292 lines
8.9 KiB
Fortran
292 lines
8.9 KiB
Fortran
! Max Tegmark 171119, 190128-31, 190218
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! Same as symbolic_regress2.f except that it fits for the symbolic formula times an arbitrary constant.
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! Loads templates.csv functions.dat and mystery.dat, returns winner.
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! scp -P2222 symbolic_regress2.f euler@tor.mit.edu:FEYNMAN
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! COMPILATION: a f 'f77 -O3 -o symbolic_regress2.x symbolic_regress2.f |& more'
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! SAMPLE USAGE: call symbolic_regress2.x 4ops.txt arity2templates.txt mysteryB3.dat results.dat
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! functions.dat contains a single line (say "0>+*-/") with the single-character symbols
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! that will be used, drawn from this list:
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!
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! Binary:
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! +: add
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! *: multiply
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! -: subtract
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! /: divide (Put "D" instead of "/" in file, since f77 can't load backslash
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!
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! Unary:
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! >: increment (x -> x+1)
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! <: decrement (x -> x-1)
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! ~: negate (x-> -x)
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! \: invert (x->1/x) (Put "I" instead of "\" in file, since f77 can't load backslash
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! L: logaritm: (x-> ln(x)
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! E: exponentiate (x->exp(x))
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! S: sin: (x->sin(x))
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! C: cos: (x->cos(x))
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! A: abs: (x->abs(x))
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! N: arcsin: (x->arcsin(x))
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! T: arctan: (x->arctan(x))
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! R: sqrt (x->sqrt(x))
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!
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! nonary:
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! 0
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! 1
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! a, b, c, ...: input variables for function (need not be listed in functions.dat)
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program symbolic_regress
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call go
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end
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subroutine go
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implicit none
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character*60 opsfile, templatefile, mysteryfile, outfile, usedfuncs
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character*60 comline, functions, ops, formula
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integer arities(21), nvar, nvarmax, nmax, lnblnk
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parameter(nvarmax=20, nmax=10000000)
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real*8 f, newloss, minloss, maxloss, rmsloss, xy(nvarmax+1,nmax), epsilon
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real*8 ymax, prefactor, DL, DL2, DL3, limit
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parameter(epsilon=0.00001)
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data arities /2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0/
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data functions /"+*-/><~\OJLESCANTR01P"/
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integer nn(0:2), ii(nmax), kk(nmax), radix(nmax)
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integer ndata, i, j, n, jmax
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integer*8 nformulas
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logical done
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character*60 func(0:2), template
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open(2,file='args.dat',status='old',err=666)
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read(2,*) opsfile, templatefile, mysteryfile, outfile
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close(2)
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comline = 'head -1 '//mysteryfile(1:lnblnk(mysteryfile))//' | wc > qaz.dat'
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if (system(comline).ne.0) stop 'DEATH ERROR counting columns'
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open(2,file='qaz.dat')
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read(2,*) i, nvar
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close(2)
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nvar = nvar - 1
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if (nvar.gt.nvarmax) stop 'DEATH ERROR: TOO MANY VARIABLES'
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write(*,'(1a24,i8)') 'Number of variables.....',nvar
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open(2,file=opsfile,status='old',err=668)
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read(2,*) usedfuncs
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close(2)
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nn(0)=0
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nn(1)=0
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nn(2)=0
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do i=1,lnblnk(usedfuncs)
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if (usedfuncs(i:i).eq.'D') usedfuncs(i:i)='/'
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if (usedfuncs(i:i).eq.'I') usedfuncs(i:i)='\'
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j = index(functions,usedfuncs(i:i))
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if (j.eq.0) then
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print *,'DEATH ERROR: Unknown function requested: ',usedfuncs(i:i)
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stop
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else
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nn(arities(j)) = nn(arities(j)) + 1
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func(arities(j))(nn(arities(j)):nn(arities(j))) = functions(j:j)
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end if
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end do
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! Add nonary ops to retrieve each of the input variables:
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do i=1,nvar
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nn(0) = nn(0) + 1
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func(0)(nn(0):nn(0)) = char(96+i)
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end do
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write(*,'(1a24,1a22)') 'Functions used..........',usedfuncs(1:lnblnk(usedfuncs))
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do i=0,2
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write(*,*) 'Arity ',i,': ',func(i)(1:nn(i))
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end do
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write(*,'(1a24)') 'Loading mystery data....'
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call LoadMatrixTranspose(nvarmax+1,nvar+1,nmax,ndata,xy,mysteryfile)
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write(*,'(1a24,i8)') 'Number of examples......',ndata
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! Find max(abs(y)) to use for normalization estimation (crucial to avoid data point where y~0):
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jmax=1
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ymax = abs(xy(1,nvar+1))
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do j=2,ndata
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if (ymax < abs(xy(nvar+1,j))) then
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ymax = abs(xy(nvar+1,j))
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jmax = j
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end if
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end do
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print *,'Mystery data has largest magnitude ',ymax,' at j=',jmax
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print *,'Searching for best fit...'
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nformulas = 0
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minloss = 1.e6
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template = ''
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ops='===================='
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open(2,file=templatefile,status='old',err=670)
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open(3,file=outfile)
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555 read(2,'(1a60)',end=665) template
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n = lnblnk(template)
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!print *,"template:",template(1:n),"#####"
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do i=1,n
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ii(i) = ichar(template(i:i))-48
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radix(i) = nn(ii(i))
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kk(i) = 0
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end do
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done = .false.
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do while ((minloss.gt.epsilon).and.(.not.done))
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nformulas = nformulas + 1
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! Analyze structure ii:
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do i=1,n
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ops(i:i) = func(ii(i))(1+kk(i):1+kk(i))
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!print *,'TEST ',i,ii(i), func(ii(i))
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end do
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!write(*,'(1f20.12,99i3)') minloss, (ii(i),i=1,n), (kk(i),i=1,n)
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!write(*,'(1a24)') ops(1:n)
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prefactor = xy(nvar+1,jmax)/f(n,ii,ops,xy(1,jmax))
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j = 1
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maxloss = 0.
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do while ((maxloss.lt.minloss).and.(j.le.ndata))
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newloss = abs(xy(nvar+1,j) - prefactor*f(n,ii,ops,xy(1,j)))
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!!!!!print *,'newloss: ',j,newloss,xy(nvar,j),f(n,ii,ops,xy(1,j))
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if (.not.((newloss.ge.0).or.(newloss.le.0))) newloss = 1.e30 ! This was a NaN :-)
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if (maxloss.lt.newloss) maxloss = newloss
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j = j + 1
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end do
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if (maxloss.lt.minloss) then ! We have a new best fit
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minloss = maxloss
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rmsloss = 0.
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do j=1,ndata
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rmsloss = rmsloss + (xy(nvar+1,j) - prefactor*f(n,ii,ops,xy(1,j)))**2
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end do
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rmsloss = sqrt(rmsloss/ndata)
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DL = log(nformulas*max(1.,minloss/epsilon))/log(2.)
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DL2 = log(nformulas*max(1.,minloss/1.e-15))/log(2.)
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DL3 = (log(1.*nformulas) + sqrt(1.*ndata)*log(max(1.,rmsloss/1.e-15)))/log(2.)
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write(*,'(2f20.12,x,1a22,1i16,4f19.4)') limit(minloss), limit(prefactor), ops(1:n), nformulas, rmsloss, DL, DL2, DL3
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write(3,'(2f20.12,x,1a22,1i16,4f19.4)') limit(minloss), limit(prefactor), ops(1:n), nformulas, rmsloss, DL, DL2, DL3
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flush(3)
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end if
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call multiloop(n,radix,kk,done)
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end do
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goto 555
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665 close(3)
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close(2)
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print *,'All done: results in ',outfile
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return
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666 stop 'DEATH ERROR: missing file args.dat'
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668 print *,'DEATH ERROR: missing file ',opsfile(1:lnblnk(opsfile))
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stop
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670 print *,'DEATH ERROR: missing file ',templatefile(1:lnblnk(templatefile))
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stop
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end
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real*8 function limit(x)
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implicit none
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real*8 x, xmax
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parameter(xmax=666.)
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if (abs(x).lt.xmax) then
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limit = x
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else
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limit = sign(xmax,x)
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end if
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return
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end
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real*8 function f(n,arities,ops,x) ! n=number of ops, x=arg vector
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implicit none
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integer nmax, n, i, j, arities(n), arity, lnblnk
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character*60 ops
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parameter(nmax=100)
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real*8 x(nmax), y, stack(nmax)
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character op
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!write(*,*) 'Evaluating function with ops = ',ops(1:n)
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!write(*,'(3f10.5,99i3)') (x(i),i=1,3), (arities(i),i=1,n)
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j = 0 ! Number of numbers on the stack
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do i=1,n
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arity = arities(i)
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op = ops(i:i)
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if (arity.eq.0) then ! This is a nonary function
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if (op.eq."0") then
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y = 0.
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else if (op.eq."1") then
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y = 1.
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else if (op.eq."P") then
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y = 4.*atan(1.) ! pi
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else
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y = x(ichar(op)-96)
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end if
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else if (arity.eq.1) then ! This is a unary function
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if (op.eq.">") then
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y = stack(j) + 1
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else if (op.eq."<") then
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y = stack(j) - 1
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else if (op.eq."~") then
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y = -stack(j)
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else if (op.eq."\") then
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y = 1./stack(j)
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else if (op.eq."L") then
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y = log(stack(j))
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else if (op.eq."E") then
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y = exp(stack(j))
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else if (op.eq."S") then
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y = sin(stack(j))
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else if (op.eq."C") then
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y =cos(stack(j))
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else if (op.eq."A") then
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y = abs(stack(j))
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else if (op.eq."N") then
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y = asin(stack(j))
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else if (op.eq."T") then
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y = atan(stack(j))
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else
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y = sqrt(stack(j))
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end if
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else ! This is a binary function
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if (op.eq."+") then
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y = stack(j-1)+stack(j)
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else if (op.eq."-") then
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y = stack(j-1)-stack(j)
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else if (op.eq."*") then
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y = stack(j-1)*stack(j)
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else
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y = stack(j-1)/stack(j)
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end if
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end if
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j = j + 1 - arity
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stack(j) = y
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! write(*,'(9f10.5)') (stack(k),k=1,j)
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end do
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if (j.ne.1) stop 'DEATH ERROR: STACK UNBALANCED'
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f = stack(1)
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!write(*,'(9f10.5)') 666.,x(1),x(2),x(3),f
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return
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end
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subroutine multiloop(n,bases,i,done)
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! Handles <n> nested loops with loop variables i(1),...i(n).
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! Example: With n=3, bases=2, repeated calls starting with i=(000) will return
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! 001, 010, 011, 100, 101, 110, 111, 000 (and done=.true. the last time).
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! All it's doing is counting in mixed radix specified by the array <bases>.
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implicit none
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integer n, bases(n), i(n), k
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logical done
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done = .false.
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k = 1
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555 i(k) = i(k) + 1
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if (i(k).lt.bases(k)) return
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i(k) = 0
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k = k + 1
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if (k.le.n) goto 555
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done = .true.
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return
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end
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subroutine LoadMatrixTranspose(nd,n,mmax,m,A,f)
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! Reads the n x m matrix A from the file named f, stored as its transpose
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implicit none
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integer nd,mmax,n,m,j
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real*8 A(nd,mmax)
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character*60 f
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open(2,file=f,status='old')
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m = 0
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555 m = m + 1
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if (m.gt.mmax) stop 'DEATH ERROR: m>mmax in LoadVectorTranspose'
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read(2,*,end=666) (A(j,m),j=1,n)
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goto 555
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666 close(2)
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m = m - 1
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print *,m,' rows read from file ',f
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return
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end
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