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pyphi.py
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"""
Phi for Python (pyPhi)
By Sal Garcia ([email protected] [email protected])
Added Jan 30 2025
* Added a pinv alternative protection in spectra_savgol for the case where
inv fails
Added Jan 20 2025
* Added the 'cca' flag to the pls routine to calculate CCA between
the Ts and each of the Ys (one by one), calculating loadings and scores
equivalent to a perfectly orthogonalized OPLS model. The covariant scores (Tcv)
the covariant Loadings (Pcv) and predictive weights (Wcv) are added
as keys to the model object.
[The covariant loadings(Pcv) are equivalent to the predictive loadings in OPLS]
* Added cca and cca-multi routines to perform PLS-CCA (alternative to OPLS)
as of now cca-multi remains unused.
Added Nov 18th, 2024
* replaced interp2d with RectBivariateSpline
* Protected SPE lim calculations for near zero residuals
* Added build_polynomial function to create linear regression
models with variable selection assited by PLS
by merge from James
* Added spectra preprocessing methods
* bootstrap PLS
by Salvador Garcia ([email protected] [email protected])
Added Dec 19th 2023
* phi.clean_htmls removes all html files in the working directory
* clean_empty_rows returns also the names of the rows removed
Added May 1st
* YMB is now added in the same structure as the XMB
* Corrected the dimensionality of the lwpls prediction, it was a double-nested array.
Added Apr 30 {feliz día de los niños}
* Modified Multi-block PLS to include the block name in the variable name
Added Apr 29
* Included the unique routine and adjusted the parse_materials routine so materials
and lots are in the same order as in the raw data
Added Apr 27
* Enhanced adapt_pls_4_pyomo to use variable names as indices if flag is sent
Added Apr 25
* Enhanced the varimax_rotation to adjust the r2 and r2pv to the rotated loadings
Added Apr 21
* Re added varimax_rotation with complete model rotation for PCA and PLS
Added Apr 17
* Added tpls and tpls_pred
Added Apr 15
* Added jrpls model and jrpls_pred
* Added routines to reconcile columns to rows identifier so that X and R materices
correspond correctly
* Added routines to reconcile rows across a list of dataframes and produces a list
of dataframes containing only those observations present in all dataframes
Added on Apr 9 2023
* Added lpls and lpls_pred routines
* Added parse_materials to read linear table and produce R or Ri
Release as of Nov 23 2022
* Added a function to export PLS model to gPROMS code
Release as of Aug 22 2022
What was done:
*Fixed access to NEOS server and use of GAMS instead of IPOPT
Release as of Aug 12 2022
What was done:
* Fixed the SPE calculations in pls_pred and pca_pred
* Changed to a more efficient inversion in pca_pred (=pls_pred)
* Added a pseudo-inverse option in pmp for pca_pred
Relase as of now Aug 2 2022
What was done:
*Added replicate_data
Release Unknown
What was done:
* Fixed a bug in kernel PCA calculations
* Changed the syntax of MBPLS arguments
* Corrected a pretty severe error in pls_pred
* Fixed a really bizzare one in mbpls
Release Dec 5, 2021
What was done:
*Added some small documentation to utilities routines
Release Jan 15, 2021
What was done:
* Added routine cat_2_matrix to conver categorical classifiers to matrices
* Added Multi-block PLS model
Release Date: NOv 16, 2020
What was done:
* Fixed small bug un clean_low_variances routine
Release Date: Sep 26 2020
What was done:
* Added rotation of loadings so that var(t) for ti>=0 is always larger
than var(t) for ti<0
Release Date: May 27 2020
What was done:
* Added the estimation of PLS models with missind data using
non-linear programming per Journal of Chemometrics, 28(7), pp.575-584.
Release Date: March 30 2020
What was done:
* Added the estimation of PCA models with missing data using
non-linear programming per Lopez-Negrete et al. J. Chemometrics 2010; 24: 301–311
Release Date: Aug 22 2019
What was done:
* This header is now included to track high level changes
* fixed LWPLS it works now for scalar and multivariable Y's
* fixed minor bug in phi.pca and phi.pls when mcsX/Y = False
"""
import numpy as np
import pandas as pd
import datetime
from scipy.special import factorial
from scipy.stats import norm
from scipy.optimize import fsolve
from scipy import interpolate
from scipy.interpolate import RectBivariateSpline
from statsmodels.distributions.empirical_distribution import ECDF
from shutil import which
import os
from numpy import eye, asarray, dot, sum, diag
from numpy.linalg import svd
import matplotlib.pyplot as plt
os.environ['NEOS_EMAIL'] = '[email protected]'
try:
from pyomo.environ import *
pyomo_ok = True
except ImportError:
pyomo_ok = False
if bool(which('gams')):
gams_ok = True
else:
gams_ok = False # GAMS is run via pyomo
# Check if an IPOPT binary available is availbale
# shutil was introduced in Python 3.2
ipopt_ok = bool(which('ipopt'))
# Check for Pyomo/GAMS interface is available
if pyomo_ok and gams_ok:
from pyomo.solvers.plugins.solvers.GAMS import GAMSDirect, GAMSShell
# exeption_flag = True (default) will throw an exception if GAMS
# is not available
gams_ok = (GAMSDirect().available(exception_flag=False)
or GAMSShell().available(exception_flag=False))
def ma57_dummy_check():
"""
Instantiates a trivial NLP to solve with IPOPT and MA57.
Returns:
ma57_ok: boolean, True if IPOPT solved with SolverStaus.ok
"""
m = ConcreteModel()
m.x = Var()
m.Obj = Objective(expr = m.x**2 -1)
s = SolverFactory('ipopt')
s.options['linear_solver'] = 'ma57'
import logging
pyomo_logger = logging.getLogger('pyomo.core')
LOG_DEFAULT = pyomo_logger.level
pyomo_logger.setLevel(logging.ERROR)
r = s.solve(m)
pyomo_logger.setLevel(LOG_DEFAULT)
ma57_ok = r.solver.status == SolverStatus.ok
if ma57_ok:
print("MA57 available to IPOPT")
return ma57_ok
if pyomo_ok and ipopt_ok:
ma57_ok = ma57_dummy_check()
else:
ma57_ok = False
if not(pyomo_ok) or (not(ipopt_ok) and not(gams_ok)):
print('Will be using the NEOS server in the absence of IPOPT and GAMS')
def clean_htmls():
''' Routine to clean html files
pyphi.clean_htmls()
Deletes all .html files in the current directory
Args:
none
Returns:
none
'''
files_here=os.listdir('.')
for f in files_here:
if 'html' in f:
os.remove(f)
return
def pca (X,A,*,mcs=True,md_algorithm='nipals',force_nipals=False,shush=False,cross_val=0):
''' Function to creat a Principal Components Analysis model
by Salvador Garcia-Munoz
pca_object = pyphi.pca (X,A,<mcs=True,md_algorithm='nipals',force_nipals=False,shush=False,cross_val=0>)
Args:
X (Dataframe or Numpy) : Data to train the model
A (int): Number of Principal Components to calculate
Other Parameters:
mcs: 'True' : Meancenter + autoscale *default if not sent*
'False' : No pre-processing
'center' : Only center
'autoscale' : Only autoscale
md_algorithm: Missing Data algorithm to use
'nipals' *default if not sent*
'nlp' Uses non-linear programming approach by Lopez-Negrete et al. J. Chemometrics 2010; 24: 301–311
force_nipals: If = True will use NIPALS.
= False if X is complete will use SVD. *default if not sent*
shush: If = True supressess all printed output
= False *default if not sent*
cross_val: If sent a scalar between 0 and 100, will cross validate
element wise removing cross_val% of the data every round
if == 0: Bypass cross-validation *default if not sent*
Returns:
A dictionary with all PCA loadings, scores and other diagnostics.
'''
if cross_val==0:
pcaobj= pca_(X,A,mcs=mcs,md_algorithm=md_algorithm,force_nipals=force_nipals,shush=shush)
pcaobj['type']='pca'
elif (cross_val > 0) and (cross_val<100):
if isinstance(X,np.ndarray):
X_=X.copy()
elif isinstance(X,pd.DataFrame):
X_=np.array(X.values[:,1:]).astype(float)
#Mean center and scale according to flags
if isinstance(mcs,bool):
if mcs:
#Mean center and autoscale
X_,x_mean,x_std = meancenterscale(X_)
else:
x_mean = np.zeros((1,X_.shape[1]))
x_std = np.ones((1,X_.shape[1]))
elif mcs=='center':
#only center
X_,x_mean,x_std = meancenterscale(X_,mcs='center')
elif mcs=='autoscale':
#only autoscale
X_,x_mean,x_std = meancenterscale(X_,mcs='autoscale')
#Generate Missing Data Map
X_nan_map = np.isnan(X_)
not_Xmiss = (np.logical_not(X_nan_map))*1
#Initialize TSS per var vector
X_,Xnanmap=n2z(X_)
TSS = np.sum(X_**2)
TSSpv = np.sum(X_**2,axis=0)
cols = X_.shape[1]
rows = X_.shape[0]
X_ = z2n(X_,Xnanmap)
for a in list(range(A)):
if not(shush):
print('Cross validating PC #'+str(a+1))
#Generate cross-val map starting from missing data
not_removed_map = not_Xmiss.copy()
not_removed_map = np.reshape(not_removed_map,(rows*cols,-1))
#Generate matrix of random numbers and zero out nans
Xrnd = np.random.random(X_.shape)*not_Xmiss
indx = np.argsort(np.reshape(Xrnd,(Xrnd.shape[0]*Xrnd.shape[1])))
elements_to_remove_per_round = int(np.ceil((X_.shape[0]*X_.shape[1]) * (cross_val/100)))
error = np.zeros((rows*cols,1))
rounds=1
while np.sum(not_removed_map) > 0 :#While there are still elements to be removed
#if not(shush):
# print('Removing samples round #'+str(rounds)+' for component :'+str(a+1))
rounds=rounds+1
X_copy=X_.copy()
if indx.size > elements_to_remove_per_round:
indx_this_round = indx[0:elements_to_remove_per_round]
indx = indx[elements_to_remove_per_round:]
else:
indx_this_round = indx
#Place NaN's
X_copy = np.reshape(X_copy,(rows*cols,1))
elements_out = X_copy[indx_this_round]
X_copy[indx_this_round] = np.nan
X_copy = np.reshape(X_copy,(rows,cols))
#update map
not_removed_map[indx_this_round] = 0
#look rows of missing data
auxmap = np.isnan(X_copy)
auxmap= (auxmap)*1
auxmap=np.sum(auxmap,axis=1)
indx2 = np.where(auxmap==X_copy.shape[1])
indx2=indx2[0].tolist()
if len(indx2) > 0:
X_copy=np.delete(X_copy,indx2,0)
pcaobj_ = pca_(X_copy,1,mcs=False,shush=True)
xhat = pcaobj_['T'] @ pcaobj_['P'].T
xhat = np.insert(xhat, indx2,np.nan,axis=0)
xhat = np.reshape(xhat,(rows*cols,1))
error[indx_this_round] = elements_out - xhat[indx_this_round]
error = np.reshape(error,(rows,cols))
error,dummy = n2z(error)
PRESSpv = np.sum(error**2,axis=0)
PRESS = np.sum(error**2)
if a==0:
q2 = 1 - PRESS/TSS
q2pv = 1 - PRESSpv/TSSpv
q2pv = q2pv.reshape(-1,1)
else:
q2 = np.hstack((q2,1 - PRESS/TSS))
aux_ = 1-PRESSpv/TSSpv
aux_ = aux_.reshape(-1,1)
q2pv = np.hstack((q2pv,aux_))
#Deflate and go to next PC
X_copy=X_.copy()
pcaobj_ = pca_(X_copy,1,mcs=False,shush=True)
xhat = pcaobj_['T'] @ pcaobj_['P'].T
X_,Xnanmap=n2z(X_)
X_ = (X_ - xhat) * not_Xmiss
if a==0:
r2 = 1-np.sum(X_**2)/TSS
r2pv = 1-np.sum(X_**2,axis=0)/TSSpv
r2pv = r2pv.reshape(-1,1)
else:
r2 = np.hstack((r2,1-np.sum(X_**2)/TSS))
aux_ = 1-np.sum(X_**2,axis=0)/TSSpv
aux_ = aux_.reshape(-1,1)
r2pv = np.hstack((r2pv,aux_))
X_ = z2n(X_,Xnanmap)
# Fit full model
pcaobj = pca_(X,A,mcs=mcs,force_nipals=True,shush=True)
for a in list(range(A-1,0,-1)):
r2[a] = r2[a]-r2[a-1]
r2pv[:,a] = r2pv[:,a]-r2pv[:,a-1]
q2[a] = q2[a]-q2[a-1]
q2pv[:,a] = q2pv[:,a]-q2pv[:,a-1]
r2xc = np.cumsum(r2)
q2xc = np.cumsum(q2)
eigs = np.var(pcaobj['T'],axis=0)
pcaobj['q2'] = q2
pcaobj ['q2pv'] = q2pv
if not(shush):
print('phi.pca using NIPALS and cross validation ('+str(cross_val)+'%) executed on: '+ str(datetime.datetime.now()) )
print('--------------------------------------------------------------')
print('PC # Eig R2X sum(R2X) Q2X sum(Q2X)')
if A>1:
for a in list(range(A)):
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f} {:.3f} {:.3f}".format(eigs[a], r2[a], r2xc[a],q2[a],q2xc[a]))
else:
d1=eigs[0]
d2=r2xc[0]
d3=q2xc[0]
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f} {:.3f} {:.3f}".format(d1, r2, d2,q2,d3))
print('--------------------------------------------------------------')
pcaobj['type']='pca'
else:
pcaobj='Cannot cross validate with those options'
return pcaobj
def pca_(X,A,*,mcs=True,md_algorithm='nipals',force_nipals=False,shush=False):
if isinstance(X,np.ndarray):
X_=X.copy()
obsidX = False
varidX = False
elif isinstance(X,pd.DataFrame):
X_=np.array(X.values[:,1:]).astype(float)
obsidX = X.values[:,0].astype(str)
obsidX = obsidX.tolist()
varidX = X.columns.values
varidX = varidX[1:]
varidX = varidX.tolist()
if isinstance(mcs,bool):
if mcs:
#Mean center and autoscale
X_,x_mean,x_std = meancenterscale(X_)
else:
x_mean = np.zeros((1,X_.shape[1]))
x_std = np.ones((1,X_.shape[1]))
elif mcs=='center':
X_,x_mean,x_std = meancenterscale(X_,mcs='center')
#only center
elif mcs=='autoscale':
#only autoscale
X_,x_mean,x_std = meancenterscale(X_,mcs='autoscale')
#Generate Missing Data Map
X_nan_map = np.isnan(X_)
not_Xmiss = (np.logical_not(X_nan_map))*1
if not(X_nan_map.any()) and not(force_nipals) and ((X_.shape[1]/X_.shape[0]>=10) or (X_.shape[0]/X_.shape[1]>=10)):
#no missing elements
if not(shush):
print('phi.pca using SVD executed on: '+ str(datetime.datetime.now()) )
TSS = np.sum(X_**2)
TSSpv = np.sum(X_**2,axis=0)
if X_.shape[1]/X_.shape[0]>=10:
[U,S,Th] = np.linalg.svd(X_ @ X_.T)
T = Th.T
T = T[:,0:A]
P = X_.T @ T
for a in list(range(A)):
P[:,a] = P[:,a]/np.linalg.norm(P[:,a])
T = X_ @ P
elif X_.shape[0]/X_.shape[1]>=10:
[U,S,Ph] = np.linalg.svd(X_.T @ X_)
P = Ph.T
P = P[:,0:A]
T = X_ @ P
for a in list(range(A)):
X_ = X_- T[:,[a]]@P[:,[a]].T
if a==0:
r2 = 1-np.sum(X_**2)/TSS
r2pv = 1-np.sum(X_**2,axis=0)/TSSpv
r2pv = r2pv.reshape(-1,1)
else:
r2 = np.hstack((r2, 1-np.sum(X_**2)/TSS))
aux_ = 1-(np.sum(X_**2,axis=0)/TSSpv)
r2pv = np.hstack((r2pv,aux_.reshape(-1,1)))
for a in list(range(A-1,0,-1)):
r2[a] = r2[a]-r2[a-1]
r2pv[:,a] = r2pv[:,a]-r2pv[:,a-1]
pca_obj={'T':T,'P':P,'r2x':r2,'r2xpv':r2pv,'mx':x_mean,'sx':x_std}
if not isinstance(obsidX,bool):
pca_obj['obsidX']=obsidX
pca_obj['varidX']=varidX
eigs = np.var(T,axis=0);
r2xc = np.cumsum(r2)
if not(shush):
print('--------------------------------------------------------------')
print('PC # Eig R2X sum(R2X) ')
if A>1:
for a in list(range(A)):
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f}".format(eigs[a], r2[a], r2xc[a]))
else:
d1=eigs[0]
d2=r2xc[0]
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f}".format(d1, r2, d2))
print('--------------------------------------------------------------')
T2 = hott2(pca_obj,Tnew=T)
n = T.shape[0]
T2_lim99 = (((n-1)*(n+1)*A)/(n*(n-A)))*f99(A,(n-A))
T2_lim95 = (((n-1)*(n+1)*A)/(n*(n-A)))*f95(A,(n-A))
speX = np.sum(X_**2,axis=1,keepdims=1)
speX_lim95,speX_lim99 = spe_ci(speX)
pca_obj['T2'] = T2
pca_obj['T2_lim99']= T2_lim99
pca_obj['T2_lim95']= T2_lim95
pca_obj['speX']= speX
pca_obj['speX_lim99']= speX_lim99
pca_obj['speX_lim95']= speX_lim95
return pca_obj
else:
if md_algorithm=='nipals':
#use nipals
if not(shush):
print('phi.pca using NIPALS executed on: '+ str(datetime.datetime.now()) )
X_,dummy=n2z(X_)
epsilon=1E-10
maxit=5000
TSS = np.sum(X_**2)
TSSpv = np.sum(X_**2,axis=0)
#T=[];
#P=[];
#r2=[];
#r2pv=[];
#numIT=[];
for a in list(range(A)):
# Select column with largest variance as initial guess
ti = X_[:,[np.argmax(std(X_))]]
Converged=False
num_it=0
while Converged==False:
#Step 1. p(i)=t' x(i)/t't
timat=np.tile(ti,(1,X_.shape[1]))
pi=(np.sum(X_*timat,axis=0))/(np.sum((timat*not_Xmiss)**2,axis=0))
#Step 2. Normalize p to unit length.
pi=pi/np.linalg.norm(pi)
#Step 3. tnew= (x*p) / (p'p);
pimat=np.tile(pi,(X_.shape[0],1))
tn= X_ @ pi.T
ptp=np.sum((pimat*not_Xmiss)**2,axis=1)
tn=tn/ptp
pi=pi.reshape(-1,1)
if abs((np.linalg.norm(ti)-np.linalg.norm(tn)))/(np.linalg.norm(ti)) < epsilon:
Converged=True
if num_it > maxit:
Converged=True
if Converged:
if (len(ti[ti<0])>0) and (len(ti[ti>0])>0): #if scores are above and below zero
if np.var(ti[ti<0]) > np.var(ti[ti>=0]):
tn=-tn
ti=-ti
pi=-pi
if not(shush):
print('# Iterations for PC #'+str(a+1)+': ',str(num_it))
if a==0:
T=tn.reshape(-1,1)
P=pi
else:
T=np.hstack((T,tn.reshape(-1,1)))
P=np.hstack((P,pi))
# Deflate X leaving missing as zeros (important!)
X_=(X_- ti @ pi.T)*not_Xmiss
if a==0:
r2 = 1-np.sum(X_**2)/TSS
r2pv = 1-np.sum(X_**2,axis=0)/TSSpv
r2pv = r2pv.reshape(-1,1)
else:
r2 = np.hstack((r2,1-np.sum(X_**2)/TSS))
aux_ = 1-np.sum(X_**2,axis=0)/TSSpv
aux_ = aux_.reshape(-1,1)
r2pv = np.hstack((r2pv,aux_))
else:
num_it = num_it + 1
ti = tn.reshape(-1,1)
if a==0:
numIT=num_it
else:
numIT=np.hstack((numIT,num_it))
for a in list(range(A-1,0,-1)):
r2[a] = r2[a]-r2[a-1]
r2pv[:,a] = r2pv[:,a]-r2pv[:,a-1]
eigs = np.var(T,axis=0);
r2xc = np.cumsum(r2)
if not(shush):
print('--------------------------------------------------------------')
print('PC # Eig R2X sum(R2X) ')
if A>1:
for a in list(range(A)):
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f}".format(eigs[a], r2[a], r2xc[a]))
else:
d1=eigs[0]
d2=r2xc[0]
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f}".format(d1, r2, d2))
print('--------------------------------------------------------------')
pca_obj={'T':T,'P':P,'r2x':r2,'r2xpv':r2pv,'mx':x_mean,'sx':x_std}
if not isinstance(obsidX,bool):
pca_obj['obsidX']=obsidX
pca_obj['varidX']=varidX
T2 = hott2(pca_obj,Tnew=T)
n = T.shape[0]
T2_lim99 = (((n-1)*(n+1)*A)/(n*(n-A)))*f99(A,(n-A))
T2_lim95 = (((n-1)*(n+1)*A)/(n*(n-A)))*f95(A,(n-A))
speX = np.sum(X_**2,axis=1,keepdims=1)
speX_lim95,speX_lim99 = spe_ci(speX)
pca_obj['T2'] = T2
pca_obj['T2_lim99']= T2_lim99
pca_obj['T2_lim95']= T2_lim95
pca_obj['speX']= speX
pca_obj['speX_lim99']= speX_lim99
pca_obj['speX_lim95']= speX_lim95
return pca_obj
elif md_algorithm=='nlp' and pyomo_ok:
#use NLP per Lopez-Negrete et al. J. Chemometrics 2010; 24: 301–311
if not(shush):
print('phi.pca using NLP with Ipopt executed on: '+ str(datetime.datetime.now()) )
pcaobj_= pca_(X,A,mcs=mcs,md_algorithm='nipals',shush=True)
pcaobj_= prep_pca_4_MDbyNLP(pcaobj_,X_)
TSS = np.sum(X_**2)
TSSpv = np.sum(X_**2,axis=0)
#Set up the model in Pyomo
model = ConcreteModel()
model.A = Set(initialize = pcaobj_['pyo_A'] )
model.N = Set(initialize = pcaobj_['pyo_N'] )
model.O = Set(initialize = pcaobj_['pyo_O'] )
model.P = Var(model.N,model.A, within = Reals,initialize = pcaobj_['pyo_P_init'])
model.T = Var(model.O,model.A, within = Reals,initialize = pcaobj_['pyo_T_init'])
model.psi = Param(model.O,model.N,initialize = pcaobj_['pyo_psi'])
model.X = Param(model.O,model.N,initialize = pcaobj_['pyo_X'])
model.delta = Param(model.A, model.A, initialize=lambda model, a1, a2: 1.0 if a1==a2 else 0)
# Constraints 20b
def _c20b_con(model, a1, a2):
return sum(model.P[j, a1] * model.P[j, a2] for j in model.N) == model.delta[a1, a2]
model.c20b = Constraint(model.A, model.A, rule=_c20b_con)
# Constraints 20c
def _20c_con(model, a1, a2):
if a2 < a1:
return sum(model.T[o, a1] * model.T[o, a2] for o in model.O) == 0
else:
return Constraint.Skip
model.c20c = Constraint(model.A, model.A, rule=_20c_con)
# Constraints 20d
def mean_zero(model,i):
return sum (model.T[o,i] for o in model.O )==0
model.eq3 = Constraint(model.A,rule=mean_zero)
def _eq_20a_obj(model):
return sum(sum((model.X[o,n]- model.psi[o,n] * sum(model.T[o,a] * model.P[n,a] for a in model.A))**2 for n in model.N) for o in model.O)
model.obj = Objective(rule=_eq_20a_obj)
# Setup our solver as either local ipopt, gams:ipopt, or neos ipopt:
if (ipopt_ok):
print("Solving NLP using local IPOPT executable")
solver = SolverFactory('ipopt')
if (ma57_ok):
solver.options['linear_solver'] = 'ma57'
results = solver.solve(model,tee=True)
elif (gams_ok):
print("Solving NLP using GAMS/IPOPT interface")
# 'just 'ipopt' could work, if no binary in path
solver = SolverFactory('gams:ipopt')
# It doesn't seem to notice the opt file when I write it
results = solver.solve(model, tee=True)
else:
print("Solving NLP using IPOPT on remote NEOS server")
solver_manager = SolverManagerFactory('neos')
results = solver_manager.solve(model, opt='ipopt', tee=True)
T=[]
for o in model.O:
t=[]
for a in model.A:
t.append(value(model.T[o,a]))
T.append(t)
T=np.array(T)
P=[]
for n in model.N:
p=[]
for a in model.A:
p.append(value(model.P[n,a]))
P.append(p)
P=np.array(P)
# Calculate R2
for a in list(range(0, A)):
ti=T[:,[a]]
pi=P[:,[a]]
if np.var(ti[ti<0]) > np.var(ti[ti>=0]):
ti=-ti
pi=-pi
T[:,[a]]=-T[:,[a]]
P[:,[a]]=-P[:,[a]]
X_=(X_- ti @ pi.T)*not_Xmiss
if a==0:
r2 = 1-np.sum(X_**2)/TSS
r2pv = 1-np.sum(X_**2,axis=0)/TSSpv
r2pv = r2pv.reshape(-1,1)
else:
r2 = np.hstack((r2,1-np.sum(X_**2)/TSS))
aux_ = 1-np.sum(X_**2,axis=0)/TSSpv
aux_ = aux_.reshape(-1,1)
r2pv = np.hstack((r2pv,aux_))
for a in list(range(A-1,0,-1)):
r2[a] = r2[a]-r2[a-1]
r2pv[:,a] = r2pv[:,a]-r2pv[:,a-1]
eigs = np.var(T,axis=0);
r2xc = np.cumsum(r2)
if not(shush):
print('--------------------------------------------------------------')
print('PC # Eig R2X sum(R2X) ')
if A>1:
for a in list(range(A)):
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f}".format(eigs[a], r2[a], r2xc[a]))
else:
d1=eigs[0]
d2=r2xc[0]
print("PC #"+str(a+1)+": {:8.3f} {:.3f} {:.3f}".format(d1, r2, d2))
print('--------------------------------------------------------------')
pca_obj={'T':T,'P':P,'r2x':r2,'r2xpv':r2pv,'mx':x_mean,'sx':x_std}
if not isinstance(obsidX,bool):
pca_obj['obsidX']=obsidX
pca_obj['varidX']=varidX
T2 = hott2(pca_obj,Tnew=T)
n = T.shape[0]
T2_lim99 = (((n-1)*(n+1)*A)/(n*(n-A)))*f99(A,(n-A))
T2_lim95 = (((n-1)*(n+1)*A)/(n*(n-A)))*f95(A,(n-A))
speX = np.sum(X_**2,axis=1,keepdims=1)
speX_lim95,speX_lim99 = spe_ci(speX)
pca_obj['T2'] = T2
pca_obj['T2_lim99']= T2_lim99
pca_obj['T2_lim95']= T2_lim95
pca_obj['speX']= speX
pca_obj['speX_lim99']= speX_lim99
pca_obj['speX_lim95']= speX_lim95
return pca_obj
elif md_algorithm=='nlp' and not( pyomo_ok):
print('Pyomo was not found in your system sorry')
print('visit http://www.pyomo.org/ ')
pca_obj=1
return pca_obj
def pls(X,Y,A,*,mcsX=True,mcsY=True,md_algorithm='nipals',force_nipals=True,shush=False,
cross_val=0,cross_val_X=False,cca=False):
''' Function to create a Projection to Latent Structures model
by Salvador Garcia-Munoz
pls_object = pyphi.pls(X,Y,A,<mcsX=True,mcsY=True,md_algorithm='nipals',force_nipals=True,shush=False,
cross_val=0,cross_val_X=False,cca=False>)
Args:
X,Y (DataFrame or Numpy) : Training Data
A (int) : Number of Latent Variables to calculate
Other Parameters:
mcsX/mcsY: 'True' : Will meancenter and autoscale the data *default if not sent*
'False' : No pre-processing
'center' : Will only center
'autoscale' : Will only autoscale
md_algorithm: 'nipals' *default*
'nlp' Uses algorithm described in Journal of Chemometrics, 28(7), pp.575-584.
force_nipals: If set to True and if X is complete, will use NIPALS.
Otherwise, if X is complete will use SVD.
shush: If set to True supressess all printed output.
cross_val: If sent a scalar between 0 and 100, will cross validate
element wise removing cross_val% of the data every round
if == 0: Bypass cross-validation *default if not sent*
cross_val_X: True : Calculates Q2 values for the X and Y matrices
False: Cross-validation strictly on Y matrix *default if not sent*
cca: True : Calculates covariable space of X with Y (analog to the predictive space in OPLS)
"Tcv" and "Pcv" and the covariant scores and loadings if more than one Y, then
there will be as many Tcv and Pcv vectors as columns in Y
Returns:
A dictionary with all PLS loadings, scores and other diagnostics.
'''
if cross_val==0:
plsobj = pls_(X,Y,A,mcsX=mcsX,mcsY=mcsY,md_algorithm=md_algorithm,force_nipals=force_nipals,shush=shush,cca=cca)
plsobj['type']='pls'
elif (cross_val > 0) and (cross_val<100):
if isinstance(X,np.ndarray):
X_=X.copy()
elif isinstance(X,pd.DataFrame):
X_=np.array(X.values[:,1:]).astype(float)
#Mean center and scale according to flags
if isinstance(mcsX,bool):
if mcsX:
#Mean center and autoscale
X_,x_mean,x_std = meancenterscale(X_)
else:
x_mean = np.zeros((1,X_.shape[1]))
x_std = np.ones((1,X_.shape[1]))
elif mcsX=='center':
#only center
X_,x_mean,x_std = meancenterscale(X_,mcs='center')
elif mcsX=='autoscale':
#only autoscale
X_,x_mean,x_std = meancenterscale(X_,mcs='autoscale')
#Generate Missing Data Map
X_nan_map = np.isnan(X_)
not_Xmiss = (np.logical_not(X_nan_map))*1
if isinstance(Y,np.ndarray):
Y_=Y.copy()
elif isinstance(Y,pd.DataFrame):
Y_=np.array(Y.values[:,1:]).astype(float)
#Mean center and scale according to flags
if isinstance(mcsY,bool):
if mcsY:
#Mean center and autoscale
Y_,y_mean,y_std = meancenterscale(Y_)
else:
y_mean = np.zeros((1,Y_.shape[1]))
y_std = np.ones((1,Y_.shape[1]))
elif mcsY=='center':
#only center
Y_,y_mean,y_std = meancenterscale(Y_,mcs='center')
elif mcsY=='autoscale':
#only autoscale
Y_,y_mean,y_std = meancenterscale(Y_,mcs='autoscale')
#Generate Missing Data Map
Y_nan_map = np.isnan(Y_)
not_Ymiss = (np.logical_not(Y_nan_map))*1
#Initialize TSS per var vector
X_,Xnanmap=n2z(X_)
TSSX = np.sum(X_**2)
TSSXpv = np.sum(X_**2,axis=0)
colsX = X_.shape[1]
rowsX = X_.shape[0]
X_ = z2n(X_,Xnanmap)
Y_,Ynanmap=n2z(Y_)
TSSY = np.sum(Y_**2)
TSSYpv = np.sum(Y_**2,axis=0)
colsY = Y_.shape[1]
rowsY = Y_.shape[0]
Y_ = z2n(Y_,Ynanmap)
for a in list(range(A)):
if not(shush):
print('Cross validating LV #'+str(a+1))
#Generate cross-val map starting from missing data
not_removed_mapY = not_Ymiss.copy()
not_removed_mapY = np.reshape(not_removed_mapY,(rowsY*colsY,-1))
#Generate matrix of random numbers and zero out nans
Yrnd = np.random.random(Y_.shape)*not_Ymiss
indxY = np.argsort(np.reshape(Yrnd,(Yrnd.shape[0]*Yrnd.shape[1])))
elements_to_remove_per_roundY = int(np.ceil((Y_.shape[0]*Y_.shape[1]) * (cross_val/100)))
errorY = np.zeros((rowsY*colsY,1))
if cross_val_X:
#Generate cross-val map starting from missing data
not_removed_mapX = not_Xmiss.copy()
not_removed_mapX = np.reshape(not_removed_mapX,(rowsX*colsX,-1))
#Generate matrix of random numbers and zero out nans
Xrnd = np.random.random(X_.shape)*not_Xmiss
indxX = np.argsort(np.reshape(Xrnd,(Xrnd.shape[0]*Xrnd.shape[1])))
elements_to_remove_per_roundX = int(np.ceil((X_.shape[0]*X_.shape[1]) * (cross_val/100)))
errorX = np.zeros((rowsX*colsX,1))
else:
not_removed_mapX=0
number_of_rounds=1
while np.sum(not_removed_mapX) > 0 or np.sum(not_removed_mapY) > 0 :#While there are still elements to be removed
#if not(shush):
# print('Random removal round #'+ str(number_of_rounds))
number_of_rounds=number_of_rounds+1
X_copy=X_.copy()
if cross_val_X:
if indxX.size > elements_to_remove_per_roundX:
indx_this_roundX = indxX[0:elements_to_remove_per_roundX]
indxX = indxX[elements_to_remove_per_roundX:]
else:
indx_this_roundX = indxX
#Place NaN's
X_copy = np.reshape(X_copy,(rowsX*colsX,1))
elements_outX = X_copy[indx_this_roundX]
X_copy[indx_this_roundX] = np.nan
X_copy = np.reshape(X_copy,(rowsX,colsX))
#update map
not_removed_mapX[indx_this_roundX] = 0
#look rows of missing data
auxmap = np.isnan(X_copy)
auxmap= (auxmap)*1
auxmap=np.sum(auxmap,axis=1)
indx2 = np.where(auxmap==X_copy.shape[1])
indx2=indx2[0].tolist()
else:
indx2=[];
Y_copy=Y_.copy()
if indxY.size > elements_to_remove_per_roundY:
indx_this_roundY = indxY[0:elements_to_remove_per_roundY]
indxY = indxY[elements_to_remove_per_roundY:]
else:
indx_this_roundY = indxY
#Place NaN's
Y_copy = np.reshape(Y_copy,(rowsY*colsY,1))
elements_outY = Y_copy[indx_this_roundY]
Y_copy[indx_this_roundY] = np.nan
Y_copy = np.reshape(Y_copy,(rowsY,colsY))
#update map
not_removed_mapY[indx_this_roundY] = 0
#look rows of missing data
auxmap = np.isnan(Y_copy)
auxmap = (auxmap)*1
auxmap = np.sum(auxmap,axis=1)
indx3 = np.where(auxmap==Y_copy.shape[1])
indx3 = indx3[0].tolist()
indx4 = np.unique(indx3+indx2)
indx4 = indx4.tolist()
if len(indx4) > 0:
X_copy=np.delete(X_copy,indx4,0)
Y_copy=np.delete(Y_copy,indx4,0)
#print('Running PLS')
plsobj_ = pls_(X_copy,Y_copy,1,mcsX=False,mcsY=False,shush=True)
#print('Done with PLS')
plspred = pls_pred(X_,plsobj_)
if cross_val_X:
xhat = plspred['Tnew'] @ plsobj_['P'].T
xhat = np.reshape(xhat,(rowsX*colsX,1))
errorX[indx_this_roundX] = elements_outX - xhat[indx_this_roundX]
yhat = plspred['Tnew'] @ plsobj_['Q'].T
yhat = np.reshape(yhat,(rowsY*colsY,1))
errorY[indx_this_roundY] = elements_outY - yhat[indx_this_roundY]
if cross_val_X:
errorX = np.reshape(errorX,(rowsX,colsX))
errorX,dummy = n2z(errorX)
PRESSXpv = np.sum(errorX**2,axis=0)
PRESSX = np.sum(errorX**2)
errorY = np.reshape(errorY,(rowsY,colsY))
errorY,dummy = n2z(errorY)
PRESSYpv = np.sum(errorY**2,axis=0)
PRESSY = np.sum(errorY**2)
if a==0:
q2Y = 1 - PRESSY/TSSY
q2Ypv = 1 - PRESSYpv/TSSYpv
q2Ypv = q2Ypv.reshape(-1,1)
if cross_val_X:
q2X = 1 - PRESSX/TSSX
q2Xpv = 1 - PRESSXpv/TSSXpv
q2Xpv = q2Xpv.reshape(-1,1)
else:
q2Y = np.hstack((q2Y,1 - PRESSY/TSSY))
aux_ = 1-PRESSYpv/TSSYpv
aux_ = aux_.reshape(-1,1)
q2Ypv = np.hstack((q2Ypv,aux_))
if cross_val_X:
q2X = np.hstack((q2X,1 - PRESSX/TSSX))
aux_ = 1-PRESSXpv/TSSXpv
aux_ = aux_.reshape(-1,1)
q2Xpv = np.hstack((q2Xpv,aux_))
#Deflate and go to next PC
X_copy=X_.copy()
Y_copy=Y_.copy()
plsobj_ = pls_(X_copy,Y_copy,1,mcsX=False,mcsY=False,shush=True)
xhat = plsobj_['T'] @ plsobj_['P'].T
yhat = plsobj_['T'] @ plsobj_['Q'].T
X_,Xnanmap=n2z(X_)
Y_,Ynanmap=n2z(Y_)
X_ = (X_ - xhat) * not_Xmiss
Y_ = (Y_ - yhat) * not_Ymiss
if a==0:
r2X = 1-np.sum(X_**2)/TSSX
r2Xpv = 1-np.sum(X_**2,axis=0)/TSSXpv
r2Xpv = r2Xpv.reshape(-1,1)
r2Y = 1-np.sum(Y_**2)/TSSY
r2Ypv = 1-np.sum(Y_**2,axis=0)/TSSYpv
r2Ypv = r2Ypv.reshape(-1,1)
else:
r2X = np.hstack((r2X,1-np.sum(X_**2)/TSSX))
aux_ = 1-np.sum(X_**2,axis=0)/TSSXpv
aux_ = aux_.reshape(-1,1)
r2Xpv = np.hstack((r2Xpv,aux_))
r2Y = np.hstack((r2Y,1-np.sum(Y_**2)/TSSY))
aux_ = 1-np.sum(Y_**2,axis=0)/TSSYpv
aux_ = aux_.reshape(-1,1)
r2Ypv = np.hstack((r2Ypv,aux_))
X_ = z2n(X_,Xnanmap)
Y_ = z2n(Y_,Ynanmap)
# Fit full model