*DECK FDJAC3
SUBROUTINE FDJAC3 (FCN, M, N, X, FVEC, FJAC, LDFJAC, IFLAG,
+ EPSFCN, WA)
C***BEGIN PROLOGUE FDJAC3
C***SUBSIDIARY
C***PURPOSE Subsidiary to SNLS1 and SNLS1E
C***LIBRARY SLATEC
C***TYPE SINGLE PRECISION (FDJAC3-S, DFDJC3-D)
C***AUTHOR (UNKNOWN)
C***DESCRIPTION
C
C This subroutine computes a forward-difference approximation
C to the M by N Jacobian matrix associated with a specified
C problem of M functions in N variables.
C
C The subroutine statement is
C
C SUBROUTINE FDJAC3(FCN,M,N,X,FVEC,FJAC,LDFJAC,IFLAG,EPSFCN,WA)
C
C where
C
C FCN is the name of the user-supplied subroutine which
C calculates the functions. FCN must be declared
C in an external statement in the user calling
C program, and should be written as follows.
C
C SUBROUTINE FCN(IFLAG,M,N,X,FVEC,FJAC,LDFJAC)
C INTEGER LDFJAC,M,N,IFLAG
C REAL X(N),FVEC(M),FJAC(LDFJAC,N)
C ----------
C When IFLAG.EQ.1 calculate the functions at X and
C return this vector in FVEC.
C ----------
C RETURN
C END
C
C The value of IFLAG should not be changed by FCN unless
C the user wants to terminate execution of FDJAC3.
C In this case set IFLAG to a negative integer.
C
C M is a positive integer input variable set to the number
C of functions.
C
C N is a positive integer input variable set to the number
C of variables. N must not exceed M.
C
C X is an input array of length N.
C
C FVEC is an input array of length M which must contain the
C functions evaluated at X.
C
C FJAC is an output M by N array which contains the
C approximation to the Jacobian matrix evaluated at X.
C
C LDFJAC is a positive integer input variable not less than M
C which specifies the leading dimension of the array FJAC.
C
C IFLAG is an integer variable which can be used to terminate
C THE EXECUTION OF FDJAC3. See description of FCN.
C
C EPSFCN is an input variable used in determining a suitable
C step length for the forward-difference approximation. This
C approximation assumes that the relative errors in the
C functions are of the order of EPSFCN. If EPSFCN is less
C than the machine precision, it is assumed that the relative
C errors in the functions are of the order of the machine
C precision.
C
C WA is a work array of length M.
C
C***SEE ALSO SNLS1, SNLS1E
C***ROUTINES CALLED R1MACH
C***REVISION HISTORY (YYMMDD)
C 800301 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 900328 Added TYPE section. (WRB)
C***END PROLOGUE FDJAC3
INTEGER M,N,LDFJAC,IFLAG
REAL EPSFCN
REAL X(*),FVEC(*),FJAC(LDFJAC,*),WA(*)
INTEGER I,J
REAL EPS,EPSMCH,H,TEMP,ZERO
REAL R1MACH
SAVE ZERO
DATA ZERO /0.0E0/
C***FIRST EXECUTABLE STATEMENT FDJAC3
EPSMCH = R1MACH(4)
C
EPS = SQRT(MAX(EPSFCN,EPSMCH))
C SET IFLAG=1 TO INDICATE THAT FUNCTION VALUES
C ARE TO BE RETURNED BY FCN.
IFLAG = 1
DO 20 J = 1, N
TEMP = X(J)
H = EPS*ABS(TEMP)
IF (H .EQ. ZERO) H = EPS
X(J) = TEMP + H
CALL FCN(IFLAG,M,N,X,WA,FJAC,LDFJAC)
IF (IFLAG .LT. 0) GO TO 30
X(J) = TEMP
DO 10 I = 1, M
FJAC(I,J) = (WA(I) - FVEC(I))/H
10 CONTINUE
20 CONTINUE
30 CONTINUE
RETURN
C
C LAST CARD OF SUBROUTINE FDJAC3.
C
END