....

fluents/lib/blmfuncs.py

@@ -693,13 +693,13 @@ class LplsOptions(Options):
         opt['mode'] = 'normal' # how much info to calculate
         opt['amax'] = 10
         opt['aopt'] = 3
-        opt['xz_alpha'] = 0.4
+        opt['xz_alpha'] = 0.6
         opt['auto_aopt'] = False
         opt['center'] = True
-        opt['center_mth'] = [2, 2, 1]
+        opt['center_mth'] = [2, 0, 2]
         opt['scale'] = 'scores'
-        opt['calc_conf'] = True
+        opt['calc_conf'] = False
-        opt['n_sets'] = 75
+        opt['n_sets'] = 7
         opt['strict'] = False
         opt['p_center'] = 'med'
         opt['alpha'] = .3

fluents/lib/cx_stats.py

@@ -1,6 +1,6 @@
 from scipy import zeros,zeros_like,sqrt,dot,trace,sign,round_,argmax,\
      sort,ravel,newaxis,asarray,diag,sum,outer,argsort,arange,ones_like,\
-     all,apply_along_axis,eye
+     all,apply_along_axis,eye,atleast_2d
 from scipy.linalg import svd,inv,norm,det,sqrtm
 from scipy.stats import mean,median
 from cx_utils import mat_center
@@ -26,8 +26,8 @@ def hotelling(Pcv, P, p_center='med', cov_center='med',
     m, n = P.shape
     n_sets, n, amax = Pcv.shape
     # allocate
-    T_sq = empty((n, ),dtype='f')
+    T_sq = empty((n, ),dtype='d')
-    Cov_i = zeros((n, amax, amax),dtype='f')
+    Cov_i = zeros((n, amax, amax),dtype='d')
     
     # rotate sub_models to full model
     if crot:
@@ -56,10 +56,12 @@ def hotelling(Pcv, P, p_center='med', cov_center='med',
     
     reg_cov = (1. - alpha)*Cov_i + alpha*Cov
     for i in xrange(n):
-        Pc = P_ctr[i,:][:,newaxis]
+        #Pc = P_ctr[i,:][:,newaxis]
+        Pc = P_ctr[i,:]
         sigma = reg_cov[i]
-        #T_sq[i] = sqrt(dot(dot(Pc.T, inv(sigma)), Pc).ravel())
+        # T_sq[i] = (dot(Pc, inv(sigma) )*Pc).sum() #slow
-        T_sq[i] = dot(dot(Pc.T, inv(sigma)), Pc).ravel()  
+        T_sq[i] = dot(dot(Pc, inv(sigma)), Pc) # dont need to care about transposes
+        #T_sq[i] = dot(dot(Pc.T, inv(sigma)), Pc).ravel()
     return T_sq
 
 def procrustes(A, B, strict=True, center=False, verbose=False):
@@ -147,10 +149,10 @@ def pls_qvals(a, b, aopt=None, alpha=.3,
     tsq_full = hotelling(Wcv, dat['W'], p_center=p_center,
                          alpha=alpha, crot=crot, strict=strict,
                          cov_center=cov_center)
-    t0 = time.time()
+    #t0 = time.time()
     Vs = shuffle_1d(bc, n_iter, axis=0)
     for i, b_shuff in enumerate(Vs):
-        t1 = time.time()
+        #t1 = time.time()
         if algo=='bridge':
             dat = bridge(ac, b_shuff, aopt, 'loads','fast')
         else:
@@ -159,23 +161,10 @@ def pls_qvals(a, b, aopt=None, alpha=.3,
         TSQ[:,i] = hotelling(Wcv, dat['W'], p_center=p_center,
                              alpha=alpha, crot=crot, strict=strict,
                              cov_center=cov_center)
-        print time.time() - t1
+        #print time.time() - t1
-    sort_index = argsort(tsq_full)[::-1]
+    
-    back_sort_index = sort_index.argsort()
+    return fdr(tsq_full, TSQ, median)
-    print time.time() - t0
     
-    # count false positives
-    tsq_full_sorted = tsq_full.take(sort_index)
-    for i in xrange(n_iter):
-        for j in xrange(n):
-            n_false[j,i] = sum(TSQ[:,i]>=tsq_full[j]) # number of false pos. genes (0-n)
-    false_pos = median(n_false, 1)
-    ll = arange(1, len(false_pos)+1, 1)
-    sort_qval = false_pos.take(sort_index)/ll
-    qval = false_pos/ll.take(back_sort_index)
-    print time.time() - t0
-    #return qval, false_pos, TSQ, tsq_full
-    return qval
 
 def ensure_strict(C, only_flips=True):
     """Ensure that a rotation matrix does only 90 degree rotations.
@@ -267,6 +256,7 @@ def pls_qvals_II(a, b, aopt=None, center=True, alpha=.3,
     qval = false_pos/ll.take(back_sort_index)
     print time.time() - t0
     #return qval, false_pos, TSQ, tsq_full
+
     return qval
 
 def leverage(aopt=1,*args):
@@ -333,3 +323,107 @@ def vnorm(x):
     This is considerably faster than linalg.norm
     """
     return sqrt(dot(x,x.conj()))
+
+def mahalanobis(a, loc=None, acov=None, invcov=None):
+    """Returns the distance of each observation in a
+    from the location estimate (loc) of the data,
+    relative to the shape of the data.
+    
+    
+    a : data matrix (n observations in rows, p variables in columns)
+    loc : location estimate of the data (p-dimensional vector)
+    covmat or invcov : scatter estimate of the data or the inverse of the scatter estimate (pxp matrix)
+
+    :Returns:
+    A vector containing the distances of all the observations to locvct.
+    
+    """
+    n, p = a.shape
+    if loc==None:
+        loc = a.mean(0)
+    loc = atleast_2d(loc)
+    if loc.shape[1]==1:
+        loc = loc.T; #ensure rowvector
+    assert(loc.shape[1]==p)
+    xc = a - loc
+    if acov==None and invcov==None:
+        acov = dot(xc.T, xc)
+        
+    if invcov != None:
+        covmat = atleast_2d(invcov)
+        if min(covmat.shape)==1:
+            covmat = diag(invcov.ravel())
+    else:
+        covmat = atleast_2d(acov)
+        if min(covmat.shape)==1:
+            covmat = diag(covmat.ravel())
+        covmat = inv(covmat)
+    # mdist = diag(dot(dot(xc, covmat),xc.T))
+    mdist = (dot(xc, covmat)*xc).sum(1)
+    return mdist
+
+def lpls_qvals(a, b, c, aopt=None, alpha=.3, zx_alpha=.5, n_iter=20,center=True,
+               sim_method='shuffle',p_center='med', cov_center='med',crot=True, strict=False):
+
+    """Returns qvals for l-pls model.
+
+    input:
+    a -- data matrix
+    b -- data matrix
+    c -- data matrix
+    aopt -- scalar, opt. number of components
+    alpha -- [0,1] regularisation parameter for T2-test
+    xz_alpha -- [0,1] how much z info to include
+    n_iter -- number of permutations
+    sim_method -- permutation method ['shuffle']
+    p_center -- location estimator for sub models ['med']
+    cov_center -- location estimator for covariance of submodels ['med']
+    crot -- bool, use rotations of sub models?
+    strict -- bool, use stict (rot/flips only) rotations?
+    """
+    
+    m, n = a.shape
+    TSQ = zeros((n, n_iter), dtype='d') # (nvars x n_subsets)
+    n_false = zeros((n, n_iter), dtype='d')
+
+
+    # Full model
+    dat = lpls(a, b, c, aopt, scale='loads')
+    Wcv = lpls_jk(a, b, c ,aopt, n_blocks=None, algo=algo,center=center)
+    tsq_x = hotelling(Wcv, dat['W'], p_center=p_center,alpha=alpha, crot=crot, strict=strict,
+                      cov_center=cov_center)
+    Lcv = lpls_jk(a, b, c ,aopt, n_blocks=None, algo=algo,center=center)
+    tsq_z = hotelling(Lcv, dat['L'], p_center=p_center,alpha=alpha, crot=crot, strict=strict,
+                      cov_center=cov_center)
+
+    # Perturbations
+    t0 = time.time()
+    Vs = shuffle_1d(b, n_iter, axis=0)
+    for i, b_shuff in enumerate(Vs):
+        t1 = time.time()
+        dat = pls(ac, b_shuff, aopt, 'loads', 'fast')
+        Wcv = pls_jkW(a, b_shuff, aopt, n_blocks=None, algo=algo)
+        TSQ[:,i] = hotelling(Wcv, dat['W'], p_center=p_center,
+                             alpha=alpha, crot=crot, strict=strict,
+                             cov_center=cov_center)
+        print time.time() - t1
+   
+    return fdr(tsq_full, TSQ, median)
+    
+
+
+def fdr(tsq, tsqp, loc_method=median):
+    n, = tsq.shape
+    k, m = tsqp.shape
+    assert(n==k)
+    n_false = empty((n, m), 'd')
+    sort_index = argsort(tsq)[::-1]
+    r_index = argsort(sort_index)
+    for i in xrange(m):
+        for j in xrange(n):
+            n_false[j,i] = (tsqp[:,i]>tsq[j]).sum()
+    
+    fp = loc_method(n_false,1)
+    n_signif = (arange(n) + 1.0)[r_index]
+    fd_rate = fp/n_signif
+    return fd_rate

fluents/lib/engines.py

@@ -4,15 +4,21 @@ There is almost no typechecking of any kind here, just focus on speed
 """
 
 import math
+import warnings
 from scipy.linalg import svd,inv
 from scipy import dot,empty,eye,newaxis,zeros,sqrt,diag,\
      apply_along_axis,mean,ones,randn,empty_like,outer,r_,c_,\
-     rand,sum,cumsum,matrix, expand_dims,minimum,where,arange
+     rand,sum,cumsum,matrix, expand_dims,minimum,where,arange,inner,tile
-has_sym=True
+has_sym = True
+has_arpack = True
 try:
     from symeig import symeig
 except:
     has_sym = False
+try:
+    from scipy.sandbox import arpack
+except:
+    has_arpack = False
 
 
 def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
@@ -45,7 +51,6 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
 
     Notes
     -----
-
     Uses kernel speed-up if m>>n or m<<n.
 
     If residuals turn rank deficient, a lower number of component than given
@@ -101,6 +106,7 @@ def pca(a, aopt,scale='scores',mode='normal',center_axis=0):
     else:
         # residuals
         E = a - dot(T, P.T)
+        #E = a
         SEP = E**2
         ssq = [SEP.sum(0), SEP.sum(1)]
         # leverages
@@ -256,6 +262,7 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
     Q = empty((l, aopt))
     T = empty((m, aopt))
     B = empty((aopt, n, l))
+    tt = empty((aopt,))
 
     if ab==None:
         ab = dot(a.T, b)
@@ -265,10 +272,10 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
             w = w/vnorm(w)
         elif n<l: # more yvars than xvars
             if has_sym:
-                s, u = symeig(dot(ab, ab.T),range=[l,l],overwrite=True)
+                s, w = symeig(dot(ab, ab.T),range=[n,n],overwrite=True)
             else:
-                u, s, vh = svd(dot(ab, ab.T))
+                w, s, vh = svd(dot(ab, ab.T))
-            w = u[:,0]
+            w = w[:,:1]
         else: # standard wide xdata
             if has_sym:
                 s, q = symeig(dot(ab.T, ab),range=[l,l],overwrite=True)
@@ -283,16 +290,16 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
                 r = r - dot(P[:,j].T, w)*R[:,j][:,newaxis]
         
         t = dot(a, r)
-        tt = vnorm(t)**2
+        tt[i] = tti = dot(t.T, t).ravel()
-        p  = dot(a.T, t)/tt
+        p  = dot(a.T, t)/tti
-        q = dot(r.T, ab).T/tt
+        q = dot(r.T, ab).T/tti
-        ab = ab - dot(p, q.T)*tt
+        ab = ab - dot(p, q.T)*tti
         T[:,i] = t.ravel()
         W[:,i] = w.ravel()
 
         if mode=='fast' and i==aopt-1:
             if scale=='loads':
-                tnorm = apply_along_axis(vnorm, 0, T)
+                tnorm = sqrt(tt)
                 T = T/tnorm
                 W = W*tnorm
             return {'T':T, 'W':W}
@@ -300,26 +307,54 @@ def pls(a, b, aopt=2, scale='scores', mode='normal', center_axis=-1, ab=None):
         P[:,i] = p.ravel()
         R[:,i] = r.ravel()
         Q[:,i] = q.ravel()
-        B[i] = dot(R[:,:i+1], Q[:,:i+1].T)
+        #B[i] = dot(R[:,:i+1], Q[:,:i+1].T)
 
+
+        
+    qnorm = apply_along_axis(vnorm, 0, Q)
+    tnorm = sqrt(tt)
+    pp = (P**2).sum(0)
     if mode=='detailed':
         E = empty((aopt, m, n))
         F = empty((aopt, k, l))
-        for i in range(1, aopt+1, 1):
+        ssqx, ssqy = [], []
-            E[i-1] = a - dot(T[:,:i], P[:,:i].T)
+        leverage = empty((aopt, m))
+        h2x = [] #hotellings T^2
+        h2y = []
+        for ai in range(aopt):
+            E[ai,:,:] = a - dot(T[:,:ai+1], P[:,:ai+1].T)
             F[i-1] = b - dot(T[:,:i], Q[:,:i].T)
+            ssqx.append([(E[ai,:,:]**2).mean(0), (E[ai,:,:]**2).mean(1)])
+            ssqy.append([(F[ai,:,:]**2).mean(0), (F[ai,:,:]**2).mean(1)])
+            leverage[ai,:] = 1./m + ((T[:,:ai+1]/tnorm[:ai+1])**2).sum(1)
+            h2y.append(1./k + ((Q[:,:ai+1]/qnorm[:ai+1])**2).sum(1))
     else:
-        E = a - dot(T[:,:aopt], P[:,:aopt].T)
+        # residuals
-        F = b - dot(T[:,:aopt], Q[:,:aopt].T)
+        E = a - dot(T, P.T)
+        F = b - dot(T, Q.T)
+        sepx = E**2
+        ssqx = [sepx.sum(0), sepx.sum(1)]
+        sepy = F**2
+        ssqy = [sepy.sum(0), sepy.sum(1)]
+        # leverage
+        leverage = 1./m + ((T/tnorm)**2).sum(1)
+        h2x = []
+        h2y = []
+    # variances
+    tp= tt*pp
+    tq = tt*qnorm*qnorm
+    expvarx = r_[0, 100*tp/(a*a).sum()]
+    expvary = r_[0, 100*tq/(b*b).sum()]
     
     if scale=='loads':
-        tnorm = apply_along_axis(vnorm, 0, T)
         T = T/tnorm
         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}
+    return {'Q':Q, 'P':P, 'T':T, 'W':W, 'R':R, 'E':E, 'F':F,
+            'expvarx':expvarx, 'expvary':expvary, 'ssqx':ssqx, 'ssqy':ssqy,
+            'leverage':leverage, 'h2':h2x}
 
 def w_simpls(aat, b, aopt):
     """ Simpls for wide matrices.
@@ -423,16 +458,6 @@ 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
@@ -442,7 +467,7 @@ def bridge(a, b, aopt, scale='scores', mode='normal', r=0):
     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):
+def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', verbose=False):
     """ L-shaped Partial Least Sqaures Regression by the nipals algorithm.
 
     (X!Z)->Y
@@ -464,6 +489,9 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
       evx : X-explained variance
       evy : Y-explained variance
       evz : Z-explained variance
+      mnx : X location
+      mny : Y location
+      mnz : Z location
 
     :Notes:
     
@@ -471,12 +499,12 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
     if mean_ctr!=None:
         xctr, yctr, zctr = mean_ctr
         X, mnX = center(X, xctr)
-        Y, mnY = center(Y, xctr)
+        Y, mnY = center(Y, yctr)
         Z, mnZ = center(Z, zctr)
 
-    varX = pow(X, 2).sum()
+    varX = (X**2).sum()
-    varY = pow(Y, 2).sum()
+    varY = (Y**2).sum()
-    varZ = pow(Z, 2).sum()
+    varZ = (Z**2).sum()
     
     m, n = X.shape
     k, l = Y.shape
@@ -491,36 +519,40 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
     K = empty((o, a_max))
     L = empty((u, a_max))
     B = empty((a_max, n, l))
-    b0 = empty((a_max, m, l))
+    #b0 = empty((a_max, 1, l))
     var_x = empty((a_max,))
     var_y = empty((a_max,))
     var_z = empty((a_max,))
 
+    MAX_ITER = 250
+    LIM = 1e-1
     for a in range(a_max):
         if verbose:
-            print "\n Working on comp. %s" %a
+            print "\nWorking on comp. %s" %a
         u = Y[:,:1]
         diff = 1
-        MAX_ITER = 200
-        lim = 1e-16
         niter = 0
-        while (diff>lim and niter<MAX_ITER):
+        while (diff>LIM and niter<MAX_ITER):
             niter += 1
             u1 = u.copy()
             w = dot(X.T, u)
             w = w/sqrt(dot(w.T, w))
+            #w = w/dot(w.T, w)
             l = dot(Z, w)
             k = dot(Z.T, l)
             k = k/sqrt(dot(k.T, k))
+            #k = k/dot(k.T, k)
             w = alpha*k + (1-alpha)*w
+            #print sqrt(dot(w.T, w))
             w = w/sqrt(dot(w.T, w))
             t = dot(X, w)
             c = dot(Y.T, t)
             c = c/sqrt(dot(c.T, c))
             u = dot(Y, c)
-            diff = abs(u1 - u).max()
+            diff = dot((u-u1).T, (u-u1))
         if verbose:
             print "Converged after %s iterations" %niter
+            print "Error: %.2E" %diff
         tt = dot(t.T, t)
         p = dot(X.T, t)/tt
         q = dot(Y.T, t)/tt
@@ -543,7 +575,8 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
         var_z[a] = pow(Z, 2).sum()
     
         B[a] = dot(dot(W[:,:a+1], inv(dot(P[:,:a+1].T, W[:,:a+1]))), Q[:,:a+1].T)
-        b0[a] = mnY - dot(mnX, B[a])
+        #b0[a] = mnY - dot(mnX, B[a])
+        
     
     # variance explained
     evx = 100.0*(1 - var_x/varX)
@@ -558,7 +591,7 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], mode='normal', sca
         L = L*knorm
         K = K/knorm
     
-    return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'L':L, 'K':K, 'B':B, 'b0':b0, 'evx':evx, 'evy':evy, 'evz':evz}    
+    return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'L':L, 'K':K, 'B':B, 'evx':evx, 'evy':evy, 'evz':evz,'mnx': mnX, 'mny': mnY, 'mnz': mnZ}    
 
 
 
@@ -670,7 +703,8 @@ def nipals_pls(X, Y, a_max, alpha=.7, ax_center=0, mode='normal', scale='scores'
         W = W*tnorm
         Q = Q*tnorm
     
-    return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'B':B, 'b0':b0, 'evx':evx, 'evy':evy}
+    return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'B':B, 'b0':b0, 'evx':evx, 'evy':evy,
+            'mnx': mnX, 'mny': mnY, 'xc': X, 'yc': Y}
 
 
 ########### Helper routines #########
@@ -691,6 +725,11 @@ def esvd(data, amax=None):
     m, n = data.shape
     if m>=n:
         kernel = dot(data.T, data)
+        if has_arpack:
+            if amax==None:
+                amax = n
+                s, v = arpack.eigen_symmetric(kernel,k=amax, which='LM',
+                                              maxiter=200,tol=1e-5)
         if has_sym:
             if amax==None:
                 amax = n
@@ -730,14 +769,32 @@ def vnorm(x):
 def center(a, axis):
     # 0 = col center, 1 = row center, 2 = double center
     # -1 = nothing
+
+    # check if we have a vector
+    is_vec = len(a.shape)==1
+    if not is_vec:
+        is_vec = a.shape[0]==1 or a.shape[1]==1
+    if is_vec:
+        if axis==2:
+            warnings.warn("Double centering of vecor ignored, using ordinary centering")
         if axis==-1:
-        mn = zeros((a.shape[1],))
+            mn = 0
+        else:
+            mn = a.mean()
+        return a - mn, mn
+    # !!!fixme: use broadcasting
+    if axis==-1:
+        mn = zeros((1,a.shape[1],))
+        #mn = tile(mn, (a.shape[0], 1))
     elif axis==0:
-        mn = a.mean(0)
+        mn = a.mean(0)[newaxis]
+        #mn = tile(mn, (a.shape[0], 1)) 
     elif axis==1:
         mn = a.mean(1)[:,newaxis]
+        #mn = tile(mn, (1, a.shape[1]))
     elif axis==2:
-        mn = a.mean(0) + a.mean(1)[:,newaxis] - a.mean()
+        mn = a.mean(0)[newaxis] + a.mean(1)[:,newaxis] - a.mean()
+        return a - mn , a.mean(0)[newaxis]
     else:
         raise IOError("input error: axis must be in [-1,0,1,2]")
 
@@ -755,3 +812,64 @@ def scale(a, axis):
 
     return a - sc, sc
 
+
+
+## #PCA CALCS
+
+## %  Calculate Q limit using unused eigenvalues
+## temp = diag(s);
+## if n < m
+##   emod = temp(lv+1:n,:);
+## else
+##   emod = temp(lv+1:m,:);
+## end
+## th1 = sum(emod);
+## th2 = sum(emod.^2);
+## th3 = sum(emod.^3);
+## h0 = 1 - ((2*th1*th3)/(3*th2^2));
+## if h0 <= 0.0
+## h0 = .0001;
+## disp('  ')
+## disp('Warning:  Distribution of unused eigenvalues indicates that')
+## disp('          you should probably retain more PCs in the model.')
+## end
+## q = th1*(((1.65*sqrt(2*th2*h0^2)/th1) + 1 + th2*h0*(h0-1)/th1^2)^(1/h0));
+## disp('  ')
+## disp('The 95% Q limit is')
+## disp(q)
+## if plots >= 1
+##   lim = [q q];
+##   plot(scl,res,scllim,lim,'--b')
+##   str = sprintf('Process Residual Q with 95 Percent Limit Based on %g PC Model',lv);
+##   title(str)
+##   xlabel('Sample Number')
+##   ylabel('Residual')
+##   pause
+## end
+## %  Calculate T^2 limit using ftest routine
+## if lv > 1
+##   if m > 300
+##     tsq = (lv*(m-1)/(m-lv))*ftest(.95,300,lv,2);
+##   else
+##     tsq = (lv*(m-1)/(m-lv))*ftest(.95,m-lv,lv,2);
+##   end
+##   disp('  ')
+##   disp('The 95% T^2 limit is')
+##   disp(tsq)
+## %  Calculate the value of T^2 by normalizing the scores to
+## %  unit variance and summing them up
+##   if plots >= 1.0
+##     temp2 = scores*inv(diag(ssq(1:lv,2).^.5));
+##     tsqvals = sum((temp2.^2)');
+##     tlim = [tsq tsq];
+##     plot(scl,tsqvals,scllim,tlim,'--b')
+##     str = sprintf('Value of T^2 with 95 Percent Limit Based on %g PC Model',lv);
+##     title(str)
+##     xlabel('Sample Number')
+##     ylabel('Value of T^2')
+##   end
+## else
+##   disp('T^2 not calculated when number of latent variables = 1')
+##   tsq = 1.96^2;
+## end
+

fluents/lib/validation.py

@@ -1,7 +1,7 @@
 """This module implements some common validation schemes from pca and pls.
 """
 from scipy import ones,mean,sqrt,dot,newaxis,zeros,sum,empty,\
-     apply_along_axis,eye,kron,array,sort,zeros_like,argmax
+     apply_along_axis,eye,kron,array,sort,zeros_like,argmax,atleast_2d
 from scipy.stats import median
 from scipy.linalg import triu,inv,svd,norm
 
@@ -9,7 +9,7 @@ from select_generators import w_pls_gen,w_pls_gen_jk,pls_gen,pca_gen,diag_pert
 from engines import w_simpls,pls,bridge,pca,nipals_lpls
 from cx_utils import m_shape
 
-def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
+def w_pls_cv_val(X, Y, amax, n_blocks=None):
     """Returns rmsep and aopt for pls tailored for wide X.
 
     The root mean square error of cross validation is calculated
@@ -62,12 +62,10 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
     for Din, Doi, Yin, Yout in V:
         ym = -sum(Yout, 0)[newaxis]/(1.0*Yin.shape[0])
         PRESS[:,0] = PRESS[:,0] + ((Yout - ym)**2).sum(0)
-        if algo=='simpls':
+        
         dat = w_simpls(Din, Yin, amax)
         Q, U, H = dat['Q'], dat['U'], dat['H']
         That = dot(Doi, dot(U, inv(triu(dot(H.T, U))) ))
-        else:
-            raise NotImplementedError
         
         Yhat = []
         for j in range(l):
@@ -78,7 +76,7 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
     #Yhat = Yin - dot(That,Q.T)
     msep = PRESS/(Y.shape[0])
     aopt = find_aopt_from_sep(msep)
-    return sqrt(msep)
+    return sqrt(msep), aopt
 
 def pls_val(X, Y, amax=2, n_blocks=10, algo='pls'):
     k, l = m_shape(Y)
@@ -108,29 +106,54 @@ def pls_val(X, Y, amax=2, n_blocks=10, algo='pls'):
     aopt = find_aopt_from_sep(msep)
     return msep, Yhat, aopt
 
-def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5):
+def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2]):
     """Performs crossvalidation to get generalisation error in lpls"""
+    assert(nsets<=X.shape[0])
+    
     cv_iter = pls_gen(X, Y, n_blocks=nsets,center=False,index_out=True)
     k, l = Y.shape
-    Yhat = empty((a_max,k,l), 'd')
+    Yc = empty((k, l), 'd')
+    Yhat = empty((a_max, k, l), 'd')
+    Yhatc = empty((a_max, k, l), 'd')
+    sep2 = empty((a_max, k, l), 'd')
     for i, (xcal,xi,ycal,yi,ind) in enumerate(cv_iter):
         dat = nipals_lpls(xcal,ycal,Z,
                           a_max=a_max,
                           alpha=alpha,
-                          mean_ctr=[2,0,1],
+                          mean_ctr=mean_ctr,
                           verbose=False)
+        
         B = dat['B']
-        b0 = dat['b0']
+        #b0 = dat['b0'] 
         for a in range(a_max):
-            Yhat[a,ind,:] = b0[a][0][0] + dot(xi-xcal.mean(0), B[a])
+            if mean_ctr[0] in [0, 2]:
+                xi = xi - dat['mnx']
+            else:
+                xi = xi - xi.mean(1)[:,newaxis] #???: cheating?
+            if mean_ctr[1] in [0, 2]:
+                ym = dat['mny']
+            else:
+                ym = yi.mean(1)[:,newaxis] #???: check this
+                
+            Yhat[a,ind,:] = atleast_2d(ym + dot(xi, B[a]))
+            #Yhat[a,ind,:] = atleast_2d(b0[a] + dot(xi, B[a]))
+            
+    # todo: need a better support for class validation
+    y_is_class = Y.dtype.char.lower() in ['i','p', 'b', 'h','?']
+    print Y.dtype.char
+    if y_is_class:
         Yhat_class = zeros_like(Yhat)
         for a in range(a_max):
             for i in range(k):
-            Yhat_class[a,i,argmax(Yhat[a,i,:])]=1.0
+                Yhat_class[a,i,argmax(Yhat[a,i,:])] = 1.0
         class_err = 100*((Yhat_class+Y)==2).sum(1)/Y.sum(0).astype('d')
+
     sep = (Y - Yhat)**2
-    rmsep = sqrt(sep.mean(1))
+    rmsep = sqrt(sep.mean(1)).T
+    #rmsep2 = sqrt(sep2.mean(1))
+    
     aopt = find_aopt_from_sep(rmsep)
+    
     return rmsep, Yhat, aopt
 
 def pca_alter_val(a, amax, n_sets=10, method='diag'):
@@ -247,7 +270,7 @@ def pca_jkP(a, aopt, n_blocks=None):
     return PP
 
 
-def lpls_jk(X, Y, Z, a_max, nsets=None, alpha=.5):
+def lpls_jk(X, Y, Z, a_max, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2]):
     cv_iter = pls_gen(X, Y, n_blocks=nsets,center=False,index_out=False)
     m, n = X.shape
     k, l = Y.shape
@@ -258,8 +281,8 @@ def lpls_jk(X, Y, Z, a_max, nsets=None, alpha=.5):
     WWz = empty((nsets, o, a_max), 'd')
     #WWy = empty((nsets, l, a_max), 'd')
     for i, (xcal,xi,ycal,yi) in enumerate(cv_iter):
-        dat = nipals_lpls(xcal,ycal,Z,a_max=a_max,alpha=alpha,
+        dat = nipals_lpls(xcal,ycal,Z,a_max=a_max,alpha=xz_alpha,
-                          mean_ctr=[2,0,1],scale='loads',verbose=False)
+                          mean_ctr=mean_ctr,scale='loads',verbose=False)
         WWx[i,:,:] = dat['W']
         WWz[i,:,:] = dat['L']
         #WWy[i,:,:] = dat['Q']