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pyphi.py
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"""
Phi for Python (pyPhi)
by Salvador Garcia ([email protected] [email protected])
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 import interpolate
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
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 pca (X,A,*,mcs=True,md_algorithm='nipals',force_nipals=False,shush=False,cross_val=0):
""" Principal Components Analysis routine
by Salvador Garcia-Munoz
Inputs:
X : Either a pandas dataframe, or a Numpy Matrix
A : Number of Principal Components to calculate
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*
Output:
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):
""" Projection to Latent Structures routine
by Salvador Garcia-Munoz
Inputs:
X,Y : Either a pandas dataframe, or a Numpy Matrix
A : Number of Principal Components to calculate
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*
Output:
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)
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
plsobj = pls_(X,Y,A,mcsX=mcsX,mcsY=mcsY,shush=True)
for a in list(range(A-1,0,-1)):
r2X[a] = r2X[a]-r2X[a-1]
r2Xpv[:,a] = r2Xpv[:,a]-r2Xpv[:,a-1]
if cross_val_X:
q2X[a] = q2X[a]-q2X[a-1]
q2Xpv[:,a] = q2Xpv[:,a]-q2Xpv[:,a-1]
else:
q2X = False
q2Xpv = False
r2Y[a] = r2Y[a]-r2Y[a-1]
r2Ypv[:,a] = r2Ypv[:,a]-r2Ypv[:,a-1]
q2Y[a] = q2Y[a]-q2Y[a-1]
q2Ypv[:,a] = q2Ypv[:,a]-q2Ypv[:,a-1]
r2xc = np.cumsum(r2X)
r2yc = np.cumsum(r2Y)
if cross_val_X:
q2xc = np.cumsum(q2X)
else:
q2xc = False
q2yc = np.cumsum(q2Y)
eigs = np.var(plsobj['T'],axis=0)
plsobj['q2Y'] = q2Y
plsobj['q2Ypv'] = q2Ypv
if cross_val_X:
plsobj['q2X'] = q2X
plsobj['q2Xpv'] = q2Xpv
if not(shush):
print('phi.pls using NIPALS and cross-validation ('+str(cross_val)+'%) executed on: '+ str(datetime.datetime.now()) )
if not(cross_val_X):
print('---------------------------------------------------------------------------------')
print('PC # Eig R2X sum(R2X) R2Y sum(R2Y) Q2Y sum(Q2Y)')
if A>1:
for a in list(range(A)):
print("PC #"+str(a+1)+":{:8.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f}".format(eigs[a], r2X[a], r2xc[a], r2Y[a], r2yc[a],q2Y[a],q2yc[a]))
else:
d1=eigs[0]
d2=r2xc[0]
d3=r2yc[0]
d4=q2yc[0]
print("PC #"+str(a+1)+":{:8.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f}".format(d1, r2X, d2,r2Y,d3,q2Y,d4))
print('---------------------------------------------------------------------------------')
else:
print('-------------------------------------------------------------------------------------------------------')
print('PC # Eig R2X sum(R2X) Q2X sum(Q2X) R2Y sum(R2Y) Q2Y sum(Q2Y)')
if A>1:
for a in list(range(A)):
print("PC #"+str(a+1)+":{:8.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f}".format(eigs[a], r2X[a], r2xc[a],q2X[a],q2xc[a], r2Y[a], r2yc[a],q2Y[a],q2yc[a]))
else:
d1=eigs[0]
d2=r2xc[0]
d3=q2xc[0]
d4=r2yc[0]
d5=q2yc[0]
print("PC #"+str(a+1)+":{:8.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f} {:.3f}".format(d1, r2X, d2,q2X,d3,r2Y,d4,q2Y,d5))
print('-------------------------------------------------------------------------------------------------------')
plsobj['type']='pls'