SLATEC Routines --- DCOV ---
*DECK DCOV
SUBROUTINE DCOV (FCN, IOPT, M, N, X, FVEC, R, LDR, INFO, WA1, WA2,
+ WA3, WA4)
C***BEGIN PROLOGUE DCOV
C***PURPOSE Calculate the covariance matrix for a nonlinear data
C fitting problem. It is intended to be used after a
C successful return from either DNLS1 or DNLS1E.
C***LIBRARY SLATEC
C***CATEGORY K1B1
C***TYPE DOUBLE PRECISION (SCOV-S, DCOV-D)
C***KEYWORDS COVARIANCE MATRIX, NONLINEAR DATA FITTING,
C NONLINEAR LEAST SQUARES
C***AUTHOR Hiebert, K. L., (SNLA)
C***DESCRIPTION
C
C 1. Purpose.
C
C DCOV calculates the covariance matrix for a nonlinear data
C fitting problem. It is intended to be used after a
C successful return from either DNLS1 or DNLS1E. DCOV
C and DNLS1 (and DNLS1E) have compatible parameters. The
C required external subroutine, FCN, is the same
C for all three codes, DCOV, DNLS1, and DNLS1E.
C
C 2. Subroutine and Type Statements.
C
C SUBROUTINE DCOV(FCN,IOPT,M,N,X,FVEC,R,LDR,INFO,
C WA1,WA2,WA3,WA4)
C INTEGER IOPT,M,N,LDR,INFO
C DOUBLE PRECISION X(N),FVEC(M),R(LDR,N),WA1(N),WA2(N),WA3(N),WA4(M)
C EXTERNAL FCN
C
C 3. Parameters. All TYPE REAL parameters are DOUBLE PRECISION
C
C FCN is the name of the user-supplied subroutine which calculates
C the functions. If the user wants to supply the Jacobian
C (IOPT=2 or 3), then FCN must be written to calculate the
C Jacobian, as well as the functions. See the explanation
C of the IOPT argument below.
C If the user wants the iterates printed in DNLS1 or DNLS1E,
C then FCN must do the printing. See the explanation of NPRINT
C in DNLS1 or DNLS1E. FCN must be declared in an EXTERNAL
C statement in the calling program and should be written as
C follows.
C
C SUBROUTINE FCN(IFLAG,M,N,X,FVEC,FJAC,LDFJAC)
C INTEGER IFLAG,LDFJAC,M,N
C DOUBLE PRECISION X(N),FVEC(M)
C ----------
C FJAC and LDFJAC may be ignored , if IOPT=1.
C DOUBLE PRECISION FJAC(LDFJAC,N) , if IOPT=2.
C DOUBLE PRECISION FJAC(N) , if IOPT=3.
C ----------
C If IFLAG=0, the values in X and FVEC are available
C for printing in DNLS1 or DNLS1E.
C IFLAG will never be zero when FCN is called by DCOV.
C The values of X and FVEC must not be changed.
C RETURN
C ----------
C If IFLAG=1, calculate the functions at X and return
C this vector in FVEC.
C RETURN
C ----------
C If IFLAG=2, calculate the full Jacobian at X and return
C this matrix in FJAC. Note that IFLAG will never be 2 unless
C IOPT=2. FVEC contains the function values at X and must
C not be altered. FJAC(I,J) must be set to the derivative
C of FVEC(I) with respect to X(J).
C RETURN
C ----------
C If IFLAG=3, calculate the LDFJAC-th row of the Jacobian
C and return this vector in FJAC. Note that IFLAG will
C never be 3 unless IOPT=3. FJAC(J) must be set to
C the derivative of FVEC(LDFJAC) with respect to X(J).
C RETURN
C ----------
C END
C
C
C The value of IFLAG should not be changed by FCN unless the
C user wants to terminate execution of DCOV. In this case, set
C IFLAG to a negative integer.
C
C
C IOPT is an input variable which specifies how the Jacobian will
C be calculated. If IOPT=2 or 3, then the user must supply the
C Jacobian, as well as the function values, through the
C subroutine FCN. If IOPT=2, the user supplies the full
C Jacobian with one call to FCN. If IOPT=3, the user supplies
C one row of the Jacobian with each call. (In this manner,
C storage can be saved because the full Jacobian is not stored.)
C If IOPT=1, the code will approximate the Jacobian by forward
C differencing.
C
C M is a positive integer input variable set to the number of
C functions.
C
C N is a positive integer input variable set to the number of
C variables. N must not exceed M.
C
C X is an array of length N. On input X must contain the value
C at which the covariance matrix is to be evaluated. This is
C usually the value for X returned from a successful run of
C DNLS1 (or DNLS1E). The value of X will not be changed.
C
C FVEC is an output array of length M which contains the functions
C evaluated at X.
C
C R is an output array. For IOPT=1 and 2, R is an M by N array.
C For IOPT=3, R is an N by N array. On output, if INFO=1,
C the upper N by N submatrix of R contains the covariance
C matrix evaluated at X.
C
C LDR is a positive integer input variable which specifies
C the leading dimension of the array R. For IOPT=1 and 2,
C LDR must not be less than M. For IOPT=3, LDR must not
C be less than N.
C
C INFO is an integer output variable. If the user has terminated
C execution, INFO is set to the (negative) value of IFLAG. See
C description of FCN. Otherwise, INFO is set as follows.
C
C INFO = 0 Improper input parameters (M.LE.0 or N.LE.0).
C
C INFO = 1 Successful return. The covariance matrix has been
C calculated and stored in the upper N by N
C submatrix of R.
C
C INFO = 2 The Jacobian matrix is singular for the input value
C of X. The covariance matrix cannot be calculated.
C The upper N by N submatrix of R contains the QR
C factorization of the Jacobian (probably not of
C interest to the user).
C
C WA1,WA2 are work arrays of length N.
C and WA3
C
C WA4 is a work array of length M.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED DENORM, DFDJC3, DQRFAC, DWUPDT, XERMSG
C***REVISION HISTORY (YYMMDD)
C 810522 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 891006 Cosmetic changes to prologue. (WRB)
C 891006 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900510 Fixed an error message. (RWC)
C***END PROLOGUE DCOV