Testing code for line search with simplex *equality* constraints and positivity constraints.

git-svn-id: https://ws10smt.googlecode.com/svn/trunk@217 ec762483-ff6d-05da-a07a-a48fb63a330f

2 files changed, 113 insertions, 0 deletions

diff --git a/gi/posterior-regularisation/linesearch.py b/gi/posterior-regularisation/linesearch.py
new file mode 100644
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+++ b/gi/posterior-regularisation/linesearch.py
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+## Automatically adapted for scipy Oct 07, 2005 by convertcode.py
+
+from scipy.optimize import minpack2
+import numpy
+
+import __builtin__
+pymin = __builtin__.min
+
+def line_search(f, myfprime, xk, pk, gfk, old_fval, old_old_fval,
+                args=(), c1=1e-4, c2=0.9, amax=50):
+
+    fc = 0
+    gc = 0
+    phi0 = old_fval
+    derphi0 = numpy.dot(gfk,pk)
+    alpha1 = pymin(1.0,1.01*2*(phi0-old_old_fval)/derphi0)
+    # trevor: added this test
+    alpha1 = pymin(alpha1,amax)
+
+    if isinstance(myfprime,type(())):
+        eps = myfprime[1]
+        fprime = myfprime[0]
+        newargs = (f,eps) + args
+        gradient = False
+    else:
+        fprime = myfprime
+        newargs = args
+        gradient = True
+
+    xtol = 1e-14
+    amin = 1e-8
+    isave = numpy.zeros((2,), numpy.intc)
+    dsave = numpy.zeros((13,), float)
+    task = 'START'
+    fval = old_fval
+    gval = gfk
+
+    while 1:
+        stp,fval,derphi,task = minpack2.dcsrch(alpha1, phi0, derphi0, c1, c2,
+                                               xtol, task, amin, amax,isave,dsave)
+        #print 'minpack2.dcsrch', alpha1, phi0, derphi0, c1, c2, xtol, task, amin, amax,isave,dsave
+        #print 'returns', stp,fval,derphi,task
+
+        if task[:2] == 'FG':
+            alpha1 = stp
+            fval = f(xk+stp*pk,*args)
+            fc += 1
+            gval = fprime(xk+stp*pk,*newargs)
+            if gradient: gc += 1
+            else: fc += len(xk) + 1
+            phi0 = fval
+            derphi0 = numpy.dot(gval,pk)
+        else:
+            break
+
+    if task[:5] == 'ERROR' or task[1:4] == 'WARN':
+        stp = None  # failed
+    return stp, fc, gc, fval, old_fval, gval
diff --git a/gi/posterior-regularisation/simplex_pg.py b/gi/posterior-regularisation/simplex_pg.py
new file mode 100644
index 00000000..5da796d3
--- /dev/null
+++ b/gi/posterior-regularisation/simplex_pg.py
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+#
+# Following Leunberger and Ye, Linear and Nonlinear Progamming, 3rd ed. p367
+# "The gradient projection method"
+# applied to an equality constraint for a simplex.
+#
+#   min f(x)
+#   s.t. x >= 0, sum_i x = d
+#
+# FIXME: enforce the positivity constraint - a limit on the line search?
+#
+
+from numpy import *
+from scipy import *
+from linesearch import line_search
+# local copy of scipy's Amijo line_search - wasn't enforcing alpha max correctly
+import sys
+
+dims = 4
+
+def f(x):
+    fv = x[0]*x[0] + x[1]*x[1] + x[2]*x[2] + x[3]*x[3] - 2*x[0] - 3*x[3]
+    # print 'evaluating f at', x, 'value', fv
+    return fv
+
+def g(x):
+    return array([2*x[0] - 2, 2*x[1], 2*x[2], 2*x[3]-3])
+
+def pg(x):
+    gv = g(x)
+    return gv - sum(gv) / dims
+
+x = ones(dims) / dims
+old_fval = None
+
+while True:
+    fv = f(x)
+    gv = g(x)
+    dv = pg(x)
+
+    print 'x', x, 'f', fv, 'g', gv, 'd', dv
+
+    if old_fval == None:
+        old_fval = fv + 0.1
+
+    # solve for maximum step size i.e. when positivity constraints kick in
+    # x - alpha d = 0   => alpha = x/d
+    amax = max(x/dv)
+    if amax < 1e-8: break
+
+    stuff = line_search(f, pg, x, -dv, dv, fv, old_fval, amax=amax)
+    alpha = stuff[0] # Nb. can avoid next evaluation of f,g,d using 'stuff'
+    if alpha < 1e-8: break
+    x -= alpha * dv
+
+    old_fval = fv