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Mostly clean ups

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This commit is contained in:
Arnar Flatberg 2007-11-27 15:05:19 +00:00
parent 2951ca4088
commit 4c809674bb
2 changed files with 98 additions and 84 deletions
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37
pyblm/crossvalidation.py
View File

@ -12,7 +12,7 @@ from numpy.random import shuffle
from engines import nipals_lpls as lpls from engines import nipals_lpls as lpls
def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2], zorth=False, verbose=True): def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2], zorth=False, verbose=False):
"""Performs crossvalidation for generalisation error in lpls. """Performs crossvalidation for generalisation error in lpls.
The L-PLS crossvalidation is estimated just like an ordinary pls The L-PLS crossvalidation is estimated just like an ordinary pls
@ -61,8 +61,8 @@ def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2], zorth=Fals
m, n = X.shape m, n = X.shape
k, l = Y.shape k, l = Y.shape
o, p = Z.shape o, p = Z.shape
assert m==k, "X (%d,%d) - Y (%d,%d) dim mismatch" %(m,n,k,l) assert m == k, "X (%d,%d) - Y (%d,%d) dim mismatch" %(m, n, k, l)
assert n==p, "X (%d,%d) - Z (%d,%d) dim mismatch" %(m,n,o,p) assert n == p, "X (%d,%d) - Z (%d,%d) dim mismatch" %(m, n, o, p)
if nsets == None: if nsets == None:
nsets = m nsets = m
if nsets > X.shape[0]: if nsets > X.shape[0]:
@ -80,11 +80,11 @@ def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2], zorth=Fals
if mean_ctr[0] != 1: if mean_ctr[0] != 1:
xi = X[val,:] - dat['mnx'] xi = X[val,:] - dat['mnx']
else: else:
xi = X[val] - X[val].mean(1)[:,newaxis] xi = X[val] - X[cal].mean(1)[:,newaxis]
if mean_ctr[2] != 1: if mean_ctr[2] != 1:
ym = dat['mny'] ym = dat['mny']
else: else:
ym = Y[val].mean(1)[:,newaxis] #???: check this ym = Y[cal].mean(1)[:,newaxis]
# predictions # predictions
for a in range(a_max): for a in range(a_max):
Yhat[a,val,:] = atleast_2d(ym + dot(xi, dat['B'][a])) Yhat[a,val,:] = atleast_2d(ym + dot(xi, dat['B'][a]))
@ -113,7 +113,7 @@ def lpls_val(X, Y, Z, a_max=2, nsets=None,alpha=.5, mean_ctr=[2,0,2], zorth=Fals
def pca_jk(a, aopt, n_blocks=None): def pca_jk(a, aopt, n_blocks=None):
"""Returns jack-knife segements from PCA. """Returns jack-knife segements from PCA.
Parameters: *Parameters*:
a : {array} a : {array}
data matrix (n x m) data matrix (n x m)
@ -122,21 +122,15 @@ def pca_jk(a, aopt, n_blocks=None):
nsets : {integer} nsets : {integer}
number of segments number of segments
Returns: *Returns*:
Pcv : {array} Pcv : {array}
Loadings collected in a three way matrix (n_segments, m, aopt) Loadings collected in a three way matrix (n_segments, m, aopt)
Notes: *Notes*:
- The loadings are scaled with the (1/samples)*eigenvalues.
- Crossvalidation method is currently set to random blocks of samples. - Crossvalidation method is currently set to random blocks of samples.
- todo: add support for T
- fixme: more efficient to add this in validation loop?
""" """
if nsets == None: if nsets == None:
nsets = a.shape[0] nsets = a.shape[0]
@ -183,7 +177,7 @@ def pls_jk(X, Y, a_opt, nsets=None, center=True, verbose=False):
""" """
m, n = X.shape m, n = X.shape
k, l = Y.shape k, l = Y.shape
assert(m==k) assert(m == k)
if nsets == None: if nsets == None:
nsets = X.shape[0] nsets = X.shape[0]
Wcv = empty((nsets, X.shape[1], a_opt), dtype=X.dtype) Wcv = empty((nsets, X.shape[1], a_opt), dtype=X.dtype)
@ -242,9 +236,9 @@ def lpls_jk(X, Y, Z, a_opt, nsets=None, xz_alpha=.5, mean_ctr=[2,0,2], verbose=F
m, n = X.shape m, n = X.shape
k, l = Y.shape k, l = Y.shape
o, p = Z.shape o, p = Z.shape
assert(m==k) assert(m == k)
assert(n==p) assert(n == p)
if nsets==None: if nsets == None:
nsets = m nsets = m
WWx = empty((nsets, n, a_opt), 'd') WWx = empty((nsets, n, a_opt), 'd')
WWz = empty((nsets, o, a_opt), 'd') WWz = empty((nsets, o, a_opt), 'd')
@ -279,12 +273,12 @@ def find_aopt_from_sep(sep, method='vanilla'):
A guess on the optimal number of components A guess on the optimal number of components
""" """
if method=='vanilla': if method == 'vanilla':
# min rmsep # min rmsep
rmsecv = sqrt(sep.mean(0)) rmsecv = sqrt(sep.mean(0))
return rmsecv.argmin() + 1 return rmsecv.argmin() + 1
elif method=='75perc': elif method == '75perc':
prct = .75 #percentile prct = .75 #percentile
ind = 1.*sep.shape[0]*prct ind = 1.*sep.shape[0]*prct
med = median(sep) med = median(sep)
@ -305,6 +299,7 @@ def cv(N, K, randomise=True, sequential=False):
of length ~N/K, *without* replacement. of length ~N/K, *without* replacement.
*Parameters*: *Parameters*:
N : {integer} N : {integer}
Total number of samples Total number of samples
K : {integer} K : {integer}
@ -333,7 +328,7 @@ def cv(N, K, randomise=True, sequential=False):
otherwise interleaved ordering is used. otherwise interleaved ordering is used.
""" """
if N>K: if N > K:
raise ValueError, "You cannot divide a list of %d samples into more than %d segments. Yout tried: %s" %(K, K, N) raise ValueError, "You cannot divide a list of %d samples into more than %d segments. Yout tried: %s" %(K, K, N)
index = xrange(N) index = xrange(N)
if randomise: if randomise:

145
pyblm/engines.py
View File

@ -9,16 +9,17 @@ from math import sqrt as msqrt
from numpy import dot,empty,zeros,apply_along_axis,newaxis,finfo,sqrt,r_,expand_dims,\ from numpy import dot,empty,zeros,apply_along_axis,newaxis,finfo,sqrt,r_,expand_dims,\
minimum minimum
from numpy.linalg import inv, svd from numpy.linalg import inv,svd
from scipy.sandbox import arpack from scipy.sandbox import arpack
def pca(X, aopt, scale='scores', mode='normal', center_axis=0): def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
""" Principal Component Analysis. """ Principal Component Analysis.
PCA is a low rank bilinear aprroximation to a data matrix that sequentially PCA is a low rank bilinear aprroximation to a data matrix that sequentially
extracts orthogonal components of maximum variance. extracts orthogonal components of maximum variance.
Parameters: *Parameters*:
X : {array} X : {array}
Data measurement matrix, (samples x variables) Data measurement matrix, (samples x variables)
@ -27,7 +28,7 @@ def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
center_axis : {integer} center_axis : {integer}
Center along given axis. If neg.: no centering (-inf,..., matrix modes) Center along given axis. If neg.: no centering (-inf,..., matrix modes)
Returns: *Returns*:
T : {array} T : {array}
Scores, (samples, components) Scores, (samples, components)
@ -47,7 +48,7 @@ def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
leverage : {array} leverage : {array}
Leverages, (samples,) Leverages, (samples,)
OtherParameters: *OtherParameters*:
scale : {string}, optional scale : {string}, optional
Where to put the weights [['scores'], 'loadings'] Where to put the weights [['scores'], 'loadings']
@ -55,7 +56,7 @@ def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
Amount of info retained, [['normal'], 'fast', 'detailed'] Amount of info retained, [['normal'], 'fast', 'detailed']
:SeeAlso: *SeeAlso*:
`center` : Data centering `center` : Data centering
@ -78,10 +79,12 @@ def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
""" """
m, n = X.shape m, n = X.shape
assert(aopt<=min(m,n)) min_aopt = min(m, n)
if center_axis>=0: if center_axis >= 0:
X = X - expand_dims(X.mean(center_axis), center_axis) X = X - expand_dims(X.mean(center_axis), center_axis)
if m>(n+100) or n>(m+100): min_aopt = min_aopt - 1
assert(aopt <= min_aopt)
if m > (n+100) or n > (m+100):
u, s, v = esvd(X, aopt) u, s, v = esvd(X, aopt)
else: else:
u, s, vt = svd(X, 0) u, s, vt = svd(X, 0)
@ -92,7 +95,7 @@ def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
# ranktest # ranktest
tol = 1e-10 tol = 1e-10
eff_rank = sum(s>s[0]*tol) eff_rank = sum(s > s[0]*tol)
aopt = minimum(aopt, eff_rank) aopt = minimum(aopt, eff_rank)
T = u*s T = u*s
s = s[:aopt] s = s[:aopt]
@ -124,7 +127,7 @@ def pca(X, aopt, scale='scores', mode='normal', center_axis=0):
sep = E**2 sep = E**2
ssq = [sep.sum(0), sep.sum(1)] ssq = [sep.sum(0), sep.sum(1)]
# leverages # leverages
if scale=='loads': if scale == 'loads':
lev = [(1./m)+(T**2).sum(1), (1./n)+((P/s)**2).sum(1)] lev = [(1./m)+(T**2).sum(1), (1./n)+((P/s)**2).sum(1)]
else: else:
lev = [(1./m)+((T/s)**2).sum(1), (1./n)+(P**2).sum(1)] lev = [(1./m)+((T/s)**2).sum(1), (1./n)+(P**2).sum(1)]
@ -139,7 +142,7 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
Performs PCR on given matrix and returns results in a dictionary. Performs PCR on given matrix and returns results in a dictionary.
Parameters: *Parameters*:
a : array a : array
Data measurement matrix, (samples x variables) Data measurement matrix, (samples x variables)
@ -148,19 +151,19 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
aopt : int aopt : int
Number of components to use, aopt<=min(samples, variables) Number of components to use, aopt<=min(samples, variables)
Returns: *Returns*:
results : dict results : dict
keys -- values, T -- scores, P -- loadings, E -- residuals, keys -- values, T -- scores, P -- loadings, E -- residuals,
levx -- leverages, ssqx -- sum of squares, expvarx -- cumulative levx -- leverages, ssqx -- sum of squares, expvarx -- cumulative
explained variance, aopt -- number of components used explained variance, aopt -- number of components used
OtherParameters: *OtherParameters*:
mode : str mode : {string}
Amount of info retained, ('fast', 'normal', 'detailed') Amount of info retained, ('fast', 'normal', 'detailed')
center_axis : int center_axis : {integer}
Center along given axis. If neg.: no centering (-inf,..., matrix modes) Center along given axis. If neg.: no centering (-inf,..., matrix modes)
SeeAlso: SeeAlso:
@ -194,21 +197,21 @@ def pcr(a, b, aopt, scale='scores',mode='normal',center_axis=0):
except: except:
b = atleast_2d(b).T b = atleast_2d(b).T
k, l = b.shape k, l = b.shape
if center_axis>=0: if center_axis >= 0:
b = b - expand_dims(b.mean(center_axis), center_axis) b = b - expand_dims(b.mean(center_axis), center_axis)
dat = pca(a, aopt=aopt, scale=scale, mode=mode, center_axis=center_axis) dat = pca(a, aopt=aopt, scale=scale, mode=mode, center_axis=center_axis)
T = dat['T'] T = dat['T']
weights = apply_along_axis(vnorm, 0, T)**2 weights = apply_along_axis(vnorm, 0, T)**2
if scale=='loads': if scale == 'loads':
Q = dot(b.T, T*weights) Q = dot(b.T, T*weights)
else: else:
Q = dot(b.T, T/weights) Q = dot(b.T, T/weights)
if mode=='fast': if mode == 'fast':
dat.update({'Q':Q}) dat.update({'Q':Q})
return dat return dat
if mode=='detailed': if mode == 'detailed':
F = empty((aopt, k, l)) F = empty((aopt, k, l))
ssqy = [] ssqy = []
for i in range(aopt): for i in range(aopt):
@ -284,7 +287,7 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
*SeeAlso*: *SeeAlso*:
`center` : data centering `center` - data centering
*Notes* *Notes*
@ -310,14 +313,16 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
except: except:
Y = atleast_2d(Y).T Y = atleast_2d(Y).T
k, l = Y.shape k, l = Y.shape
assert(m==k) assert(m == k)
assert(aopt<min(m, n)) mnx, mny = 0, 0
mnx, mny = 0,0 min_aopt = min(m, n)
if center_axis>=0: if center_axis >= 0:
mnx = expand_dims(X.mean(center_axis), center_axis) mnx = expand_dims(X.mean(center_axis), center_axis)
X = X - mnx X = X - mnx
min_aopt = min_aopt - 1
mny = expand_dims(Y.mean(center_axis), center_axis) mny = expand_dims(Y.mean(center_axis), center_axis)
Y = Y - mny Y = Y - mny
assert(aopt > 0 and aopt < min_aopt)
W = empty((n, aopt)) W = empty((n, aopt))
P = empty((n, aopt)) P = empty((n, aopt))
@ -329,10 +334,10 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
XY = dot(X.T, Y) XY = dot(X.T, Y)
for i in range(aopt): for i in range(aopt):
if XY.shape[1]==1: #pls 1 if XY.shape[1] == 1: #pls 1
w = XY.reshape(n, l) w = XY.reshape(n, l)
w = w/vnorm(w) w = w/vnorm(w)
elif n<l: # more yvars than xvars elif n < l: # more yvars than xvars
s, w = arpack.eigen_symmetric(dot(XY, XY.T),k=1, tol=1e-10, maxiter=100) s, w = arpack.eigen_symmetric(dot(XY, XY.T),k=1, tol=1e-10, maxiter=100)
#w, s, vh = svd(dot(XY, XY.T)) #w, s, vh = svd(dot(XY, XY.T))
#w = w[:,:1] #w = w[:,:1]
@ -344,7 +349,7 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
w = dot(XY, q) w = dot(XY, q)
w = w/vnorm(w) w = w/vnorm(w)
r = w.copy() r = w.copy()
if i>0: if i > 0:
for j in range(0, i, 1): for j in range(0, i, 1):
r = r - dot(P[:,j].T, w)*R[:,j][:,newaxis] r = r - dot(P[:,j].T, w)*R[:,j][:,newaxis]
@ -356,8 +361,8 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
T[:,i] = t.ravel() T[:,i] = t.ravel()
W[:,i] = w.ravel() W[:,i] = w.ravel()
if mode=='fast' and i==aopt-1: if mode == 'fast' and i == (aopt - 1):
if scale=='loads': if scale == 'loads':
tnorm = sqrt(tt) tnorm = sqrt(tt)
T = T/tnorm T = T/tnorm
W = W*tnorm W = W*tnorm
@ -371,7 +376,7 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
qnorm = apply_along_axis(vnorm, 0, Q) qnorm = apply_along_axis(vnorm, 0, Q)
tnorm = sqrt(tt) tnorm = sqrt(tt)
pp = (P**2).sum(0) pp = (P**2).sum(0)
if mode=='detailed': if mode == 'detailed':
E = empty((aopt, m, n)) E = empty((aopt, m, n))
F = empty((aopt, k, l)) F = empty((aopt, k, l))
ssqx, ssqy = [], [] ssqx, ssqy = [], []
@ -401,7 +406,7 @@ def pls(X, Y, aopt=2, scale='scores', mode='normal', center_axis=-1):
expvarx = r_[0, 100*tp/(X*X).sum()] expvarx = r_[0, 100*tp/(X*X).sum()]
expvary = r_[0, 100*tq/(Y*Y).sum()] expvary = r_[0, 100*tq/(Y*Y).sum()]
if scale=='loads': if scale == 'loads':
T = T/tnorm T = T/tnorm
W = W*tnorm W = W*tnorm
Q = Q*tnorm Q = Q*tnorm
@ -495,11 +500,11 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 2], scale='scores', zo
m, n = X.shape m, n = X.shape
k, l = Y.shape k, l = Y.shape
u, o = Z.shape u, o = Z.shape
max_rank = min(m, n) max_rank = min(m, n) + 1
assert (a_max>0 and a_max<max_rank), "Number of comp error:\ assert (a_max > 0 and a_max < max_rank), "Number of comp error:\
tried:%d, max_rank:%d" %(a_max,max_rank) tried: %d, max_rank: %d" %(a_max, max_rank)
if mean_ctr!=None: if mean_ctr != None:
xctr, yctr, zctr = mean_ctr xctr, yctr, zctr = mean_ctr
X, mnX = center(X, xctr) X, mnX = center(X, xctr)
Y, mnY = center(Y, yctr) Y, mnY = center(Y, yctr)
@ -537,7 +542,7 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 2], scale='scores', zo
l = G[:,:1] l = G[:,:1]
diff = 1 diff = 1
niter = 0 niter = 0
while (diff>LIM and niter<MAX_ITER): while (diff > LIM and niter < MAX_ITER):
niter += 1 niter += 1
u1 = u.copy() u1 = u.copy()
w1 = w.copy() w1 = w.copy()
@ -562,7 +567,7 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 2], scale='scores', zo
u = dot(F, c) u = dot(F, c)
diff = dot((u - u1).T, (u - u1)) diff = dot((u - u1).T, (u - u1))
if verbose: if verbose:
if niter==MAX_ITER: if niter == MAX_ITER:
print "Maximum nunber of iterations reached!" print "Maximum nunber of iterations reached!"
print "Iterations: %d " %niter print "Iterations: %d " %niter
print "Error: %.2E" %diff print "Error: %.2E" %diff
@ -606,7 +611,7 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 2], scale='scores', zo
evy = 100.*(1 - var_y/varY) evy = 100.*(1 - var_y/varY)
evz = 100.*(1 - var_z/varZ) evz = 100.*(1 - var_z/varZ)
if scale=='loads': if scale == 'loads':
tnorm = apply_along_axis(vnorm, 0, T) tnorm = apply_along_axis(vnorm, 0, T)
T = T/tnorm T = T/tnorm
W = W*tnorm W = W*tnorm
@ -617,6 +622,20 @@ def nipals_lpls(X, Y, Z, a_max, alpha=.7, mean_ctr=[2, 0, 2], scale='scores', zo
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} 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}
def lpls_predict(model_dict, x, aopt):
"""Predict lpls reponses from existing model on new data.
"""
try:
m, n = x.shape
except:
x = atleast_2d(x.shape)
m, n = x.shape
if 'B0' in model_dict.keys():
y = model_dict['B0'] + dot()
def vnorm(a): def vnorm(a):
"""Returns the norm of a vector. """Returns the norm of a vector.
@ -654,28 +673,28 @@ def center(a, axis):
""" """
# check if we have a vector # check if we have a vector
is_vec = len(a.shape)==1 is_vec = len(a.shape) == 1
if not is_vec: if not is_vec:
is_vec = a.shape[0]==1 or a.shape[1]==1 is_vec = a.shape[0] == 1 or a.shape[1] == 1
if is_vec: if is_vec:
if axis==2: if axis == 2:
warnings.warn("Double centering of vecor ignored, using ordinary centering") warnings.warn("Double centering of vecor ignored, using ordinary centering")
if axis==-1: if axis == -1:
mn = 0 mn = 0
else: else:
mn = a.mean() mn = a.mean()
return a - mn, mn return a - mn, mn
# !!!fixme: use broadcasting # !!!fixme: use broadcasting
if axis==-1: if axis == -1:
mn = zeros((1,a.shape[1],)) mn = zeros((1,a.shape[1],))
#mn = tile(mn, (a.shape[0], 1)) #mn = tile(mn, (a.shape[0], 1))
elif axis==0: elif axis == 0:
mn = a.mean(0)[newaxis] mn = a.mean(0)[newaxis]
#mn = tile(mn, (a.shape[0], 1)) #mn = tile(mn, (a.shape[0], 1))
elif axis==1: elif axis == 1:
mn = a.mean(1)[:,newaxis] mn = a.mean(1)[:,newaxis]
#mn = tile(mn, (1, a.shape[1])) #mn = tile(mn, (1, a.shape[1]))
elif axis==2: elif axis == 2:
mn = a.mean(0)[newaxis] + a.mean(1)[:,newaxis] - a.mean() mn = a.mean(0)[newaxis] + a.mean(1)[:,newaxis] - a.mean()
return a - mn , a.mean(0)[newaxis] return a - mn , a.mean(0)[newaxis]
else: else:
@ -702,11 +721,11 @@ def _scale(a, axis):
Scaling vector/matrix Scaling vector/matrix
""" """
if axis==-1: if axis == -1:
sc = zeros((a.shape[1],)) sc = zeros((a.shape[1],))
elif axis==0: elif axis == 0:
sc = a.std(0) sc = a.std(0)
elif axis==1: elif axis == 1:
sc = a.std(1)[:,newaxis] sc = a.std(1)[:,newaxis]
else: else:
raise IOError("input error: axis must be in [-1,0,1]") raise IOError("input error: axis must be in [-1,0,1]")
@ -714,19 +733,19 @@ def _scale(a, axis):
return a - sc, sc return a - sc, sc
def esvd(data, a_max=None): def esvd(data, a_max=None):
""" SVD with kernel calculation """SVD with kernel calculation.
Calculate subspaces of X'X or XX' depending on the shape Calculate subspaces of X'X or XX' depending on the shape
of the matrix. of the matrix.
Parameters: *Parameters*:
data : {array} data : {array}
Data matrix Data matrix
a_max : {integer} a_max : {integer}
Number of components to extract Number of components to extract
Returns: *Returns*:
u : {array} u : {array}
Right hand eigenvectors Right hand eigenvectors
@ -735,20 +754,20 @@ def esvd(data, a_max=None):
v : {array} v : {array}
Left hand eigenvectors Left hand eigenvectors
notes: *Notes*:
Uses Anoldi iterations (ARPACK) Uses Anoldi iterations for the symmetric eigendecomp (ARPACK)
""" """
m, n = data.shape m, n = data.shape
if m>=n: if m >= n:
kernel = dot(data.T, data) kernel = dot(data.T, data)
if a_max==None: if a_max == None:
a_max = n - 1 a_max = n - 1
s, v = arpack.eigen_symmetric(kernel,k=a_max, which='LM', s, v = arpack.eigen_symmetric(kernel, k=a_max, which='LM',
maxiter=200,tol=1e-5) maxiter=200, tol=1e-5)
s = s[::-1] s = s[::-1]
v = v[:,::-1] v = v[:,::-1]
#u, s, vt = svd(kernel) #u, s, vt = svd(kernel)
@ -757,10 +776,10 @@ def esvd(data, a_max=None):
u = dot(data, v)/s u = dot(data, v)/s
else: else:
kernel = dot(data, data.T) kernel = dot(data, data.T)
if a_max==None: if a_max == None:
a_max = m -1 a_max = m -1
s, u = arpack.eigen_symmetric(kernel,k=a_max, which='LM', s, u = arpack.eigen_symmetric(kernel, k=a_max, which='LM',
maxiter=200,tol=1e-5) maxiter=200, tol=1e-5)
s = s[::-1] s = s[::-1]
u = u[:,::-1] u = u[:,::-1]
#u, s, vt = svd(kernel) #u, s, vt = svd(kernel)