257 lines
7.8 KiB
Python
257 lines
7.8 KiB
Python
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from scipy import zeros,zeros_like,sqrt,dot,trace,sign,round_,argmax,\
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sort,ravel,newaxis,asarray,diag,sum,outer,argsort,arange,ones_like,\
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all,apply_along_axis,eye
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from scipy.linalg import svd,inv,norm,det,sqrtm
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from scipy.stats import mean,median
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from cx_utils import mat_center
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from validation import pls_jkW
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from select_generators import shuffle_1d
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from engines import *
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import time
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def hotelling(P, Pfull, p_center='med', cov_center='med',
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alpha=0.3, crot=True, strict=False, metric=None):
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"""Returns regularized hotelling T^2.
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alpha -- regularisation towards pooled cov estimates
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beta -- regularisation for unstable eigenvalues
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p_center -- location method for submodels
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cov_center -- location method for sub coviariances
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alpha -- regularisation
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crot -- rotate submodels toward full?
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strict -- only rotate 90 degree ?
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metric -- inverse metric matrix (if P and Pfull from metric pca/pls)
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"""
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m, n = Pfull.shape
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if metric==None:
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metric = eye(m, dtype='<f8')
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Pfull = dot(metric.T, asarray(Pfull))
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n_sets,n,amax = P.shape
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# allocate
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T_sq = empty((n, ),dtype='f')
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Cov_i = zeros((n, amax, amax),dtype='f')
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# rotate sub_models to full model
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if crot:
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for i,Pi in enumerate(P):
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Pi = dot(metric.T, Pi)
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P[i] = procrustes(Pfull, Pi, strict=strict)
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# center of pnull
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if p_center=='med':
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P_ctr = median(P, 0)
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elif p_center=='mean':
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# fixme: mean is unstable
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P_ctr = mean(P, 0)
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else: #use full
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P_ctr = Pfull
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for i in xrange(n):
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Pi = P[:,i,:] # (n_sets x amax)
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Pi_ctr = P_ctr[i,:] # (1 x amax)
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Pim = (Pi - Pi_ctr[newaxis])*sqrt(n_sets-1)
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Cov_i[i] = (1./n_sets)*dot(Pim.T, Pim)
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if cov_center == 'med':
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Cov = median(Cov_i, 0)
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else:
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Cov = mean(Cov_i, 0)
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reg_cov = (1. - alpha)*Cov_i + alpha*Cov
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for i in xrange(n):
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Pc = P_ctr[i,:][:,newaxis]
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sigma = reg_cov[i]
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#T_sq[i] = sqrt(dot(dot(Pc.T, inv(sigma)), Pc).ravel())
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T_sq[i] = dot(dot(Pc.T, inv(sigma)), Pc).ravel()
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return T_sq
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def procrustes(A, B, strict=True, center=False, verbose=False):
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"""Rotation of B to A.
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strict -- Only do flipping and shuffling
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center -- Center before rotation, translate back after
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verbose -- Print ssq
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No scaling calculated.
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Output B_rot = Rotated B
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"""
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if center:
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A,mn_A = mat_center(A, ret_mn=True)
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B,mn_B = mat_center(B, ret_mn=True)
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u,s,vh = svd(dot(B.T, A))
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v = vh.T
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Cm = dot(u, v.T) #orthogonal rotation matrix
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if strict: # just inverting and flipping
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Cm = ensure_strict(Cm)
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b_rot = dot(B, Cm)
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if verbose:
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print Cm.round()
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fit = sum(ravel(B - b_rot)**2)
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print "Sum of squares: %s" %fit
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if center:
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return mn_B + b_rot
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else:
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return b_rot
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def expl_var_x(X, T):
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"""Returns explained variance of X."""
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# centered X,Y
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exp_var_x = diag(dot(T.T, T))*100/(sum(X**2))
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return exp_var_x
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def expl_var_y(Y, T, Q):
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"""Returns explained variance of Y.
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"""
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# centered Y
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exp_var_y = zeros((Q.shape[1], ))
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for a in range(Q.shape[1]):
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Ya = outer(T[:,a], Q[:,a])
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exp_var_y[a] = 100*sum(Ya**2)/sum(Y**2)
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return exp_var_y
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def pls_qvals(a, b, aopt=None, alpha=.3,
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n_iter=20, algo='pls',
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sim_method='shuffle',
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p_center='med', cov_center='med',
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crot=True, strict=False, metric=None):
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"""Returns qvals for pls model.
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input:
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a -- centered data matrix
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b -- centered data matrix
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aopt -- scalar, opt. number of components
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alpha -- [0,1] regularisation parameter for T2-test
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n_iter -- number of permutations
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sim_method -- permutation method ['shuffle']
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p_center -- location estimator for sub models ['med']
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cov_center -- location estimator for covariance of submodels ['med']
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crot -- bool, use rotations of sub models?
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strict -- bool, use stict (rot/flips only) rotations?
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metric -- bool, use row metric?
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"""
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m, n = a.shape
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TSQ = zeros((n, n_iter), dtype='<f8') # (nvars x n_subsets)
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n_false = zeros((n, n_iter), dtype='<f8')
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#full model
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if algo=='bridge':
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dat = bridge(a, b, aopt, 'loads', 'fast')
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else:
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dat = pls(a, b, aopt, 'loads', 'fast')
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W = pls_jkW(a, b, aopt, n_blocks=None, algo=algo)
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tsq_full = hotelling(W, dat['W'], p_center=p_center,
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alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center, metric=metric)
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t0 = time.time()
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Vs = shuffle_1d(b, n_iter)
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for i,b_shuff in enumerate(Vs):
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t1 = time.time()
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if algo=='bridge':
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dat = bridge(a, b_shuff, aopt, 'loads','fast')
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else:
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dat = pls(a, b, aopt, 'loads', 'fast')
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W = pls_jkW(a, b_shuff, aopt, n_blocks=None, algo=algo)
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TSQ[:,i] = hotelling(W, dat['W'],p_center=p_center,
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alpha=alpha, crot=crot, strict=strict,
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cov_center=cov_center, metric=metric)
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print time.time() - t1
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sort_index = argsort(tsq_full)[::-1]
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back_sort_index = sort_index.argsort()
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print time.time() - t0
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# count false positives
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tsq_full_sorted = tsq_full.take(sort_index)
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for i in xrange(n_iter):
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for j in xrange(n):
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n_false[j,i] = sum(TSQ[:,i]>=tsq_full[j])
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false_pos = median(n_false, 1)
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ll = arange(1, len(false_pos)+1, 1)
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sort_qval = false_pos.take(sort_index)/ll
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qval = false_pos/ll.take(back_sort_index)
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print time.time() - t0
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return qval, false_pos, TSQ, tsq_full
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def ensure_strict(C, only_flips=True):
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"""Ensure that a rotation matrix does only 90 degree rotations.
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In multiplication with pcs this allows flips and reordering.
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if only_flips is True there will onlt be flips allowed
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"""
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Cm = C
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S = sign(C) # signs
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if only_flips==True:
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C = eye(Cm.shape[0])*S
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return C
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Cm = zeros_like(C)
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Cm.putmask(1.,abs(C)>.6)
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if det(Cm)>1:
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raise ValueError,"Implement this!"
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return Cm*S
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def leverage(aopt=1,*args):
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"""Returns leverages
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input : aopt, number of components to base leverage calculations on
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*args, matrices of normed blm-paramters
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output: leverages
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For PCA typical inputs are normalised T or normalised P
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For PLSR typical inputs are normalised T or normalised W
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"""
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if aopt<1:
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raise ValueError,"Leverages only make sense for aopt>0"
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lev = []
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for u in args:
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lev_u = 1./u.shape[0] + dot(u[:,:aopt], u[:,:aopt].T).diagonal()
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lev.append(lev_u)
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return lev
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def variances(a,t,p):
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"""Returns explained variance and ind. var from blm-params.
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input:
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a -- full centered matrix
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t,p -- parameters from a bilinear approx of the above matrix.
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output:
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var -- variance of each component
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var_exp -- cumulative explained variance in percentage
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Typical inputs are: X(centered),T,P for PCA or
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X(centered),T,P / Y(centered),T,Q for PLSR.
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"""
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tot_var = sum(a**2)
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var = 100*(sum(p**2, 0)*sum(t**2, 0))/tot_var
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var_exp = cumsum(var)
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return var, var_exp
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def residual_diagnostics(Y, Yhat, aopt=1):
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"""Root mean errors and press values.
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R2 vals
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"""
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pass
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def ssq(E, axis=0, weights=None):
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"""Sum of squares, supports weights."""
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n = E.shape[axis]
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if weights==None:
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weights = eye(n)
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else:
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weigths = diag(weigths)
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if axis==0:
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Ew = dot(weights, E)
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elif axis==1:
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Ew = dot(E, weights)
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else:
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raise NotImplementedError, "Higher order modes not supported"
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return pow(Ew,2).sum(axis)
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