+++ /dev/null
-*DECK CHKDER
- SUBROUTINE CHKDER (M, N, X, FVEC, FJAC, LDFJAC, XP, FVECP, MODE,
- + ERR)
-C***BEGIN PROLOGUE CHKDER
-C***PURPOSE Check the gradients of M nonlinear functions in N
-C variables, evaluated at a point X, for consistency
-C with the functions themselves.
-C***LIBRARY SLATEC
-C***CATEGORY F3, G4C
-C***TYPE SINGLE PRECISION (CHKDER-S, DCKDER-D)
-C***KEYWORDS GRADIENTS, JACOBIAN, MINPACK, NONLINEAR
-C***AUTHOR Hiebert, K. L. (SNLA)
-C***DESCRIPTION
-C
-C This subroutine is a companion routine to SNLS1,SNLS1E,SNSQ,and
-C SNSQE which may be used to check the calculation of the Jacobian.
-C
-C SUBROUTINE CHKDER
-C
-C This subroutine checks the gradients of M nonlinear functions
-C in N variables, evaluated at a point X, for consistency with
-C the functions themselves. The user must call CKDER twice,
-C first with MODE = 1 and then with MODE = 2.
-C
-C MODE = 1. On input, X must contain the point of evaluation.
-C On output, XP is set to a neighboring point.
-C
-C MODE = 2. On input, FVEC must contain the functions and the
-C rows of FJAC must contain the gradients
-C of the respective functions each evaluated
-C at X, and FVECP must contain the functions
-C evaluated at XP.
-C On output, ERR contains measures of correctness of
-C the respective gradients.
-C
-C The subroutine does not perform reliably if cancellation or
-C rounding errors cause a severe loss of significance in the
-C evaluation of a function. Therefore, none of the components
-C of X should be unusually small (in particular, zero) or any
-C other value which may cause loss of significance.
-C
-C The SUBROUTINE statement is
-C
-C SUBROUTINE CHKDER(M,N,X,FVEC,FJAC,LDFJAC,XP,FVECP,MODE,ERR)
-C
-C where
-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.
-C
-C X is an input array of length N.
-C
-C FVEC is an array of length M. On input when MODE = 2,
-C FVEC must contain the functions evaluated at X.
-C
-C FJAC is an M by N array. On input when MODE = 2,
-C the rows of FJAC must contain the gradients of
-C the respective functions evaluated at X.
-C
-C LDFJAC is a positive integer input parameter not less than M
-C which specifies the leading dimension of the array FJAC.
-C
-C XP is an array of length N. On output when MODE = 1,
-C XP is set to a neighboring point of X.
-C
-C FVECP is an array of length M. On input when MODE = 2,
-C FVECP must contain the functions evaluated at XP.
-C
-C MODE is an integer input variable set to 1 on the first call
-C and 2 on the second. Other values of MODE are equivalent
-C to MODE = 1.
-C
-C ERR is an array of length M. On output when MODE = 2,
-C ERR contains measures of correctness of the respective
-C gradients. If there is no severe loss of significance,
-C then if ERR(I) is 1.0 the I-th gradient is correct,
-C while if ERR(I) is 0.0 the I-th gradient is incorrect.
-C For values of ERR between 0.0 and 1.0, the categorization
-C is less certain. In general, a value of ERR(I) greater
-C than 0.5 indicates that the I-th gradient is probably
-C correct, while a value of ERR(I) less than 0.5 indicates
-C that the I-th gradient is probably incorrect.
-C
-C***REFERENCES M. J. D. Powell, A hybrid method for nonlinear equa-
-C tions. In Numerical Methods for Nonlinear Algebraic
-C Equations, P. Rabinowitz, Editor. Gordon and Breach,
-C 1988.
-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 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 CHKDER
- INTEGER M,N,LDFJAC,MODE
- REAL X(*),FVEC(*),FJAC(LDFJAC,*),XP(*),FVECP(*),ERR(*)
- INTEGER I,J
- REAL EPS,EPSF,EPSLOG,EPSMCH,FACTOR,ONE,TEMP,ZERO
- REAL R1MACH
- SAVE FACTOR, ONE, ZERO
-C
- DATA FACTOR,ONE,ZERO /1.0E2,1.0E0,0.0E0/
-C***FIRST EXECUTABLE STATEMENT CHKDER
- EPSMCH = R1MACH(4)
-C
- EPS = SQRT(EPSMCH)
-C
- IF (MODE .EQ. 2) GO TO 20
-C
-C MODE = 1.
-C
- DO 10 J = 1, N
- TEMP = EPS*ABS(X(J))
- IF (TEMP .EQ. ZERO) TEMP = EPS
- XP(J) = X(J) + TEMP
- 10 CONTINUE
- GO TO 70
- 20 CONTINUE
-C
-C MODE = 2.
-C
- EPSF = FACTOR*EPSMCH
- EPSLOG = LOG10(EPS)
- DO 30 I = 1, M
- ERR(I) = ZERO
- 30 CONTINUE
- DO 50 J = 1, N
- TEMP = ABS(X(J))
- IF (TEMP .EQ. ZERO) TEMP = ONE
- DO 40 I = 1, M
- ERR(I) = ERR(I) + TEMP*FJAC(I,J)
- 40 CONTINUE
- 50 CONTINUE
- DO 60 I = 1, M
- TEMP = ONE
- IF (FVEC(I) .NE. ZERO .AND. FVECP(I) .NE. ZERO
- 1 .AND. ABS(FVECP(I)-FVEC(I)) .GE. EPSF*ABS(FVEC(I)))
- 2 TEMP = EPS*ABS((FVECP(I)-FVEC(I))/EPS-ERR(I))
- 3 /(ABS(FVEC(I)) + ABS(FVECP(I)))
- ERR(I) = ONE
- IF (TEMP .GT. EPSMCH .AND. TEMP .LT. EPS)
- 1 ERR(I) = (LOG10(TEMP) - EPSLOG)/EPSLOG
- IF (TEMP .GE. EPS) ERR(I) = ZERO
- 60 CONTINUE
- 70 CONTINUE
-C
- RETURN
-C
-C LAST CARD OF SUBROUTINE CHKDER.
-C
- END
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