| 1 | ! **************************************************************
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| 2 | !
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| 3 | ! This file contains the subroutines: mincjg
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| 4 | !
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| 5 | ! Copyright 2003-2005 Frank Eisenmenger, U.H.E. Hansmann,
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| 6 | ! Shura Hayryan, Chin-Ku
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| 7 | ! Copyright 2007 Frank Eisenmenger, U.H.E. Hansmann,
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| 8 | ! Jan H. Meinke, Sandipan Mohanty
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| 9 | !
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| 10 | ! ********************************************************************
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| 11 | subroutine mincjg(n,mxn,x,f,g,acur,d,xa,ga,dt,yt,gt,maxfun,nfun)
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| 12 |
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| 13 | ! ....................................................................
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| 14 | !
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| 15 | ! Conjugate Gradient Minimizer
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| 16 | !
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| 17 | ! INPUT: X,F,G - variables, value of FUNC, gradient at START/
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| 18 | ! ACUR - convergence is assumed if ACUR > SUM ( G(I)**2 )
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| 19 | ! MAXFUN - maximum overall number of function calls
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| 20 | !
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| 21 | ! OUTPUT: X,F,G - variables, value of FUNC, gradient at MINIMUM
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| 22 | ! NFUN - overall number of function calls used
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| 23 | !
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| 24 | ! ARRAYS: D,XA,GA,YT,DT,GT - dimension N
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| 25 | !
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| 26 | ! CALLS: MOVE - calculate function & its gradients for current X
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| 27 | !
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| 28 | ! PARAMETERS: AMF - rough estimate of first reduction in F, used
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| 29 | ! to guess initial step of 1st line search
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| 30 | ! MXFCON - see 'ier=4'
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| 31 | ! MAXLIN -
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| 32 | !
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| 33 | ! DIAGNOSTICS (ier)
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| 34 | !
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| 35 | ! = 0: minimization completed successfully
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| 36 | ! = 1: number of steps reached MAXFUN
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| 37 | ! = 2: line search was abandoned
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| 38 | ! = 3: search direction is uphill
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| 39 | ! = 4: two consecutive line searches failed to reduce F
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| 40 | ! ....................................................................
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| 41 |
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| 42 | double precision amf, tol, eps, gsqrd, fmin, f, t, g, ga, d, xa, x
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| 43 | double precision gsq2, gnew, dfpr, stmin, fuit, gdit, gt, gdmi
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| 44 | double precision sbound, stepch, step, wo, sum, fch, acur, ddspln
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| 45 | double precision gspln, beta, gama, yt, dt, gamden, di
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| 46 |
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| 47 | integer mxfcon, maxlin, mxn, ier, iter, iterfm, iterrs, nfun
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| 48 | integer nfopt, i, n, nfbeg, iretry, maxfun
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| 49 |
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| 50 | parameter (AMF = 10.d0,
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| 51 | & MXFCON = 2,
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| 52 | & MAXLIN = 5,
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| 53 | & TOL = 1.d-7, ! controls 'stepch'
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| 54 | & EPS = .7d0)
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| 55 |
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| 56 | dimension x(mxn),g(mxn),
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| 57 | & d(mxn),xa(mxn),ga(mxn),dt(mxn),yt(mxn),gt(mxn)
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| 58 |
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| 59 |
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| 60 | ier = 0
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| 61 | iter = 0
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| 62 | iterfm = 0
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| 63 | iterrs = 0
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| 64 | nfun = 0
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| 65 | nfopt = nfun
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| 66 |
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| 67 | gsqrd = 0.d0
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| 68 | fmin = f
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| 69 |
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| 70 | do i=1,n
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| 71 | t = g(i)
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| 72 | ga(i) = t
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| 73 | d(i) = -t
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| 74 | gsqrd = gsqrd + t**2
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| 75 | xa(i) = x(i)
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| 76 | enddo
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| 77 |
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| 78 | gsq2 = .2d0 * gsqrd
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| 79 | gnew = -gsqrd
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| 80 | dfpr = AMF
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| 81 | stmin = AMF / gsqrd
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| 82 |
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| 83 | 1 iter = iter + 1
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| 84 |
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| 85 | fuit = f
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| 86 | gdit = 0.d0
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| 87 |
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| 88 | do i=1,n
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| 89 | t = g(i)
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| 90 | gt(i) = t
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| 91 | gdit = gdit + d(i) * t
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| 92 | enddo
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| 93 |
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| 94 | if ( gdit .ge. 0.d0 ) then
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| 95 | write(*,*) ' mincjg> search direction is uphill'
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| 96 | ier = 3
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| 97 | goto 6
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| 98 | endif
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| 99 |
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| 100 | gdmi = gdit
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| 101 | sbound = -1.d0
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| 102 | nfbeg = nfun
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| 103 | iretry = -1
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| 104 |
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| 105 | stepch = min( stmin, abs ( (dfpr/gdit) ) )
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| 106 | stmin = 0.d0
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| 107 |
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| 108 | 2 step = stmin + stepch
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| 109 | wo = 0.d0
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| 110 |
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| 111 | do i=1,n
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| 112 | t = stepch * d(i)
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| 113 | wo = max( wo, abs( t ) )
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| 114 | x(i) = xa(i) + t
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| 115 | enddo
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| 116 |
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| 117 | if ( wo .gt. TOL ) then
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| 118 |
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| 119 | nfun = nfun + 1
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| 120 | call move(nfun,n,f,x,g)
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| 121 |
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| 122 | gnew = 0.d0
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| 123 | sum = 0.d0
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| 124 |
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| 125 | do i=1,n
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| 126 | t = g(i)
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| 127 | gnew = gnew + d(i) * t
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| 128 | sum = sum + t**2
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| 129 | enddo
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| 130 |
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| 131 | fch = f - fmin
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| 132 |
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| 133 | if ( fch .le. 0.d0 ) then
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| 134 |
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| 135 | if ( fch .lt. 0.d0 .or. (gnew/gdmi) .ge. -1.d0 ) then
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| 136 |
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| 137 | fmin = f
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| 138 | gsqrd = sum
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| 139 | gsq2 = .2d0 * gsqrd
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| 140 | nfopt = nfun
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| 141 |
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| 142 | do i=1,n
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| 143 | xa(i) = x(i)
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| 144 | ga(i) = g(i)
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| 145 | enddo
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| 146 |
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| 147 | endif
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| 148 |
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| 149 | if ( sum .le. ACUR ) return ! normal end
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| 150 |
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| 151 | endif
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| 152 |
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| 153 | if ( nfun .eq. MAXFUN ) then
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| 154 | ier = 1
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| 155 | return
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| 156 | endif
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| 157 |
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| 158 | else ! stepch is effectively zero
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| 159 |
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| 160 | if ( nfun .gt. (nfbeg + 1) .or.
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| 161 | & abs(gdmi/gdit) .gt. EPS ) then
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| 162 |
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| 163 | ier=2
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| 164 | write(*,*) ' mincjg> too small step in search direction'
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| 165 | endif
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| 166 |
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| 167 | goto 6
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| 168 |
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| 169 | endif
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| 170 |
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| 171 | wo = (fch + fch) / stepch - gnew - gdmi
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| 172 | ddspln = (gnew - gdmi) / stepch
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| 173 |
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| 174 | if ( nfun .le. nfopt ) then
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| 175 |
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| 176 | if ( gdmi * gnew .le. 0.d0 ) sbound = stmin
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| 177 |
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| 178 | stmin = step
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| 179 | gdmi = gnew
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| 180 | stepch = -stepch
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| 181 |
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| 182 | else
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| 183 |
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| 184 | sbound = step
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| 185 |
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| 186 | endif
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| 187 |
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| 188 | if ( fch .ne. 0.d0 ) ddspln = ddspln + (wo + wo) / stepch
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| 189 |
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| 190 | if ( gdmi .eq. 0.d0 ) goto 6
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| 191 |
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| 192 | if ( nfun .le. (nfbeg + 1) ) goto 4
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| 193 |
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| 194 | if ( abs(gdmi/gdit) .le. EPS ) goto 6
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| 195 |
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| 196 | 3 if ( nfun .ge. (nfopt + MAXLIN) ) then
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| 197 |
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| 198 | ier = 2
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| 199 | goto 6
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| 200 |
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| 201 | endif
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| 202 |
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| 203 | 4 if ( sbound .lt. -.5d0 ) then
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| 204 | stepch = 9.d0 * stmin
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| 205 | else
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| 206 | stepch = .5d0 * ( sbound - stmin )
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| 207 | endif
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| 208 |
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| 209 | gspln = gdmi + stepch * ddspln
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| 210 |
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| 211 | if ( (gdmi * gspln) .lt. 0.d0 ) stepch = stepch * gdmi /
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| 212 | & (gdmi - gspln)
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| 213 |
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| 214 | goto 2
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| 215 |
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| 216 | 5 sum = 0.d0
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| 217 | do i=1,n
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| 218 | sum = sum + g(i) * gt(i)
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| 219 | enddo
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| 220 |
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| 221 | beta = (gsqrd - sum) / (gdmi - gdit)
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| 222 |
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| 223 | if ( abs(beta * gdmi) .gt. gsq2) then
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| 224 | iretry = iretry + 1
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| 225 | if (iretry .le. 0) goto 3
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| 226 | endif
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| 227 |
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| 228 | if ( f .lt. fuit ) iterfm = iter
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| 229 |
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| 230 | if ( iter .ge. (iterfm + MXFCON) ) then
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| 231 | ier = 4
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| 232 | write(*,*) ' mincjg> line search failed to reduce function'
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| 233 | return
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| 234 | endif
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| 235 |
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| 236 | dfpr = stmin * gdit
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| 237 |
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| 238 | if ( iretry .gt. 0 ) then
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| 239 |
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| 240 | do i=1,n
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| 241 | d(i) = -g(i)
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| 242 | enddo
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| 243 |
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| 244 | iterrs = 0
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| 245 |
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| 246 | else
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| 247 |
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| 248 | if (iterrs .ne. 0 .and. (iter - iterrs) .lt. (n-1) .and.
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| 249 | & abs(sum) .lt. gsq2 ) then
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| 250 |
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| 251 | gama = 0.d0
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| 252 | sum = 0.d0
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| 253 |
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| 254 | do i=1,n
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| 255 | t = g(i)
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| 256 | gama = gama + t * yt(i)
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| 257 | sum = sum + t * dt(i)
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| 258 | enddo
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| 259 |
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| 260 | gama = gama / gamden
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| 261 |
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| 262 | if ( abs( (beta * gdmi + gama * sum) ) .lt. gsq2) then
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| 263 |
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| 264 | do i=1,n
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| 265 | d(i) = -g(i) + beta * d(i) + gama * dt(i)
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| 266 | enddo
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| 267 |
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| 268 | goto 1
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| 269 |
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| 270 | endif
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| 271 |
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| 272 | endif
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| 273 |
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| 274 | gamden = gdmi - gdit
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| 275 |
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| 276 | do i=1,n
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| 277 | t = g(i)
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| 278 | di = d(i)
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| 279 | dt(i) = di
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| 280 | yt(i) = t - gt(i)
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| 281 | d(i) = -t + beta * di
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| 282 | enddo
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| 283 |
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| 284 | iterrs = iter
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| 285 |
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| 286 | endif
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| 287 |
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| 288 | goto 1
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| 289 |
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| 290 | 6 if ( nfun .ne. nfopt ) then
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| 291 |
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| 292 | f = fmin
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| 293 |
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| 294 | do i=1,n
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| 295 | x(i) = xa(i)
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| 296 | g(i) = ga(i)
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| 297 | enddo
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| 298 |
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| 299 | endif
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| 300 |
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| 301 | if ( ier .eq. 0 ) goto 5
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| 302 |
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| 303 | nfun = nfun + 1
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| 304 | call move(nfun,n,f,x,g)
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| 305 |
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| 306 | write(*,*) ' mincjg> ier = ',ier
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| 307 |
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| 308 | return
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| 309 | end
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| 310 |
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