SUBROUTINE PDA_DCOV (FCN, IOPT, M, N, X, FVEC, R, LDR, INFO, WA1,
+ WA2, WA3, WA4, STATUS)
***BEGIN PROLOGUE PDA_DCOV
***PURPOSE Calculate the covariance matrix for a nonlinear data
fitting problem. It is intended to be used after a
successful return from either PDA_DNLS1 or PDA_DNLS1E.
***LIBRARY SLATEC
***CATEGORY K1B1
***TYPE DOUBLE PRECISION (SCOV-S, DCOV-D)
***KEYWORDS COVARIANCE MATRIX, NONLINEAR DATA FITTING,
NONLINEAR LEAST SQUARES
***AUTHOR Hiebert, K. L., (SNLA)
***DESCRIPTION
1. Purpose.
PDA_DCOV calculates the covariance matrix for a nonlinear data
fitting problem. It is intended to be used after a successful
return from either PDA_DNLS1 or PDA_DNLS1E. PDA_DCOV and
PDA_DNLS1 (and PDA_DNLS1E) have compatible parameters. The
required external subroutine, FCN, is the same for all three
codes, PDA_DCOV, PDA_DNLS1, and PDA_DNLS1E.
2. Subroutine and Type Statements.
SUBROUTINE PDA_DCOV(FCN,IOPT,M,N,X,FVEC,R,LDR,INFO,
WA1,WA2,WA3,WA4)
INTEGER IOPT,M,N,LDR,INFO
DOUBLE PRECISION X(N),FVEC(M),R(LDR,N),WA1(N),WA2(N),WA3(N),WA4(M)
EXTERNAL FCN
3. Parameters. All TYPE REAL parameters are DOUBLE PRECISION
FCN is the name of the user-supplied subroutine which calculates
the functions. If the user wants to supply the Jacobian
(IOPT=2 or 3), then FCN must be written to calculate the
Jacobian, as well as the functions. See the explanation
of the IOPT argument below.
If the user wants the iterates printed in PDA_DNLS1 or PDA_DNLS1E,
then FCN must do the printing. See the explanation of NPRINT
in PDA_DNLS1 or PDA_DNLS1E. FCN must be declared in an EXTERNAL
statement in the calling program and should be written as
follows.
SUBROUTINE FCN(IFLAG,M,N,X,FVEC,FJAC,LDFJAC)
INTEGER IFLAG,LDFJAC,M,N
DOUBLE PRECISION X(N),FVEC(M)
----------
FJAC and LDFJAC may be ignored , if IOPT=1.
DOUBLE PRECISION FJAC(LDFJAC,N) , if IOPT=2.
DOUBLE PRECISION FJAC(N) , if IOPT=3.
----------
If IFLAG=0, the values in X and FVEC are available
for printing in PDA_DNLS1 or PDA_DNLS1E.
IFLAG will never be zero when FCN is called by PDA_DCOV.
The values of X and FVEC must not be changed.
RETURN
----------
If IFLAG=1, calculate the functions at X and return
this vector in FVEC.
RETURN
----------
If IFLAG=2, calculate the full Jacobian at X and return
this matrix in FJAC. Note that IFLAG will never be 2 unless
IOPT=2. FVEC contains the function values at X and must
not be altered. FJAC(I,J) must be set to the derivative
of FVEC(I) with respect to X(J).
RETURN
----------
If IFLAG=3, calculate the LDFJAC-th row of the Jacobian
and return this vector in FJAC. Note that IFLAG will
never be 3 unless IOPT=3. FJAC(J) must be set to
the derivative of FVEC(LDFJAC) with respect to X(J).
RETURN
----------
END
The value of IFLAG should not be changed by FCN unless the
user wants to terminate execution of PDA_DCOV. In this case, set
IFLAG to a negative integer.
IOPT is an input variable which specifies how the Jacobian will
be calculated. If IOPT=2 or 3, then the user must supply the
Jacobian, as well as the function values, through the
subroutine FCN. If IOPT=2, the user supplies the full
Jacobian with one call to FCN. If IOPT=3, the user supplies
one row of the Jacobian with each call. (In this manner,
storage can be saved because the full Jacobian is not stored.)
If IOPT=1, the code will approximate the Jacobian by forward
differencing.
M is a positive integer input variable set to the number of
functions.
N is a positive integer input variable set to the number of
variables. N must not exceed M.
X is an array of length N. On input X must contain the value
at which the covariance matrix is to be evaluated. This is
usually the value for X returned from a successful run of
PDA_DNLS1 (or PDA_DNLS1E). The value of X will not be changed.
FVEC is an output array of length M which contains the functions
evaluated at X.
R is an output array. For IOPT=1 and 2, R is an M by N array.
For IOPT=3, R is an N by N array. On output, if INFO=1,
the upper N by N submatrix of R contains the covariance
matrix evaluated at X.
LDR is a positive integer input variable which specifies
the leading dimension of the array R. For IOPT=1 and 2,
LDR must not be less than M. For IOPT=3, LDR must not
be less than N.
INFO is an integer output variable. If the user has terminated
execution, INFO is set to the (negative) value of IFLAG. See
description of FCN. Otherwise, INFO is set as follows.
INFO = 0 Improper input parameters (M.LE.0 or N.LE.0).
INFO = 1 Successful return. The covariance matrix has been
calculated and stored in the upper N by N
submatrix of R.
INFO = 2 The Jacobian matrix is singular for the input value
of X. The covariance matrix cannot be calculated.
The upper N by N submatrix of R contains the QR
factorization of the Jacobian (probably not of
interest to the user).
WA1,WA2 are work arrays of length N.
and WA3
WA4 is a work array of length M.
STATUS is an INTEGER error status. Set to zero on entry.
If an error has occurred and has been reported then
this will be non-zero on exit.
***REFERENCES (NONE)
***ROUTINES CALLED DENORM, DFDJC3, DQRFAC, DWUPDT, XERMSG
***REVISION HISTORY (YYMMDD)
810522 DATE WRITTEN
890831 Modified array declarations. (WRB)
891006 Cosmetic changes to prologue. (WRB)
891006 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
900510 Fixed an error message. (RWC)
970224 Now called PDA_DCOV. (PWD)
***END PROLOGUE DCOV
PDA [1ex