def check_2PC_abc(Csf):
out = []
n = len(Csf)
P = Csf[0][0].shape
z = sym.zeros(*P)
for a in range(n):
for b in range(n):
for c in range(n):
temp = matrix_multiply_elementwise(
Csf[a][c], Csf[c][b]) - matrix_multiply_elementwise(Csf[c][c], Csf[a][b])
check = temp.expand().simplify().as_real_imag()
out.append(check[0] == z and check[1] == z)
return all(out)
def conv(a, b):
af = dft(sym.conjugate(a))
bf = dft(b)
return idft(
matrix_multiply_elementwise(
sym.conjugate(af),
bf)).expand().simplify()
def backProp(self, prevNodes, goal, learningRate):
functionDerivative = (prevNodes * self.weights +
self.biases).applyfunc(
lambdify(x, self.derivative))
#goal -= self.nodes
#WEIGHTS
weightChange = prevNodes.T * functionDerivative
weightScalar = ((goal - self.nodes).T * prevNodes).T
#print(pretty(N(weightChange, precision), use_unicode=True))
#print(pretty(N(weightScalar, precision), use_unicode=True))
weightChange = matrix_multiply_elementwise(weightChange, weightScalar)
#print(pretty(N(weightChange, precision), use_unicode=True))
self.weights += weightChange
#print(weightChange.shape, self.weights.shape)
#BIASES
biasChange = functionDerivative
#print(biasChange.shape, self.biases.shape)
#NODES
nodeChange = (self.weights * functionDerivative.T).T
def test_multiplication():
a = ArithmeticOnlyMatrix((
(1, 2),
(3, 1),
(0, 6),
))
b = ArithmeticOnlyMatrix((
(1, 2),
(3, 0),
))
raises(ShapeError, lambda: b * a)
raises(TypeError, lambda: a * {})
c = a * b
assert c[0, 0] == 7
assert c[0, 1] == 2
assert c[1, 0] == 6
assert c[1, 1] == 6
assert c[2, 0] == 18
assert c[2, 1] == 0
try:
eval('c = a @ b')
except SyntaxError:
pass
else:
assert c[0, 0] == 7
assert c[0, 1] == 2
assert c[1, 0] == 6
assert c[1, 1] == 6
assert c[2, 0] == 18
assert c[2, 1] == 0
h = a.multiply_elementwise(c)
assert h == matrix_multiply_elementwise(a, c)
assert h[0, 0] == 7
assert h[0, 1] == 4
assert h[1, 0] == 18
assert h[1, 1] == 6
assert h[2, 0] == 0
assert h[2, 1] == 0
raises(ShapeError, lambda: a.multiply_elementwise(b))
c = b * Symbol("x")
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == x
assert c[0, 1] == 2 * x
assert c[1, 0] == 3 * x
assert c[1, 1] == 0
c2 = x * b
assert c == c2
c = 5 * b
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == 5
assert c[0, 1] == 2 * 5
assert c[1, 0] == 3 * 5
assert c[1, 1] == 0
try:
eval('c = 5 @ b')
except SyntaxError:
pass
else:
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == 5
assert c[0, 1] == 2 * 5
assert c[1, 0] == 3 * 5
assert c[1, 1] == 0
def test_multiplication():
a = ArithmeticOnlyMatrix((
(1, 2),
(3, 1),
(0, 6),
))
b = ArithmeticOnlyMatrix((
(1, 2),
(3, 0),
))
raises(ShapeError, lambda: b*a)
raises(TypeError, lambda: a*{})
c = a*b
assert c[0, 0] == 7
assert c[0, 1] == 2
assert c[1, 0] == 6
assert c[1, 1] == 6
assert c[2, 0] == 18
assert c[2, 1] == 0
try:
eval('c = a @ b')
except SyntaxError:
pass
else:
assert c[0, 0] == 7
assert c[0, 1] == 2
assert c[1, 0] == 6
assert c[1, 1] == 6
assert c[2, 0] == 18
assert c[2, 1] == 0
h = a.multiply_elementwise(c)
assert h == matrix_multiply_elementwise(a, c)
assert h[0, 0] == 7
assert h[0, 1] == 4
assert h[1, 0] == 18
assert h[1, 1] == 6
assert h[2, 0] == 0
assert h[2, 1] == 0
raises(ShapeError, lambda: a.multiply_elementwise(b))
c = b * Symbol("x")
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == x
assert c[0, 1] == 2*x
assert c[1, 0] == 3*x
assert c[1, 1] == 0
c2 = x * b
assert c == c2
c = 5 * b
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == 5
assert c[0, 1] == 2*5
assert c[1, 0] == 3*5
assert c[1, 1] == 0
try:
eval('c = 5 @ b')
except SyntaxError:
pass
else:
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == 5
assert c[0, 1] == 2*5
assert c[1, 0] == 3*5
assert c[1, 1] == 0
def test_multiplication():
a = ArithmeticOnlyMatrix((
(1, 2),
(3, 1),
(0, 6),
))
b = ArithmeticOnlyMatrix((
(1, 2),
(3, 0),
))
raises(ShapeError, lambda: b * a)
raises(TypeError, lambda: a * {})
c = a * b
assert c[0, 0] == 7
assert c[0, 1] == 2
assert c[1, 0] == 6
assert c[1, 1] == 6
assert c[2, 0] == 18
assert c[2, 1] == 0
try:
eval('c = a @ b')
except SyntaxError:
pass
else:
assert c[0, 0] == 7
assert c[0, 1] == 2
assert c[1, 0] == 6
assert c[1, 1] == 6
assert c[2, 0] == 18
assert c[2, 1] == 0
h = a.multiply_elementwise(c)
assert h == matrix_multiply_elementwise(a, c)
assert h[0, 0] == 7
assert h[0, 1] == 4
assert h[1, 0] == 18
assert h[1, 1] == 6
assert h[2, 0] == 0
assert h[2, 1] == 0
raises(ShapeError, lambda: a.multiply_elementwise(b))
c = b * Symbol("x")
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == x
assert c[0, 1] == 2 * x
assert c[1, 0] == 3 * x
assert c[1, 1] == 0
c2 = x * b
assert c == c2
c = 5 * b
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == 5
assert c[0, 1] == 2 * 5
assert c[1, 0] == 3 * 5
assert c[1, 1] == 0
try:
eval('c = 5 @ b')
except SyntaxError:
pass
else:
assert isinstance(c, ArithmeticOnlyMatrix)
assert c[0, 0] == 5
assert c[0, 1] == 2 * 5
assert c[1, 0] == 3 * 5
assert c[1, 1] == 0
# https://github.com/sympy/sympy/issues/22353
A = Matrix(ones(3, 1))
_h = -Rational(1, 2)
B = Matrix([_h, _h, _h])
assert A.multiply_elementwise(B) == Matrix([[_h], [_h], [_h]])
def ODESS(filename,
injections=[],
givenCQs=[],
neglect=[],
sparsifyLevel = 2,
outputFormat='R'):
filename=str(filename)
file=csv.reader(open(filename), delimiter=',')
print('Reading csv-file ...')
L=[]
nrrow=0
nrcol=0
for row in file:
nrrow=nrrow+1
nrcol=len(row)
L.append(row)
nrspecies=nrcol-2
##### Remove injections
counter=0
for i in range(1,len(L)):
if(L[i-counter][1] in injections):
L.remove(L[i-counter])
counter=counter+1
##### Define flux vector F
F=[]
for i in range(1,len(L)):
F.append(L[i][1])
#print(F)
F[i-1]=F[i-1].replace('^','**')
F[i-1]=parse_expr(F[i-1])
for inj in injections:
F[i-1]=F[i-1].subs(parse_expr(inj),0)
F=Matrix(F)
#print(F)
##### Define state vector X
X=[]
X=L[0][2:]
for i in range(len(X)):
X[i]=parse_expr(X[i])
X=Matrix(X)
#print(X)
Xo=X.copy()
##### Define stoichiometry matrix SM
SM=[]
for i in range(len(L)-1):
SM.append(L[i+1][2:])
for i in range(len(SM)):
for j in range(len(SM[0])):
if (SM[i][j]==''):
SM[i][j]='0'
SM[i][j]=parse_expr(SM[i][j])
SM=Matrix(SM)
SM=SM.T
SMorig=SM.copy()
##### Check for zero fluxes
icounter=0
jcounter=0
for i in range(len(F)):
if(F[i-icounter]==0):
F.row_del(i-icounter)
for j in range(len(SM.col(i-icounter))):
if(SM[j-jcounter,i-icounter]!=0):
#UsedRC.append(X[j-jcounter])
X.row_del(j-jcounter)
SM.row_del(j-jcounter)
SMorig.row_del(j-jcounter)
jcounter=jcounter+1
SM.col_del(i-icounter)
SMorig.col_del(i-icounter)
icounter=icounter+1
print('Removed '+str(icounter)+' fluxes that are a priori zero!')
nrspecies=nrspecies-icounter
#printmatrix(SM)
#print(F)
#print(X)
#print(UsedRC)
#####Check if some species are zero and remove them from the system
zeroStates=[]
NegRows=checkNegRows(SM)
PosRows=checkPosRows(SM)
#print(PosRows)
#print(NegRows)
while((NegRows!=[]) | (PosRows!=[])):
#print(PosRows)
#print(NegRows)
if(NegRows!=[]):
row=NegRows[0]
zeroStates.append(X[row])
counter=0
for i in range(len(F)):
if(F[i-counter].subs(X[row],1)!=F[i-counter] and F[i-counter].subs(X[row],0)==0):
F.row_del(i-counter)
SM.col_del(i-counter)
counter=counter+1
else:
if(F[i-counter].subs(X[row],1)!=F[i-counter] and F[i-counter].subs(X[row],0)!=0):
F[i-counter]=F[i-counter].subs(X[row],0)
X.row_del(row)
SM.row_del(row)
else:
row=PosRows[0]
zeroFluxes=[]
for j in range(len(SM.row(row))):
if(SM.row(row)[j]!=0):
zeroFluxes.append(F[j])
for k in zeroFluxes:
StateinFlux=[]
for state in X:
if(k.subs(state,1)!=k):
StateinFlux.append(state)
if(len(StateinFlux)==1):
zeroStates.append(StateinFlux[0])
row=list(X).index(StateinFlux[0])
counter=0
for i in range(len(F)):
if(F[i-counter].subs(X[row],1)!=F[i-counter]):
if(F[i-counter].subs(X[row],0)==0):
F.row_del(i-counter)
SM.col_del(i-counter)
else:
F[i-counter]=F[i-counter].subs(X[row],0)
counter=counter+1
#printmatrix(SM)
NegRows=checkNegRows(SM)
PosRows=checkPosRows(SM)
#printmatrix(SM)
#print(F)
#print(X)
nrspecies=nrspecies-len(zeroStates)
if(nrspecies==0):
print('All states are zero!')
return(0)
else:
if(zeroStates==[]):
print('No states found that are a priori zero!')
else:
print('These states are zero:')
for state in zeroStates:
print('\t'+str(state))
nrspecies=nrspecies+len(zeroStates)
##### Identify linearities, bilinearities and multilinearities
Xsquared=[]
for i in range(len(X)):
Xsquared.append(X[i]*X[i])
Xsquared=Matrix(Xsquared)
BLList=[]
MLList=[]
for i in range(len(SM*F)):
LHS=str(expand((SM*F)[i]))
LHS=LHS.replace(' ','')
LHS=LHS.replace('-','+')
LHS=LHS.replace('**2','tothepowerof2')
LHS=LHS.replace('**3','tothepowerof3')
exprList=LHS.split('+')
for expr in exprList:
VarList=expr.split('*')
counter=0
factors=[]
for j in range(len(X)):
anz=0
if(str(X[j]) in VarList):
anz=1
factors.append(X[j])
if((str(X[j])+'tothepowerof2') in VarList):
anz=2
factors.append(X[j])
factors.append(X[j])
if((str(X[j])+'tothepowerof3') in VarList):
anz=3
factors.append(X[j])
factors.append(X[j])
factors.append(X[j])
counter=counter+anz
if(counter==2):
string=''
for l in range(len(factors)):
if(l==len(factors)-1):
string=string+str(factors[l])
else:
string=string+str(factors[l])+'*'
if(not(string in BLList)):
BLList.append(string)
if(counter>2):
string=''
for l in range(len(factors)):
if(l==len(factors)-1):
string=string+str(factors[l])
else:
string=string+str(factors[l])+'*'
if(not(string in MLList)):
MLList.append(string)
COPlusLIPlusBL=[]
for i in range(len(SM*F)):
COPlusLIPlusBL.append((SM*F)[i])
for j in range(len(MLList)):
ToSubs=expand((SM*F)[i]).coeff(MLList[j])
COPlusLIPlusBL[i]=expand(COPlusLIPlusBL[i]-ToSubs*parse_expr(MLList[j]))
COPlusLI=[]
for i in range(len(COPlusLIPlusBL)):
COPlusLI.append(COPlusLIPlusBL[i])
for j in range(len(BLList)):
ToSubs=expand((COPlusLIPlusBL)[i]).coeff(BLList[j])
COPlusLI[i]=expand(COPlusLI[i]-ToSubs*parse_expr(BLList[j]))
##### C*X contains linear terms
C=zeros(len(COPlusLI),len(X))
for i in range(len(COPlusLI)):
for j in range(len(X)):
C[i*len(X)+j]=expand((COPlusLI)[i]).coeff(X[j])
##### ML contains multilinearities
ML=expand(Matrix(SM*F)-Matrix(COPlusLIPlusBL))
##### BL contains bilinearities
BL=expand(Matrix(COPlusLIPlusBL)-Matrix(COPlusLI))
#### CM is coefficient matrix of linearities
CM=C
#####CMBL gives coefficient matrix of bilinearities
CMBL=[]
if(BLList!=[]):
for i in range(len(BLList)):
CVBL=[]
for k in range(len(BL)):
CVBL.append(BL[k].coeff(BLList[i]))
CMBL.append(CVBL)
else:
CVBL=[]
for k in range(len(BL)):
CVBL.append(0)
CMBL.append(CVBL)
CMBL=Matrix(CMBL).T
#####CMML gives coefficient matrix of multilinearities
#####Summarize multilinearities and bilinearities
if(MLList!=[]):
CMML=[]
for i in range(len(MLList)):
CVML=[]
for k in range(len(ML)):
CVML.append(expand(ML[k]).coeff(MLList[i]))
CMML.append(CVML)
CMML=Matrix(CMML).T
BLList=BLList+MLList
CMBL=Matrix(concatenate((CMBL,CMML),axis=1))
for i in range(len(BLList)):
BLList[i]=parse_expr(BLList[i])
if(BLList!=[]):
CMbig=Matrix(concatenate((CM,CMBL),axis=1))
else:
CMbig=Matrix(CM)
#### Save ODE equations for testing solutions at the end
print('Rank of SM is '+str(SM.rank()) + '!')
SMorig=SM.copy()
ODE=SMorig*F
#### Get Flux Parameters
fluxpars=[]
for flux in F:
if(flux.args!=()):
foundFluxpar=False
for el in flux.args:
if(not foundFluxpar and el not in X and not is_number(str(el))):
if(flux.subs(el, 0)==0):
fluxpars.append(el)
foundFluxpar=True
else:
fluxpars.append(flux)
##### Increase Sparsity of stoichiometry matrix SM
print('Sparsify stoichiometry matrix with sparsify-level '+str(sparsifyLevel)+'!')
newSM=(Sparsify(SM.T, level=sparsifyLevel, sparseIter=1)).T
if(newSM!=SM):
print("Sparsified!")
SM=newSM
#### Find conserved quantities
#printmatrix(CMbig)
#print(X)
if(givenCQs==[]):
print('\nFinding conserved quantities ...')
LCLs, rowsToDel=FindLCL(CMbig.transpose(), X)
else:
print('\nI took the given conserved quantities!')
LCLs=givenCQs
if(LCLs!=[]):
print(LCLs)
else:
print('System has no conserved quantities!')
#### Define graph structure
print('\nDefine graph structure ...\n')
SSgraph=DetermineGraphStructure(SM, F, X, neglect)
#printgraph(SSgraph)
#print(fluxpars)
#### Check for Cycles
cycle=FindCycle(SSgraph, X)
#### Remove cycles step by step
gesnew=0
eqOut=[]
while(cycle!=None):
print('Removing cycle '+str(counter))
#printmatrix(SM)
#print(F)
minType, state2Rem, fp2Rem, signChanged = GetBestPair(cycle, SM, fluxpars, X, LCLs, neglect)
#print(cycle)
#print(state2Rem)
#print(fp2Rem)
#print(minType)
if(minType==-1):
print(" The cycle")
print(" "+str(cycle))
print(" cannot be removed. Set more parameters free or enable steady-state expressions with minus signs. The latter is not yet provided by the tool.")
return(0)
if(minType==0):
for LCL in LCLs:
ls=parse_expr(LCL.split(' = ')[0])
if(ls.subs(parse_expr(state2Rem),1)!=ls):
LCL2Rem=LCL
LCLs.remove(LCL2Rem)
index=list(X).index(parse_expr(state2Rem))
eqOut.append(state2Rem+' = '+state2Rem)
print(' '+str(state2Rem)+' --> '+'Done by CQ')
if(minType==1):
index=list(X).index(parse_expr(state2Rem))
eq=(SM*F)[index]
sol=solve(eq, fp2Rem, simplify=False)[0]
eqOut.append(str(fp2Rem)+' = '+str(sol))
print(' '+str(state2Rem)+' --> '+str(fp2Rem))
if(minType==2):
anz, sign=GetDimension(state2Rem, X, SM, getSign=True)
index=list(X).index(parse_expr(state2Rem))
negs, sumnegs, negfps=GetOutfluxes(state2Rem, X, SM, F, fluxpars)
poss, sumposs, posfps=GetInfluxes(state2Rem, X, SM, F, fluxpars)
if(anz==1):
print("Error in Type Determination. Please report this bug!")
return(0)
else:
nenner=1
for j in range(anz):
if(j>0):
nenner=nenner+parse_expr('r_'+state2Rem+'_'+str(j))
trafoList=[]
if((sign=="minus" and not signChanged) or (sign=="plus" and signChanged)):
for j in range(len(negs)):
flux=negs[j]
fp=negfps[j]
prefactor=flux/fp
if(j==0):
trafoList.append(str(fp)+' = ('+str(sumposs)+')*1/('+str(nenner)+')*1/('+str(prefactor)+')')
else:
gesnew=gesnew+1
trafoList.append(str(fp)+' = ('+str(sumposs)+')*'+'r_'+state2Rem+'_'+str(j)+'/('+str(nenner)+')*1/('+str(prefactor)+')')
print(' '+str(state2Rem)+' --> '+str(negfps))
else:
for j in range(len(poss)):
flux=poss[j]
fp=posfps[j]
prefactor=flux/fp
if(j==0):
trafoList.append(str(fp)+' = ('+str(sumnegs)+')*1/('+str(nenner)+')*1/('+str(prefactor)+')')
else:
gesnew=gesnew+1
trafoList.append(str(fp)+' = ('+str(sumnegs)+')*'+'r_'+state2Rem+'_'+str(j)+'/('+str(nenner)+')*1/('+str(prefactor)+')')
print(' '+str(state2Rem)+' --> '+str(posfps))
for eq in trafoList:
eqOut.append(eq)
if(minType==3):
anz, sign=GetDimension(state2Rem, X, SM, getSign=True)
index=list(X).index(parse_expr(state2Rem))
negs, sumnegs, negfps=GetOutfluxes(state2Rem, X, SM, F, fluxpars)
poss, sumposs, posfps=GetInfluxes(state2Rem, X, SM, F, fluxpars)
if(anz==1):
if((sign=="minus" and not signChanged) or (sign=="plus" and signChanged)):
fp2Rem=negfps[0]
flux=negs[0]
else:
fp2Rem=posfps[0]
flux=poss[0]
eq=(SM*F)[index]
sol=solve(eq, fp2Rem, simplify=False)[0]
eqOut.append(str(fp2Rem)+' = '+str(sol))
FsearchFlux = matrix_multiply_elementwise(abs(SM[index,:]),F.T)
colindex=list(FsearchFlux).index(flux)
for row2repl in range(len(SM.col(0))):
if(SM[row2repl,colindex]!=0 and row2repl!=index):
SM=SM.row_insert(row2repl,SM.row(row2repl)-(SM[row2repl,colindex]/SM[index,colindex])*SM.row(index))
SM.row_del(row2repl+1)
else:
nenner=1
for j in range(anz):
if(j>0):
nenner=nenner+parse_expr('r_'+state2Rem+'_'+str(j))
trafoList=[]
if((sign=="minus" and not signChanged) or (sign=="plus" and signChanged)):
for j in range(len(negs)):
flux=negs[j]
fp=negfps[j]
prefactor=flux/fp
if(j==0):
trafoList.append(str(fp)+' = ('+str(sumposs)+')*1/('+str(nenner)+')*1/('+str(prefactor)+')')
else:
gesnew=gesnew+1
trafoList.append(str(fp)+' = ('+str(sumposs)+')*'+'r_'+state2Rem+'_'+str(j)+'/('+str(nenner)+')*1/('+str(prefactor)+')')
FsearchFlux = matrix_multiply_elementwise(abs(SM[index,:]),F.T)
colindex=list(FsearchFlux).index(flux)
for k in range(len(posfps)):
SM=SM.col_insert(len(SM.row(0)),SM.col(colindex))
F=F.row_insert(len(F),Matrix(1,1,[poss[k]/nenner]))
fluxpars.append(posfps[k])
SM.col_del(colindex)
F.row_del(colindex)
fluxpars.__delitem__(colindex)
print(' '+str(state2Rem)+' --> '+str(negfps))
else:
for j in range(len(poss)):
flux=poss[j]
fp=posfps[j]
prefactor=flux/fp
if(j==0):
trafoList.append(str(fp)+' = ('+str(sumnegs)+')*1/('+str(nenner)+')*1/('+str(prefactor)+')')
else:
gesnew=gesnew+1
trafoList.append(str(fp)+' = ('+str(sumnegs)+')*'+'r_'+state2Rem+'_'+str(j)+'/('+str(nenner)+')*1/('+str(prefactor)+')')
FsearchFlux = matrix_multiply_elementwise(abs(SM[index,:]),F.T)
colindex=list(FsearchFlux).index(flux)
for k in range(len(negfps)):
SM=SM.col_insert(len(SM.row(0)),SM.col(colindex))
F=F.row_insert(len(F),Matrix(1,1,[negs[k]/nenner]))
fluxpars.append(negfps[k])
SM.col_del(colindex)
F.row_del(colindex)
fluxpars.__delitem__(colindex)
print(' '+str(state2Rem)+' --> '+str(posfps))
for eq in trafoList:
eqOut.append(eq)
X.row_del(index)
SM.row_del(index)
SSgraph=DetermineGraphStructure(SM, F, X, neglect)
#print(X)
#printgraph(SSgraph)
cycle=FindCycle(SSgraph, X)
counter=counter+1
print('There is no cycle in the system!\n')
#### Solve remaining equations
eqOut.reverse()
print('Solving remaining equations ...\n')
while(SSgraph!={}):
#print(SSgraph)
node=FindNodeToSolve(SSgraph)
#print(node)
index=list(X).index(parse_expr(node))
#print((SM*F)[index])
sol=solve((SM*F)[index],parse_expr(node), simplify=True)
#print(sol)
eqOut.insert(0,node+' = '+str(sol[0]))
for f in range(len(F)):
F[f]=F[f].subs(parse_expr(node), sol[0])
#print(node+' = '+str(sol[0]))
X.row_del(index)
SM.row_del(index)
SSgraph=DetermineGraphStructure(SM, F, X, neglect=[])
#### Test Solution
print('Testing Steady State...\n')
NonSteady=False
#print(eqOut)
#print(ODE)
#print(SM*F)
for i in range(len(ODE)):
expr=parse_expr(str(ODE[i]))
for j in range(len(zeroStates)):
zeroState=zeroStates[j]
expr=expr.subs(zeroState, 0)
#print(len(eqOut))
for j in range(len(eqOut)):
ls, rs = eqOut[-(j+1)].split('=')
#print(ls)
ls=parse_expr(ls)
#print(rs)
rs=parse_expr(rs)
expr=expr.subs(ls, rs)
#print(simplify(expr))
expr=simplify(expr)
#print(expr)
if(expr!=0):
print(' Equation '+str(ODE[i]))
print(' results:'+str(expr))
NonSteady=True
if(NonSteady):
print('Solution is wrong!\n')
else:
print('Solution is correct!\n')
#### Print Equations
print('I obtained the following equations:\n')
if(outputFormat=='M'):
for state in zeroStates:
print('\tinit_'+str(state)+' "0"'+'\n')
eqOutReturn=[]
for i in range(len(eqOut)):
ls, rs = eqOut[i].split('=')
ls=parse_expr(ls)
rs=parse_expr(rs)
for j in range(i,len(eqOut)):
ls2, rs2 = eqOut[j].split('=')
rs2=parse_expr(rs2)
rs2=rs2.subs(ls,rs)
eqOut[j]=str(ls2)+'='+str(rs2)
for state in Xo:
ls=ls.subs(state, parse_expr('init_'+str(state)))
rs=rs.subs(state, parse_expr('init_'+str(state)))
eqOut[i]=str(ls)+' "'+str(rs)+'"'
for i in range(len(eqOut)):
eqOut[i]=eqOut[i].replace('**','^')
for eq in eqOut:
print('\t'+eq+'\n')
eqOutReturn.append(eq)
else:
for state in zeroStates:
print('\t'+str(state)+' = 0'+'\n')
eqOutReturn=[]
for eq in eqOut:
ls, rs = eq.split(' = ')
print('\t'+ls+' = "'+rs+'",'+'\n')
eqOutReturn.append(ls+'='+rs)
print('Number of Species: '+str(nrspecies))
print('Number of Equations: '+str(len(eqOut)+len(zeroStates)))
print('Number of new introduced variables: '+str(gesnew))
return(eqOutReturn)
