299 lines
8.0 KiB
Python
299 lines
8.0 KiB
Python
"""Module contain algorithms for low-rank L-shaped model.
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"""
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__all__ = ['nipals_lpls']
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__docformat__ = "restructuredtext en"
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from math import sqrt as msqrt
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from numpy import dot,empty,zeros,apply_along_axis,newaxis,finfo
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from numpy.linalg import inv
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def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 1], scale='scores', verbose=False):
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""" L-shaped Partial Least Sqaures Regression by the nipals algorithm.
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An L-shaped low rank model aproximates three matrices in a hyploid
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structure. That means that the main matrix (X), has one matrix asociated
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with its row space and one to its column space. A simultanously low rank estiamte
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of these three matrices tries to discover common directions/subspaces.
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*Parameters*:
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X : {array}
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Main data matrix (m, n)
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Y : {array}
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External row data (m, l)
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Z : {array}
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External column data (n, o)
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a_max : {integer}
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Maximum number of components to calculate (0, min(m,n))
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alpha : {float}, optional
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Parameter to control the amount of influence from Z-matrix.
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0 is none, which returns a pls-solution, 1 is max
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mean_center : {array-like}, optional
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A three element array-like structure with elements in [-1,0,1,2],
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that decides the type of centering used.
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-1 : nothing
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0 : row center
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1 : column center
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2 : double center
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scale : {'scores', 'loads'}, optional
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Option to decide on where the scale goes.
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verbose : {boolean}, optional
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Verbosity of console output. For use in debugging.
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*Returns*:
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T : {array}
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X-scores
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W : {array}
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X-weights/Z-weights
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P : {array}
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X-loadings
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Q : {array}
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Y-loadings
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U : {array}
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X-Y relation
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L : {array}
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Z-scores
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K : {array}
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Z-loads
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B : {array}
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Regression coefficients X->Y
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evx : {array}
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X-explained variance
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evy : {array}
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Y-explained variance
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evz : {array}
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Z-explained variance
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mnx : {array}
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X location
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mny : {array}
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Y location
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mnz : {array}
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Z location
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*References*
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Saeboe et al., LPLS-regression: a method for improved prediction and
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classification through inclusion of background information on
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predictor variables, J. of chemometrics and intell. laboratory syst.
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Martens et.al, Regression of a data matrix on descriptors of
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both its rows and of its columns via latent variables: L-PLSR,
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Computational statistics & data analysis, 2005
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"""
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m, n = X.shape
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k, l = Y.shape
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u, o = Z.shape
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max_rank = min(m, n)
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assert (a_max>0 and a_max<max_rank), "Number of comp error:\
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tried:%d, max_rank:%d" %(a_max,max_rank)
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if mean_ctr!=None:
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xctr, yctr, zctr = mean_ctr
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X, mnX = center(X, xctr)
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Y, mnY = center(Y, yctr)
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Z, mnZ = center(Z, zctr)
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varX = (X**2).sum()
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varY = (Y**2).sum()
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varZ = (Z**2).sum()
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# initialize
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U = empty((k, a_max))
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Q = empty((l, a_max))
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T = zeros((m, a_max))
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W = empty((n, a_max))
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P = empty((n, a_max))
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K = empty((o, a_max))
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L = empty((u, a_max))
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B = empty((a_max, n, l))
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E = X.copy()
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F = Y.copy()
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G = Z.copy()
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#b0 = empty((a_max, 1, l))
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var_x = empty((a_max,))
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var_y = empty((a_max,))
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var_z = empty((a_max,))
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MAX_ITER = 450
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LIM = finfo(X.dtype).resolution
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is_rd = False
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for a in range(a_max):
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if verbose:
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print "\nWorking on comp. %s" %a
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u = F[:,:1]
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diff = 1
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niter = 0
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while (diff>LIM and niter<MAX_ITER):
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niter += 1
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u1 = u.copy()
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w = dot(E.T, u)
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wn = msqrt(dot(w.T, w))
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if wn < LIM:
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print "Rank exhausted in X! Comp: %d " %a
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is_rd = True
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break
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w = w/wn
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#w = w/dot(w.T, w)
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l = dot(G, w)
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k = dot(G.T, l)
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k = k/msqrt(dot(k.T, k))
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#k = k/dot(k.T, k)
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w = alpha*k + (1-alpha)*w
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w = w/msqrt(dot(w.T, w))
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t = dot(E, w)
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c = dot(F.T, t)
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c = c/msqrt(dot(c.T, c))
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u = dot(F, c)
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diff = dot((u-u1).T, (u-u1))
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if verbose:
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print "Converged after %s iterations" %niter
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print "Error: %.2E" %diff
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if is_rd:
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print "Hei og haa ... rank deficient, this should really not happen"
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break
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tt = dot(t.T, t)
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p = dot(X.T, t)/tt
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q = dot(Y.T, t)/tt
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l = dot(Z, w)
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#k = dot(Z.T, l)/dot(l.T, l)
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U[:,a] = u.ravel()
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W[:,a] = w.ravel()
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P[:,a] = p.ravel()
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T[:,a] = t.ravel()
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Q[:,a] = q.ravel()
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L[:,a] = l.ravel()
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K[:,a] = k.ravel()
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E = E - dot(t, p.T)
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F = F - dot(t, q.T)
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G = (G.T - dot(k, l.T)).T
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var_x[a] = pow(E, 2).sum()
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var_y[a] = pow(F, 2).sum()
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var_z[a] = pow(G, 2).sum()
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B[a] = dot(dot(W[:,:a+1], inv(dot(P[:,:a+1].T, W[:,:a+1]))), Q[:,:a+1].T)
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#b0[a] = mnY - dot(mnX, B[a])
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# variance explained
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evx = 100.*(1 - var_x/varX)
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evy = 100.*(1 - var_y/varY)
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evz = 100.*(1 - var_z/varZ)
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if scale=='loads':
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tnorm = apply_along_axis(vnorm, 0, T)
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T = T/tnorm
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W = W*tnorm
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Q = Q*tnorm
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knorm = apply_along_axis(vnorm, 0, K)
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L = L*knorm
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K = K/knorm
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return {'T':T, 'W':W, 'P':P, 'Q':Q, 'U':U, 'L':L, 'K':K, 'B':B, 'E': E, 'F': F, 'G': G, 'evx':evx, 'evy':evy, 'evz':evz,'mnx': mnX, 'mny': mnY, 'mnz': mnZ}
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def vnorm(a):
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"""Returns the norm of a vector.
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*Parameters*:
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a : {array}
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Input data, 1-dim, or column vector (m, 1)
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*Returns*:
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a_norm : {array}
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Norm of input vector
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"""
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return msqrt(dot(a.T,a))
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def center(a, axis):
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""" Matrix centering.
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*Parameters*:
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a : {array}
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Input data
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axis : {integer}
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Which centering to perform.
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0 = col center, 1 = row center, 2 = double center
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-1 = nothing
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*Returns*:
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a_centered : {array}
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Centered data matrix
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mn : {array}
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Location vector/matrix
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"""
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# check if we have a vector
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is_vec = len(a.shape)==1
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if not is_vec:
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is_vec = a.shape[0]==1 or a.shape[1]==1
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if is_vec:
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if axis==2:
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warnings.warn("Double centering of vecor ignored, using ordinary centering")
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if axis==-1:
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mn = 0
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else:
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mn = a.mean()
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return a - mn, mn
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# !!!fixme: use broadcasting
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if axis==-1:
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mn = zeros((1,a.shape[1],))
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#mn = tile(mn, (a.shape[0], 1))
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elif axis==0:
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mn = a.mean(0)[newaxis]
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#mn = tile(mn, (a.shape[0], 1))
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elif axis==1:
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mn = a.mean(1)[:,newaxis]
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#mn = tile(mn, (1, a.shape[1]))
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elif axis==2:
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mn = a.mean(0)[newaxis] + a.mean(1)[:,newaxis] - a.mean()
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return a - mn , a.mean(0)[newaxis]
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else:
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raise IOError("input error: axis must be in [-1,0,1,2]")
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return a - mn, mn
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def _scale(a, axis):
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""" Matrix scaling to unit variance.
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*Parameters*:
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a : {array}
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Input data
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axis : {integer}
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Which scaling to perform.
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0 = column, 1 = row, -1 = nothing
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*Returns*:
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a_scaled : {array}
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Scaled data matrix
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mn : {array}
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Scaling vector/matrix
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"""
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if axis==-1:
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sc = zeros((a.shape[1],))
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elif axis==0:
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sc = a.std(0)
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elif axis==1:
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sc = a.std(1)[:,newaxis]
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else:
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raise IOError("input error: axis must be in [-1,0,1]")
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return a - sc, sc
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