF (IMPL .EQ. 1) THEN
CALL FA (N, T, Y, A, MATDIM, ML, MU, NDE)
IF (N .EQ. 0) THEN
JSTATE = 9
RETURN
END IF
DO 210 J = 1,N
DO 210 I = 1,N
210 DFDY(I,J) = DFDY(I,J) + A(I,J)
ELSE IF (IMPL .EQ. 2) THEN
CALL FA (N, T, Y, A, MATDIM, ML, MU, NDE)
IF (N .EQ. 0) THEN
JSTATE = 9
RETURN
END IF
DO 230 I = 1,NDE
230 DFDY(I,I) = DFDY(I,I) + A(I,1)
ELSE IF (IMPL .EQ. 3) THEN
CALL FA (N, T, Y, A, MATDIM, ML, MU, NDE)
IF (N .EQ. 0) THEN
JSTATE = 9
RETURN
END IF
DO 220 J = 1,NDE
DO 220 I = 1,NDE
220 DFDY(I,J) = DFDY(I,J) + A(I,J)
END IF
CALL SGEFA (DFDY, MATDIM, N, IPVT, INFO)
IF (INFO .NE. 0) IER = .TRUE.
ELSE IF (MITER .EQ. 4 .OR. MITER .EQ. 5) THEN
IF (MITER .EQ. 4) THEN
CALL JACOBN (N, T, Y, DFDY(ML+1,1), MATDIM, ML, MU)
IF (N .EQ. 0) THEN
JSTATE = 8
RETURN
END IF
FACTOR = -EL(1,NQ)*H
MW = ML + MU + 1
DO 260 J = 1,N
DO 260 I = MAX(ML+1, MW+1-J), MIN(MW+N-J, MW+ML)
260 DFDY(I,J) = FACTOR*DFDY(I,J)
ELSE IF (MITER .EQ. 5) THEN
BR = UROUND**(.875E0)
BL = UROUND**(.75E0)
BP = UROUND**(-.15E0)
FACMIN = UROUND**(.78E0)
MW = ML + MU + 1
J2 = MIN(MW, N)
DO 340 J = 1,J2
DO 290 K = J,N,MW
YS = MAX(ABS(YWT(K)), ABS(Y(K)))
280 DY = FAC(K)*YS
IF (DY .EQ. 0.E0) THEN
IF (FAC(K) .LT. FACMAX) THEN
FAC(K) = MIN(100.E0*FAC(K), FACMAX)
GO TO 280
ELSE
DY = YS
END IF
END IF
IF (NQ .EQ. 1) THEN
DY = SIGN(DY, SAVE2(K))
ELSE
DY = SIGN(DY, YH(K,3))
END IF
DY = (Y(K) + DY) - Y(K)
DFDY(MW,K) = Y(K)
290 Y(K) = Y(K) + DY
CALL F (N, T, Y, SAVE1)
IF (N .EQ. 0) THEN
JSTATE = 6
RETURN
END IF
DO 330 K = J,N,MW
Y(K) = DFDY(MW,K)
YS = MAX(ABS(YWT(K)), ABS(Y(K)))
DY = FAC(K)*YS
IF (DY .EQ. 0.E0) DY = YS
IF (NQ .EQ. 1) THEN
DY = SIGN(DY, SAVE2(K))
ELSE
DY = SIGN(DY, YH(K,3))
END IF
DY = (Y(K) + DY) - Y(K)
FACTOR = -EL(1,NQ)*H/DY
DO 300 I = MAX(ML+1, MW+1-K), MIN(MW+N-K, MW+ML)
300 DFDY(I,K) = FACTOR*(SAVE1(I+K-MW) - SAVE2(I+K-MW))
C Step 1
IMAX = MAX(1, K - MU)
DIFF = ABS(SAVE2(IMAX) - SAVE1(IMAX))
DO 310 I = MAX(1, K - MU)+1, MIN(K + ML, N)
IF (ABS(SAVE2(I) - SAVE1(I)) .GT. DIFF) THEN
IMAX = I
DIFF = ABS(SAVE2(I) - SAVE1(I))
END IF
310 CONTINUE
C Step 2
IF (MIN(ABS(SAVE2(IMAX)), ABS(SAVE1(IMAX))) .GT.0.E0) THEN
SCALE = MAX(ABS(SAVE2(IMAX)), ABS(SAVE1(IMAX)))
C Step 3
IF (DIFF .GT. BU*SCALE) THEN
FAC(J) = MAX(FACMIN, FAC(J)*.5E0)
ELSE IF (BR*SCALE .LE.DIFF .AND. DIFF .LE.BL*SCALE) THEN
FAC(J) = MIN(FAC(J)*2.E0, FACMAX)
C Step 4
ELSE IF (DIFF .LT. BR*SCALE) THEN
FAC(K) = MIN(BP*FAC(K), FACMAX)
END IF
END IF
330 CONTINUE
340 CONTINUE
NFE = NFE + J2
END IF
IF (ISWFLG .EQ. 3) THEN
DFDYMX = 0.E0
DO 345 J = 1,N
DO 345 I = MAX(ML+1, MW+1-J), MIN(MW+N-J, MW+ML)
345 DFDYMX = MAX(DFDYMX, ABS(DFDY(I,J)))
BND = 0.E0
IF (DFDYMX .NE. 0.E0) THEN
DO 350 J = 1,N
DO 350 I = MAX(ML+1, MW+1-J), MIN(MW+N-J, MW+ML)
350 BND = BND + (DFDY(I,J)/DFDYMX)**2
BND = DFDYMX*SQRT(BND)/(-EL(1,NQ)*H)
END IF
END IF
IF (IMPL .EQ. 0) THEN
DO 360 J = 1,N
360 DFDY(MW,J) = DFDY(MW,J) + 1.E0
ELSE IF (IMPL .EQ. 1) THEN
CALL FA (N, T, Y, A(ML+1,1), MATDIM, ML, MU, NDE)
IF (N .EQ. 0) THEN
JSTATE = 9
RETURN
END IF
DO 380 J = 1,N
DO 380 I = MAX(ML+1, MW+1-J), MIN(MW+N-J, MW+ML)
380 DFDY(I,J) = DFDY(I,J) + A(I,J)
ELSE IF (IMPL .EQ. 2) THEN
CALL FA (N, T, Y, A, MATDIM, ML, MU, NDE)
IF (N .EQ. 0) THEN
JSTATE = 9
RETURN
END IF
DO 400 J = 1,NDE
400 DFDY(MW,J) = DFDY(MW,J) + A(J,1)
ELSE IF (IMPL .EQ. 3) THEN
CALL FA (N, T, Y, A(ML+1,1), MATDIM, ML, MU, NDE)
IF (N .EQ. 0) THEN
JSTATE = 9
RETURN
END IF
DO 390 J = 1,NDE
DO 390 I = MAX(ML+1, MW+1-J), MIN(MW+NDE-J, MW+ML)
390 DFDY(I,J) = DFDY(I,J) + A(I,J)
END IF
CALL SGBFA (DFDY, MATDIM, N, ML, MU, IPVT, INFO)
IF (INFO .NE. 0) IER = .TRUE.
ELSE IF (MITER .EQ. 3) THEN
IFLAG = 1
CALL USERS (Y, YH(1,2), YWT, SAVE1, SAVE2, T, H, EL(1,NQ), IMPL,
8 N, NDE, IFLAG)
IF (IFLAG .EQ. -1) THEN
IER = .TRUE.
RETURN
END IF
IF (N .EQ. 0) THEN
JSTATE = 10
RETURN
END IF
END IF
RETURN
END
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