Add files via upload

Code/S_snap.py

@@ -0,0 +1,78 @@
+# The following are snap functions for finding a best approximated integer or rational number for a real number:
+
+import numpy as np
+
+def bestApproximation(x,imax):
+    # The input is a numpy parameter vector p.
+    # The output is an integer specifying which parameter to change,
+    # and a float specifying the new value.
+    def float2contfrac(x,nmax):
+        x = float(x)
+        c = [np.floor(x)];
+        y = x - np.floor(x)
+        k = 0
+        while np.abs(y)!=0 and k<nmax:
+            y = 1 / float(y)
+            i = np.floor(y)
+            c.append(i)
+            y = y - i
+            k = k + 1
+        return c
+    
+    def contfrac2frac(seq):
+        ''' Convert the simple continued fraction in `seq`
+            into a fraction, num / den
+            '''
+        num, den = 1, 0
+        for u in reversed(seq):
+            num, den = den + num*u, num
+        return num, den
+    
+    def contFracRationalApproximations(c):
+        return np.array(list(contfrac2frac(c[:i+1]) for i in range(len(c))))
+    
+    def contFracApproximations(c):
+        q = contFracRationalApproximations(c)
+        return q[:,0] / float(q[:,1])
+    
+    def truncateContFrac(q,imax):
+        k = 0
+        while k < len(q) and np.maximum(np.abs(q[k,0]), q[k,1]) <= imax:
+            k = k + 1
+        return q[:k]
+    
+    def pval(p):
+        p = p.astype(float)
+        return 1 - np.exp(-p ** 0.87 / 0.36)
+    
+    xsign = np.sign(x)
+    q = truncateContFrac(contFracRationalApproximations(float2contfrac(abs(x),20)),imax)
+    
+    if len(q) > 0:
+        p = np.abs(q[:,0] / q[:,1] - abs(x)).astype(float) * (1 + np.abs(q[:,0])) * q[:,1]
+        p = pval(p)
+        i = np.argmin(p)
+        return (xsign * q[i,0] / float(q[i,1]), xsign* q[i,0], q[i,1], p[i])
+    else:
+        return (None, 0, 0, 1)
+
+def integerSnap(p, top=1):
+    p = np.array(p)
+    metric = np.abs(p - np.round(p.astype(np.double)))
+    chosen = np.argsort(metric)[:top]
+    return list(zip(chosen, np.round(p.astype(np.double))[chosen]))
+
+
+def zeroSnap(p, top=1):
+    p = np.array(p)
+    metric = np.abs(p)
+    chosen = np.argsort(metric)[:top]
+    return list(zip(chosen, np.zeros(len(chosen))))
+
+
+def rationalSnap(p, top=1):
+    """Snap to nearest rational number using continued fraction."""
+    p = np.array(p)
+    snaps = np.array(list(bestApproximation(x,100) for x in p))
+    chosen = np.argsort(snaps[:, 3])[:top]
+    return list(zip(chosen, snaps[chosen, 0:3]))