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r[j:n-1,j] = r[j,j:n-1]
x = r[delm]
wa = qtb
;; Below may look strange, but it's so we can keep the right precision
zero = qtb[0]*0.
half = zero + 0.5
quart = zero + 0.25
;; Eliminate the diagonal matrix d using a givens rotation
for j = 0L, n-1 do begin
l = ipvt[j]
if diag[l] EQ 0 then goto, STORE_RESTORE
sdiag[j:*] = 0
sdiag[j] = diag[l]
;; The transformations to eliminate the row of d modify only a
;; single element of (q transpose)*b beyond the first n, which
;; is initially zero.
qtbpj = zero
for k = j, n-1 do begin
if sdiag[k] EQ 0 then goto, ELIM_NEXT_LOOP
if abs(r[k,k]) LT abs(sdiag[k]) then begin
cotan = r[k,k]/sdiag[k]
sine = half/sqrt(quart + quart*cotan*cotan)
cosine = sine*cotan
endif else begin
tang = sdiag[k]/r[k,k]
cosine = half/sqrt(quart + quart*tang*tang)
sine = cosine*tang
endelse
;; Compute the modified diagonal element of r and the
;; modified element of ((q transpose)*b,0).
r[k,k] = cosine*r[k,k] + sine*sdiag[k]
temp = cosine*wa[k] + sine*qtbpj
qtbpj = -sine*wa[k] + cosine*qtbpj
wa[k] = temp
;; Accumulate the transformation in the row of s
if n GT k+1 then begin
temp = cosine*r[k+1:n-1,k] + sine*sdiag[k+1:n-1]
sdiag[k+1:n-1] = -sine*r[k+1:n-1,k] + cosine*sdiag[k+1:n-1]
r[k+1:n-1,k] = temp
endif
ELIM_NEXT_LOOP:
endfor
STORE_RESTORE:
sdiag[j] = r[j,j]
r[j,j] = x[j]
endfor
;; Solve the triangular system for z. If the system is singular
;; then obtain a least squares solution
nsing = n
wh = where(sdiag EQ 0, ct)
if ct GT 0 then begin
nsing = wh[0]
wa[nsing:*] = 0
endif
if nsing GE 1 then begin
wa[nsing-1] = wa[nsing-1]/sdiag[nsing-1] ;; Degenerate case
;; *** Reverse loop ***
for j=nsing-2,0,-1 do begin
sum = total(r[j+1:nsing-1,j]*wa[j+1:nsing-1])
wa[j] = (wa[j]-sum)/sdiag[j]
endfor
endif
;; Permute the components of z back to components of x
x[ipvt] = wa
; profvals.qrsolv = profvals.qrsolv + (systime(1) - prof_start)
return
end
;
; subroutine lmpar
;
; given an m by n matrix a, an n by n nonsingular diagonal
; matrix d, an m-vector b, and a positive number delta,
; the problem is to determine a value for the parameter
; par such that if x solves the system
;
; a*x = b , sqrt(par)*d*x = 0 ,
;
; in the least squares sense, and dxnorm is the euclidean
; norm of d*x, then either par is zero and
;
; (dxnorm-delta) .le. 0.1*delta ,
;
; or par is positive and
;
; abs(dxnorm-delta) .le. 0.1*delta .
;
; this subroutine completes the solution of the problem
; if it is provided with the necessary information from the
; qr factorization, with column pivoting, of a. that is, if
; a*p = q*r, where p is a permutation matrix, q has orthogonal
; columns, and r is an upper triangular matrix with diagonal
; elements of nonincreasing magnitude, then lmpar expects
; the full upper triangle of r, the permutation matrix p,
; and the first n components of (q transpose)*b. on output
; lmpar also provides an upper triangular matrix s such that
;
; t t t
; p *(a *a + par*d*d)*p = s *s .
;
; s is employed within lmpar and may be of separate interest.
;
; only a few iterations are generally needed for convergence
; of the algorithm. if, however, the limit of 10 iterations
; is reached, then the output par will contain the best
; value obtained so far.
;
; the subroutine statement is
;
; subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag,
; wa1,wa2)
;
; where
;
; n is a positive integer input variable set to the order of r.
;
; r is an n by n array. on input the full upper triangle
; must contain the full upper triangle of the matrix r.
; on output the full upper triangle is unaltered, and the
; strict lower triangle contains the strict upper triangle
; (transposed) of the upper triangular matrix s.
;
; ldr is a positive integer input variable not less than n
; which specifies the leading dimension of the array r.
;
; ipvt is an integer input array of length n which defines the
; permutation matrix p such that a*p = q*r. column j of p
; is column ipvt(j) of the identity matrix.
;
; diag is an input array of length n which must contain the
; diagonal elements of the matrix d.
;
; qtb is an input array of length n which must contain the first
; n elements of the vector (q transpose)*b.
;
; delta is a positive input variable which specifies an upper
; bound on the euclidean norm of d*x.
;
; par is a nonnegative variable. on input par contains an
; initial estimate of the levenberg-marquardt parameter.
; on output par contains the final estimate.
;
; x is an output array of length n which contains the least
; squares solution of the system a*x = b, sqrt(par)*d*x = 0,
; for the output par.
;
; sdiag is an output array of length n which contains the
; diagonal elements of the upper triangular matrix s.
;
; wa1 and wa2 are work arrays of length n.
;
; subprograms called
;
; minpack-supplied ... dpmpar,enorm,qrsolv
;
; fortran-supplied ... dabs,dmax1,dmin1,dsqrt
;
; argonne national laboratory. minpack project. march 1980.
; burton s. garbow, kenneth e. hillstrom, jorge j. more
;
function mpfit_lmpar, r, ipvt, diag, qtb, delta, x, sdiag, par=par
COMPILE_OPT strictarr
common mpfit_machar, machvals
common mpfit_profile, profvals
; prof_start = systime(1)
MACHEP0 = machvals.machep
DWARF = machvals.minnum
sz = size(r)
m = sz[1]
n = sz[2]
delm = lindgen(n) * (m+1) ;; Diagonal elements of r
;; Compute and store in x the gauss-newton direction. If the
;; jacobian is rank-deficient, obtain a least-squares solution
nsing = n
wa1 = qtb
rthresh = max(abs(r[delm]))*MACHEP0
wh = where(abs(r[delm]) LT rthresh, ct)
if ct GT 0 then begin
nsing = wh[0]
wa1[wh[0]:*] = 0
endif
if nsing GE 1 then begin
;; *** Reverse loop ***
for j=nsing-1,0,-1 do begin
wa1[j] = wa1[j]/r[j,j]
if (j-1 GE 0) then $
wa1[0:(j-1)] = wa1[0:(j-1)] - r[0:(j-1),j]*wa1[j]
endfor
endif
;; Note: ipvt here is a permutation array
x[ipvt] = wa1
;; Initialize the iteration counter. Evaluate the function at the
;; origin, and test for acceptance of the gauss-newton direction
iter = 0L
wa2 = diag * x
dxnorm = mpfit_enorm(wa2)
fp = dxnorm - delta
if fp LE 0.1*delta then goto, TERMINATE
;; If the jacobian is not rank deficient, the newton step provides a
;; lower bound, parl, for the zero of the function. Otherwise set
;; this bound to zero.
zero = wa2[0]*0.
parl = zero
if nsing GE n then begin
wa1 = diag[ipvt]*wa2[ipvt]/dxnorm
wa1[0] = wa1[0] / r[0,0] ;; Degenerate case
for j=1L, n-1 do begin ;; Note "1" here, not zero
sum = total(r[0:(j-1),j]*wa1[0:(j-1)])
wa1[j] = (wa1[j] - sum)/r[j,j]
endfor
temp = mpfit_enorm(wa1)
parl = ((fp/delta)/temp)/temp
endif
;; Calculate an upper bound, paru, for the zero of the function
for j=0L, n-1 do begin
sum = total(r[0:j,j]*qtb[0:j])
wa1[j] = sum/diag[ipvt[j]]
endfor
gnorm = mpfit_enorm(wa1)
paru = gnorm/delta
if paru EQ 0 then paru = DWARF/min([delta,0.1])
;; If the input par lies outside of the interval (parl,paru), set
;; par to the closer endpoint
par = max([par,parl])
par = min([par,paru])
if par EQ 0 then par = gnorm/dxnorm
;; Beginning of an interation
ITERATION:
iter = iter + 1
;; Evaluate the function at the current value of par
if par EQ 0 then par = max([DWARF, paru*0.001])
temp = sqrt(par)
wa1 = temp * diag
mpfit_qrsolv, r, ipvt, wa1, qtb, x, sdiag
wa2 = diag*x
dxnorm = mpfit_enorm(wa2)
temp = fp
fp = dxnorm - delta
if (abs(fp) LE 0.1D*delta) $
OR ((parl EQ 0) AND (fp LE temp) AND (temp LT 0)) $
OR (iter EQ 10) then goto, TERMINATE
;; Compute the newton correction
wa1 = diag[ipvt]*wa2[ipvt]/dxnorm
for j=0L,n-2 do begin
wa1[j] = wa1[j]/sdiag[j]
wa1[j+1:n-1] = wa1[j+1:n-1] - r[j+1:n-1,j]*wa1[j]
endfor
wa1[n-1] = wa1[n-1]/sdiag[n-1] ;; Degenerate case
temp = mpfit_enorm(wa1)
parc = ((fp/delta)/temp)/temp
;; Depending on the sign of the function, update parl or paru
if fp GT 0 then parl = max([parl,par])
if fp LT 0 then paru = min([paru,par])
;; Compute an improved estimate for par
par = max([parl, par+parc])
;; End of an iteration
goto, ITERATION
TERMINATE:
;; Termination
; profvals.lmpar = profvals.lmpar + (systime(1) - prof_start)
if iter EQ 0 then return, par[0]*0.
return, par
end
;; Procedure to tie one parameter to another.
pro mpfit_tie, p, _ptied
COMPILE_OPT strictarr
if n_elements(_ptied) EQ 0 then return
if n_elements(_ptied) EQ 1 then if _ptied[0] EQ '' then return
for _i = 0L, n_elements(_ptied)-1 do begin
if _ptied[_i] EQ '' then goto, NEXT_TIE
_cmd = 'p['+strtrim(_i,2)+'] = '+_ptied[_i]
_err = execute(_cmd)
if _err EQ 0 then begin
message, 'ERROR: Tied expression "'+_cmd+'" failed.'
return
endif
NEXT_TIE:
endfor
end
;; Default print procedure
pro mpfit_defprint, p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, $
p11, p12, p13, p14, p15, p16, p17, p18, $
format=format, unit=unit0, _EXTRA=extra
COMPILE_OPT strictarr
if n_elements(unit0) EQ 0 then unit = -1 else unit = round(unit0[0])
if n_params() EQ 0 then printf, unit, '' $
else if n_params() EQ 1 then printf, unit, p1, format=format $
else if n_params() EQ 2 then printf, unit, p1, p2, format=format $
else if n_params() EQ 3 then printf, unit, p1, p2, p3, format=format $
else if n_params() EQ 4 then printf, unit, p1, p2, p4, format=format
return
end
;; Default procedure to be called every iteration. It simply prints
;; the parameter values.
pro mpfit_defiter, fcn, x, iter, fnorm, FUNCTARGS=fcnargs, $
quiet=quiet, iterstop=iterstop, iterkeybyte=iterkeybyte, $
parinfo=parinfo, iterprint=iterprint0, $
format=fmt, pformat=pformat, dof=dof0, _EXTRA=iterargs
COMPILE_OPT strictarr
common mpfit_error, mperr
mperr = 0
if keyword_set(quiet) then goto, DO_ITERSTOP
if n_params() EQ 3 then begin
fvec = mpfit_call(fcn, x, _EXTRA=fcnargs)
fnorm = mpfit_enorm(fvec)^2
endif
;; Determine which parameters to print
nprint = n_elements(x)
iprint = lindgen(nprint)
if n_elements(iterprint0) EQ 0 then iterprint = 'MPFIT_DEFPRINT' $
else iterprint = strtrim(iterprint0[0],2)
if n_elements(dof0) EQ 0 then dof = 1L else dof = floor(dof0[0])
call_procedure, iterprint, iter, fnorm, dof, $
format='("Iter ",I6," CHI-SQUARE = ",G15.8," DOF = ",I0)', $
_EXTRA=iterargs
if n_elements(fmt) GT 0 then begin
call_procedure, iterprint, x, format=fmt, _EXTRA=iterargs
endif else begin
if n_elements(pformat) EQ 0 then pformat = '(G20.6)'
parname = 'P('+strtrim(iprint,2)+')'
pformats = strarr(nprint) + pformat
if n_elements(parinfo) GT 0 then begin
parinfo_tags = tag_names(parinfo)
wh = where(parinfo_tags EQ 'PARNAME', ct)
if ct EQ 1 then begin
wh = where(parinfo.parname NE '', ct)
if ct GT 0 then $
parname[wh] = strmid(parinfo[wh].parname,0,25)
endif
wh = where(parinfo_tags EQ 'MPPRINT', ct)
if ct EQ 1 then begin
iprint = where(parinfo.mpprint EQ 1, nprint)
if nprint EQ 0 then goto, DO_ITERSTOP
endif
wh = where(parinfo_tags EQ 'MPFORMAT', ct)
if ct EQ 1 then begin
wh = where(parinfo.mpformat NE '', ct)
if ct GT 0 then pformats[wh] = parinfo[wh].mpformat
endif
endif
for i = 0L, nprint-1 do begin
call_procedure, iterprint, parname[iprint[i]], x[iprint[i]], $
format='(" ",A0," = ",'+pformats[iprint[i]]+')', $
_EXTRA=iterargs
endfor
endelse
DO_ITERSTOP:
if n_elements(iterkeybyte) EQ 0 then iterkeybyte = 7b
if keyword_set(iterstop) then begin
k = get_kbrd(0)
if k EQ string(iterkeybyte[0]) then begin
message, 'WARNING: minimization not complete', /info
print, 'Do you want to terminate this procedure? (y/n)', $
format='(A,$)'
k = ''
read, k
if strupcase(strmid(k,0,1)) EQ 'Y' then begin
message, 'WARNING: Procedure is terminating.', /info
mperr = -1
endif
endif
endif
return
end
;; Procedure to parse the parameter values in PARINFO
pro mpfit_parinfo, parinfo, tnames, tag, values, default=def, status=status, $
n_param=n
COMPILE_OPT strictarr
status = 0
if n_elements(n) EQ 0 then n = n_elements(parinfo)
if n EQ 0 then begin
if n_elements(def) EQ 0 then return
values = def
status = 1
return
endif
if n_elements(parinfo) EQ 0 then goto, DO_DEFAULT
if n_elements(tnames) EQ 0 then tnames = tag_names(parinfo)
wh = where(tnames EQ tag, ct)
if ct EQ 0 then begin
DO_DEFAULT:
if n_elements(def) EQ 0 then return
values = make_array(n, value=def[0])
values[0] = def
endif else begin
values = parinfo.(wh[0])
np = n_elements(parinfo)
nv = n_elements(values)
values = reform(values[*], nv/np, np)
endelse
status = 1
return
end
; **********
;
; subroutine covar
;
; given an m by n matrix a, the problem is to determine
; the covariance matrix corresponding to a, defined as
;
; t
; inverse(a *a) .
;
; this subroutine completes the solution of the problem
; if it is provided with the necessary information from the
; qr factorization, with column pivoting, of a. that is, if
; a*p = q*r, where p is a permutation matrix, q has orthogonal
; columns, and r is an upper triangular matrix with diagonal
; elements of nonincreasing magnitude, then covar expects
; the full upper triangle of r and the permutation matrix p.
; the covariance matrix is then computed as
;
; t t
; p*inverse(r *r)*p .
;
; if a is nearly rank deficient, it may be desirable to compute
; the covariance matrix corresponding to the linearly independent
; columns of a. to define the numerical rank of a, covar uses
; the tolerance tol. if l is the largest integer such that
;
; abs(r(l,l)) .gt. tol*abs(r(1,1)) ,
;
; then covar computes the covariance matrix corresponding to
; the first l columns of r. for k greater than l, column
; and row ipvt(k) of the covariance matrix are set to zero.
;
; the subroutine statement is
;
; subroutine covar(n,r,ldr,ipvt,tol,wa)
;
; where
;
; n is a positive integer input variable set to the order of r.
;
; r is an n by n array. on input the full upper triangle must
; contain the full upper triangle of the matrix r. on output
; r contains the square symmetric covariance matrix.
;
; ldr is a positive integer input variable not less than n
; which specifies the leading dimension of the array r.
;
; ipvt is an integer input array of length n which defines the
; permutation matrix p such that a*p = q*r. column j of p
; is column ipvt(j) of the identity matrix.
;
; tol is a nonnegative input variable used to define the
; numerical rank of a in the manner described above.
;
; wa is a work array of length n.
;
; subprograms called
;
; fortran-supplied ... dabs
;
; argonne national laboratory. minpack project. august 1980.
; burton s. garbow, kenneth e. hillstrom, jorge j. more
;
; **********
function mpfit_covar, rr, ipvt, tol=tol
COMPILE_OPT strictarr
sz = size(rr)
if sz[0] NE 2 then begin
message, 'ERROR: r must be a two-dimensional matrix'
return, -1L
endif
n = sz[1]
if n NE sz[2] then begin
message, 'ERROR: r must be a square matrix'
return, -1L
endif
zero = rr[0] * 0.
one = zero + 1.
if n_elements(ipvt) EQ 0 then ipvt = lindgen(n)
r = rr
r = reform(rr, n, n, /overwrite)
;; Form the inverse of r in the full upper triangle of r
l = -1L
if n_elements(tol) EQ 0 then tol = one*1.E-14
tolr = tol * abs(r[0,0])
for k = 0L, n-1 do begin
if abs(r[k,k]) LE tolr then goto, INV_END_LOOP
r[k,k] = one/r[k,k]
for j = 0L, k-1 do begin
temp = r[k,k] * r[j,k]
r[j,k] = zero
r[0,k] = r[0:j,k] - temp*r[0:j,j]
endfor
l = k
endfor
INV_END_LOOP:
;; Form the full upper triangle of the inverse of (r transpose)*r
;; in the full upper triangle of r
if l GE 0 then $
for k = 0L, l do begin
for j = 0L, k-1 do begin
temp = r[j,k]
r[0,j] = r[0:j,j] + temp*r[0:j,k]
endfor
temp = r[k,k]
r[0,k] = temp * r[0:k,k]
endfor
;; Form the full lower triangle of the covariance matrix
;; in the strict lower triangle of r and in wa
wa = replicate(r[0,0], n)
for j = 0L, n-1 do begin
jj = ipvt[j]
sing = j GT l
for i = 0L, j do begin
if sing then r[i,j] = zero
ii = ipvt[i]
if ii GT jj then r[ii,jj] = r[i,j]
if ii LT jj then r[jj,ii] = r[i,j]
endfor
wa[jj] = r[j,j]
endfor
;; Symmetrize the covariance matrix in r
for j = 0L, n-1 do begin
r[0:j,j] = r[j,0:j]
r[j,j] = wa[j]
endfor
return, r
end
;; Parse the RCSID revision number
function mpfit_revision
;; NOTE: this string is changed every time an RCS check-in occurs
revision = '$Revision: 1.82 $'
;; Parse just the version number portion
revision = stregex(revision,'\$'+'Revision: *([0-9.]+) *'+'\$',/extract,/sub)
revision = revision[1]
return, revision
end
;; Parse version numbers of the form 'X.Y'
function mpfit_parse_version, version
sz = size(version)
if sz[sz[0]+1] NE 7 then return, 0
s = stregex(version[0], '^([0-9]+)\.([0-9]+)$', /extract,/sub)
if s[0] NE version[0] then return, 0
return, long(s[1:2])
end
;; Enforce a minimum version number
function mpfit_min_version, version, min_version
mv = mpfit_parse_version(min_version)
if mv[0] EQ 0 then return, 0
v = mpfit_parse_version(version)
;; Compare version components
if v[0] LT mv[0] then return, 0
if v[1] LT mv[1] then return, 0
return, 1
end
; Manually reset recursion fencepost if the user gets in trouble
pro mpfit_reset_recursion
common mpfit_fencepost, mpfit_fencepost_active
mpfit_fencepost_active = 0
end
; **********
;
; subroutine lmdif
;
; the purpose of lmdif is to minimize the sum of the squares of
; m nonlinear functions in n variables by a modification of
; the levenberg-marquardt algorithm. the user must provide a
; subroutine which calculates the functions. the jacobian is
; then calculated by a forward-difference approximation.
;
; the subroutine statement is
;
; subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,
; diag,mode,factor,nprint,info,nfev,fjac,
; ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4)
;
; where
;
; fcn is the name of the user-supplied subroutine which
; calculates the functions. fcn must be declared
; in an external statement in the user calling
; program, and should be written as follows.
;
; subroutine fcn(m,n,x,fvec,iflag)
; integer m,n,iflag
; double precision x(n),fvec(m)
; ----------
; calculate the functions at x and
; return this vector in fvec.
; ----------
; return
; end
;
; the value of iflag should not be changed by fcn unless
; the user wants to terminate execution of lmdif.
; in this case set iflag to a negative integer.
;
; 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
; an initial estimate of the solution vector. on output x
; contains the final estimate of the solution vector.
;
; fvec is an output array of length m which contains
; the functions evaluated at the output x.
;
; ftol is a nonnegative input variable. termination
; occurs when both the actual and predicted relative
; reductions in the sum of squares are at most ftol.
; therefore, ftol measures the relative error desired
; in the sum of squares.
;
; xtol is a nonnegative input variable. termination
; occurs when the relative error between two consecutive
; iterates is at most xtol. therefore, xtol measures the
; relative error desired in the approximate solution.
;
; gtol is a nonnegative input variable. termination
; occurs when the cosine of the angle between fvec and
; any column of the jacobian is at most gtol in absolute
; value. therefore, gtol measures the orthogonality
; desired between the function vector and the columns
; of the jacobian.
;
; maxfev is a positive integer input variable. termination
; occurs when the number of calls to fcn is at least
; maxfev by the end of an iteration.
;
; epsfcn is an input variable used in determining a suitable
; step length for the forward-difference approximation. this
; approximation assumes that the relative errors in the
; functions are of the order of epsfcn. if epsfcn is less
; than the machine precision, it is assumed that the relative
; errors in the functions are of the order of the machine
; precision.
;
; diag is an array of length n. if mode = 1 (see
; below), diag is internally set. if mode = 2, diag
; must contain positive entries that serve as
; multiplicative scale factors for the variables.
;
; mode is an integer input variable. if mode = 1, the
; variables will be scaled internally. if mode = 2,
; the scaling is specified by the input diag. other
; values of mode are equivalent to mode = 1.
;
; factor is a positive input variable used in determining the
; initial step bound. this bound is set to the product of
; factor and the euclidean norm of diag*x if nonzero, or else
; to factor itself. in most cases factor should lie in the
; interval (.1,100.). 100. is a generally recommended value.
;
; nprint is an integer input variable that enables controlled
; printing of iterates if it is positive. in this case,
; fcn is called with iflag = 0 at the beginning of the first
; iteration and every nprint iterations thereafter and
; immediately prior to return, with x and fvec available
; for printing. if nprint is not positive, no special calls
; of fcn with iflag = 0 are made.
;
; 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.
;
; info = 1 both actual and predicted relative reductions
; in the sum of squares are at most ftol.
;
; info = 2 relative error between two consecutive iterates
; is at most xtol.
;
; info = 3 conditions for info = 1 and info = 2 both hold.
;
; info = 4 the cosine of the angle between fvec and any
; column of the jacobian is at most gtol in
; absolute value.
;
; info = 5 number of calls to fcn has reached or
; exceeded maxfev.
;
; info = 6 ftol is too small. no further reduction in
; the sum of squares is possible.
;
; info = 7 xtol is too small. no further improvement in
; the approximate solution x is possible.
;
; info = 8 gtol is too small. fvec is orthogonal to the
; columns of the jacobian to machine precision.
;
; nfev is an integer output variable set to the number of
; calls to fcn.
;
; fjac is an output m by n array. the upper n by n submatrix
; of fjac contains an upper triangular matrix r with
; diagonal elements of nonincreasing magnitude such that
;
; t t t
; p *(jac *jac)*p = r *r,
;
; where p is a permutation matrix and jac is the final
; calculated jacobian. column j of p is column ipvt(j)
; (see below) of the identity matrix. the lower trapezoidal
; part of fjac contains information generated during
; the computation of r.
;
; ldfjac is a positive integer input variable not less than m
; which specifies the leading dimension of the array fjac.
;
; ipvt is an integer output array of length n. ipvt
; defines a permutation matrix p such that jac*p = q*r,
; where jac is the final calculated jacobian, q is
; orthogonal (not stored), and r is upper triangular
; with diagonal elements of nonincreasing magnitude.
; column j of p is column ipvt(j) of the identity matrix.
;
; qtf is an output array of length n which contains
; the first n elements of the vector (q transpose)*fvec.
;
; wa1, wa2, and wa3 are work arrays of length n.
;
; wa4 is a work array of length m.
;
; subprograms called
;
; user-supplied ...... fcn
;
; minpack-supplied ... dpmpar,enorm,fdjac2,lmpar,qrfac
;
; fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod
;
; argonne national laboratory. minpack project. march 1980.
; burton s. garbow, kenneth e. hillstrom, jorge j. more
;
; **********
function mpfit, fcn, xall, FUNCTARGS=fcnargs, SCALE_FCN=scalfcn, $
ftol=ftol0, xtol=xtol0, gtol=gtol0, epsfcn=epsfcn, $
resdamp=damp0, $
nfev=nfev, maxiter=maxiter, errmsg=errmsg, $
factor=factor0, nprint=nprint0, STATUS=info, $
iterproc=iterproc0, iterargs=iterargs, iterstop=ss,$
iterkeystop=iterkeystop, $
niter=iter, nfree=nfree, npegged=npegged, dof=dof, $
diag=diag, rescale=rescale, autoderivative=autoderiv0, $
pfree_index=ifree, $
perror=perror, covar=covar, nocovar=nocovar, $
bestnorm=fnorm, best_resid=fvec, $
best_fjac=output_fjac, calc_fjac=calc_fjac, $
parinfo=parinfo, quiet=quiet, nocatch=nocatch, $
fastnorm=fastnorm0, proc=proc, query=query, $
external_state=state, external_init=extinit, $
external_fvec=efvec, external_fjac=efjac, $
version=version, min_version=min_version0
COMPILE_OPT strictarr
info = 0L
errmsg = ''
;; Compute the revision number, to be returned in the VERSION and
;; QUERY keywords.
common mpfit_revision_common, mpfit_revision_str
if n_elements(mpfit_revision_str) EQ 0 then $
mpfit_revision_str = mpfit_revision()
version = mpfit_revision_str
if keyword_set(query) then begin
if n_elements(min_version0) GT 0 then $
if mpfit_min_version(version, min_version0[0]) EQ 0 then $
return, 0
return, 1
endif
if n_elements(min_version0) GT 0 then $
if mpfit_min_version(version, min_version0[0]) EQ 0 then begin
message, 'ERROR: minimum required version '+min_version0[0]+' not satisfied', /info
return, !values.d_nan
endif
if n_params() EQ 0 then begin
message, "USAGE: PARMS = MPFIT('MYFUNCT', START_PARAMS, ... )", /info
return, !values.d_nan
endif
;; Use of double here not a problem since f/x/gtol are all only used
;; in comparisons
if n_elements(ftol0) EQ 0 then ftol = 1.D-10 else ftol = ftol0[0]
if n_elements(xtol0) EQ 0 then xtol = 1.D-10 else xtol = xtol0[0]
if n_elements(gtol0) EQ 0 then gtol = 1.D-10 else gtol = gtol0[0]
if n_elements(factor0) EQ 0 then factor = 100. else factor = factor0[0]
if n_elements(nprint0) EQ 0 then nprint = 1 else nprint = nprint0[0]
if n_elements(iterproc0) EQ 0 then iterproc = 'MPFIT_DEFITER' else iterproc = iterproc0[0]
if n_elements(autoderiv0) EQ 0 then autoderiv = 1 else autoderiv = autoderiv0[0]
if n_elements(fastnorm0) EQ 0 then fastnorm = 0 else fastnorm = fastnorm0[0]
if n_elements(damp0) EQ 0 then damp = 0 else damp = damp0[0]
;; These are special configuration parameters that can't be easily
;; passed by MPFIT directly.
;; FASTNORM - decide on which sum-of-squares technique to use (1)
;; is fast, (0) is slower
;; PROC - user routine is a procedure (1) or function (0)
;; QANYTIED - set to 1 if any parameters are TIED, zero if none
;; PTIED - array of strings, one for each parameter
common mpfit_config, mpconfig
mpconfig = {fastnorm: keyword_set(fastnorm), proc: 0, nfev: 0L, damp: damp}
common mpfit_machar, machvals
iflag = 0L
catch_msg = 'in MPFIT'
nfree = 0L
npegged = 0L
dof = 0L
output_fjac = 0L
;; Set up a persistent fencepost that prevents recursive calls
common mpfit_fencepost, mpfit_fencepost_active
if n_elements(mpfit_fencepost_active) EQ 0 then mpfit_fencepost_active = 0
if mpfit_fencepost_active then begin
errmsg = 'ERROR: recursion detected; you cannot run MPFIT recursively'
goto, TERMINATE
endif
;; Only activate the fencepost if we are not in debugging mode
if NOT keyword_set(nocatch) then mpfit_fencepost_active = 1
;; Parameter damping doesn't work when user is providing their own
;; gradients.
if damp NE 0 AND NOT keyword_set(autoderiv) then begin
errmsg = 'ERROR: keywords DAMP and AUTODERIV are mutually exclusive'
goto, TERMINATE
endif
;; Process the ITERSTOP and ITERKEYSTOP keywords, and turn this into
;; a set of keywords to pass to MPFIT_DEFITER.
if strupcase(iterproc) EQ 'MPFIT_DEFITER' AND n_elements(iterargs) EQ 0 $
AND keyword_set(ss) then begin
if n_elements(iterkeystop) GT 0 then begin
sz = size(iterkeystop)
tp = sz[sz[0]+1]
if tp EQ 7 then begin
;; String - convert first char to byte
iterkeybyte = (byte(iterkeystop[0]))[0]
endif
if (tp GE 1 AND tp LE 3) OR (tp GE 12 AND tp LE 15) then begin
;; Integer - convert to byte
iterkeybyte = byte(iterkeystop[0])
endif
if n_elements(iterkeybyte) EQ 0 then begin
errmsg = 'ERROR: ITERKEYSTOP must be either a BYTE or STRING'
goto, TERMINATE
endif
iterargs = {iterstop: 1, iterkeybyte: iterkeybyte}
endif else begin
iterargs = {iterstop: 1, iterkeybyte: 7b}
endelse
endif
;; Handle error conditions gracefully
if NOT keyword_set(nocatch) then begin
catch, catcherror
if catcherror NE 0 then begin ;; An error occurred!!!
catch, /cancel
mpfit_fencepost_active = 0
err_string = ''+!error_state.msg
message, /cont, 'Error detected while '+catch_msg+':'
message, /cont, err_string
message, /cont, 'Error condition detected. Returning to MAIN level.'
if errmsg EQ '' then $
errmsg = 'Error detected while '+catch_msg+': '+err_string
if info EQ 0 then info = -18
return, !values.d_nan
endif
endif
mpconfig = create_struct(mpconfig, 'NOCATCH', keyword_set(nocatch))
;; Parse FCN function name - be sure it is a scalar string
sz = size(fcn)
if sz[0] NE 0 then begin
FCN_NAME:
errmsg = 'ERROR: MYFUNCT must be a scalar string'
goto, TERMINATE
endif
if sz[sz[0]+1] NE 7 then goto, FCN_NAME
isext = 0
if fcn EQ '(EXTERNAL)' then begin
if n_elements(efvec) EQ 0 OR n_elements(efjac) EQ 0 then begin
errmsg = 'ERROR: when using EXTERNAL function, EXTERNAL_FVEC '+$
'and EXTERNAL_FJAC must be defined'
goto, TERMINATE
endif
nv = n_elements(efvec)
nj = n_elements(efjac)
if (nj MOD nv) NE 0 then begin
errmsg = 'ERROR: the number of values in EXTERNAL_FJAC must be '+ $
'a multiple of the number of values in EXTERNAL_FVEC'
goto, TERMINATE
endif
isext = 1
endif
;; Parinfo:
;; --------------- STARTING/CONFIG INFO (passed in to routine, not changed)
;; .value - starting value for parameter
;; .fixed - parameter is fixed
;; .limited - a two-element array, if parameter is bounded on
;; lower/upper side
;; .limits - a two-element array, lower/upper parameter bounds, if
;; limited vale is set
;; .step - step size in Jacobian calc, if greater than zero
catch_msg = 'parsing input parameters'
;; Parameters can either be stored in parinfo, or x. Parinfo takes
;; precedence if it exists.
if n_elements(xall) EQ 0 AND n_elements(parinfo) EQ 0 then begin
errmsg = 'ERROR: must pass parameters in P or PARINFO'
goto, TERMINATE
endif
;; Be sure that PARINFO is of the right type
if n_elements(parinfo) GT 0 then begin
;; Make sure the array is 1-D
parinfo = parinfo[*]
parinfo_size = size(parinfo)
if parinfo_size[parinfo_size[0]+1] NE 8 then begin
errmsg = 'ERROR: PARINFO must be a structure.'
goto, TERMINATE