clean up

ups

fluents/lib/engines.py

@@ -1,6 +1,6 @@
-"""Module contain algorithms for  (burdensome) calculations.
+"""Module contain algorithms for low-rank models.
 
-There is no typechecking of any kind here, just focus on speed
+There is almost no typechecking of any kind here, just focus on speed
 """
 
 import math
@@ -56,40 +56,47 @@ def pca(a, aopt, scale='scores', mode='normal'):
 
 
 def pcr(a, b, aopt=2, scale='scores', mode='normal'):
-    """Returns Principal component regression model."""
-    m, n = a.shape
-    try:
-        k, l = b.shape
-    except:
-        k = b.shape[0]
-        l = 1
-    B = empty((aopt, n, l))
-    U, s, Vt = svd(a, full_matrices=True)
-    T = U*s
-    T = T[:,:aopt]
-    P = Vt[:aopt,:].T
-    Q = dot(dot(inv(dot(T.T, T)), T.T), b).T
-    for i in range(aopt):
-        ti = T[:,:i+1]
-        r = dot(dot(inv(dot(ti.T,ti)), ti.T), b)
-        B[i] = dot(P[:,:i+1], r)
-    E = a - dot(T, P.T)
-    F = b - dot(T, Q.T)
+    """Principal Component Regression.
+
+    Returns 
+
+    """
+    m, n = m_shape(a)
+    B = empty((aopt, n, l))
+    dat = pca(a, aopt=aopt, scale=scale, mode='normal', center_axis=0)
+    T = dat['T']
+    weigths = apply_along_axis(vnorm, 0, T)
+    if scale=='loads':
+        # fixme: check weights
+        Q = dot(b.T, T*weights)
+    else:
+        Q = dot(b.T, T/weights**2)
+
+    if mode=='fast':
+        return {'T', T:, 'P':P, 'Q':Q}
+    if mode=='detailed':
+        for i in range(1, aopt+1, 1):
+            F[i,:,:] = b - dot(T[:,i],Q[:,:i].T)
+    else:
+        F = b - dot(T, Q.T)
+    #fixme: explained variance in Y + Y-var leverages
+    dat.update({'Q',Q, 'F':F})
+    return dat
 
-    return {'T':T, 'P':P,'Q': Q, 'B':B, 'E':E, 'F':F}
-    
 def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
-    """Kernel pls for tall/wide matrices.
+    """Partial Least Squares Regression.
+
+    Applies plsr to given matrices and returns results in a dictionary.
 
     Fast pls for calibration. Only inefficient for many Y-vars.
-    
     """
     m, n = a.shape
     if ab!=None:
-        mm, l = m_shape(ab)
+        mm, ll = m_shape(ab)
     else:
-        k, l = m_shape(b)
-
+         k, l = m_shape(b)
+    assert(m==mm)
+    assert(l==ll)
     W = empty((n, aopt))
     P = empty((n, aopt))
     R = empty((n, aopt))
@@ -97,7 +104,7 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
     T = empty((m, aopt))
     B = empty((aopt, n, l))
 
-    if ab==None: 
+    if ab==None:
         ab = dot(a.T, b)
     for i in range(aopt):
         if ab.shape[1]==1:
@@ -105,11 +112,11 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
         else:
             u, s, vh = svd(dot(ab.T, ab))
             w = dot(ab, u[:,:1])
-    
+
         w = w/vnorm(w)
         r = w.copy()
-        if i>0:
-            for j in range(0,i,1):
+        if i>0: # recursive estimate to 
+            for j in range(0, i, 1):
                 r = r - dot(P[:,j].T, w)*R[:,j][:,newaxis]
         t = dot(a, r)
         tt = vnorm(t)**2
@@ -130,7 +137,7 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
 
         Q[:,i] = q.ravel()
         B[i] = dot(R[:,:i+1], Q[:,:i+1].T)
-    
+
     if mode=='detailed':
         E = empty((aopt, m, n))
         F = empty((aopt, k, l))
@@ -147,13 +154,13 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', ab=None):
         W = W*tnorm
         Q = Q*tnorm
         P = P*tnorm
-        
+
     return {'B':B, 'Q':Q, 'P':P, 'T':T, 'W':W, 'R':R, 'E':E, 'F':F}
 
 def w_simpls(aat, b, aopt):
     """ Simpls for wide matrices.
     Fast pls for crossval, used in calc rmsep for wide X
-    There is no P,W.  T is normalised
+    There is no P or W.  T is normalised
     """
     bb = b.copy()
     m, m = aat.shape
@@ -181,7 +188,7 @@ def w_simpls(aat, b, aopt):
 def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
     """Undeflated Ridged svd(X'Y)
     """
-    m, n = a.shape
+    m, n = m_shape(a)
     k, l = m_shape(b)
     u, s, vt = svd(b, full_matrices=0)
     g0 = dot(u*s, u.T)
@@ -204,7 +211,7 @@ def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
     B = zeros((aopt, n, l), dtype='f')
     for i in range(aopt):
         B[i] = dot(W[:,:i+1], Q[:,:i+1].T)
-    
+
     if mode == 'detailed':
         E = empty((aopt, m, n))
         F = empty((aopt, k, l))
@@ -214,14 +221,23 @@ def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
     else: #normal
         F = b - dot(a, B[-1])
         E = a - dot(T, W.T)
+    # leverages
+    # fixme: probably need an orthogonal basis for row-space leverage
+    #        T (scores) are not orthogonal
+    #        Using a qr decomp to get an orthonormal basis for row-space
+    #Tq = qr(T)[0]
+    #s_lev,v_lev = leverage(aopt,Tq,W)
+    # explained variance
+    #var_x, exp_var_x = variances(a,T,W)
+    #qnorm = apply_along_axis(norm, 0, Q)
+    #var_y, exp_var_y = variances(b,U,Q/qnorm)
 
     if scale=='loads':
         T = T/tnorm
         W = W*tnorm
         Q = Q*tnorm
-        
+
     return {'B':B, 'W':W, 'T':T, 'Q':Q, 'E':E, 'F':F, 'U':U, 'P':W}
-    
 
 
 def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', scale='scores', verbose=False):