From bb15ced14472cdc2b2f81afd98a0f4aa16ab0999 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Mon, 21 Jan 2019 13:00:06 +0100 Subject: [PATCH] Advanced the new implementation of diff_to_diffalg - The computation of the vector v is still needed. --- ajpastor/dd_functions/toDiffAlgebraic.py | 137 +++++++++++++++++---- releases/diff_defined_functions__0.6.zip | Bin 129370 -> 130371 bytes ...f_defined_functions__0.6__19.01.21_13:00:05.zip | Bin 0 -> 130371 bytes 3 files changed, 113 insertions(+), 24 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__19.01.21_13:00:05.zip diff --git a/ajpastor/dd_functions/toDiffAlgebraic.py b/ajpastor/dd_functions/toDiffAlgebraic.py index cf44b8b..3420a99 100644 --- a/ajpastor/dd_functions/toDiffAlgebraic.py +++ b/ajpastor/dd_functions/toDiffAlgebraic.py @@ -191,7 +191,7 @@ def diffalg_reduction(poly, _infinite=False, _debug=False): ## Step 2: simplification of coefficients __dprint("-- Starting step 2", _debug); - poset, relation = __simplify_coefficients(R, coeffs, l_of_derivatives, _debug); + poset, relations = __simplify_coefficients(R, coeffs, l_of_derivatives, _debug); maximal_elements = poset.maximal_elements(); ## Detecting case: all coefficients are already simpler @@ -205,23 +205,23 @@ def diffalg_reduction(poly, _infinite=False, _debug=False): ## Step 3: simplification with the derivatives __dprint("-- Starting step 3", _debug); - drelation = __simplify_derivatives(l_of_derivatives, _debug); + drelations = __simplify_derivatives(l_of_derivatives, _debug); ## Building the vector of final generators gens = []; if(-1 in poset): gens = [1]; - gens = sum([l_of_derivatives[:drelation[i]] for i in range(len(coeffs))], gens); + gens = sum([l_of_derivatives[i][:drelations[i][0]] for i in range(len(coeffs))], gens); S = len(gens); __dprint("Resulting vector of generators: %s" %gens, _debug); ## Step 4: build the derivation matrix __dprint("-- Starting step 4", _debug); - C = __build_derivation_matrix(coeffs, drelation, _debug); + C = __build_derivation_matrix(gens, coeffs, drelations, _debug); ## Step 5: build the vector v __dprint("-- Starting step 5", _debug); - v = __build_vector(ocoeffs, monomials, poset, relation, drelation, _debug); + v = __build_vector(ocoeffs, monomials, poset, relations, drelations, gens, _debug); ## Step 6: build the square matrix M = (v, v',...) __dprint("-- Starting step 6", _debug); @@ -270,7 +270,7 @@ def __check_input(poly, _debug=False): return (parent, poly, dR); -def __simplify_coefficients(R, coeffs, derivatives, _debug=False): +def __simplify_coefficients(base, coeffs, derivatives, _debug=False): ''' Method that get the relations for the coefficients within their derivatives. The list 'coeffs' is the list to simplify and ;derivatives' is a list of lists with the derivatives of each element of 'coeffs' that we will consider. @@ -290,7 +290,7 @@ def __simplify_coefficients(R, coeffs, derivatives, _debug=False): # Checking the simplest cases (coeff[i] in R) for i in range(n): - if(coeffs[i] in R): + if(coeffs[i] in base): if((-1) not in E): E += [-1]; R += [(i,-1)]; @@ -349,11 +349,14 @@ def __find_relation(g,df, _debug=False): It returns a tuple (k,res) where: - k: the first index which we found a relation - res: the relation (see __find_linear_relation to see how such relation is expressed). + + Then the following statement is always True: + g == df[k]*res[0] + res[1] ''' - for k in range(len(derivatives)): + for k in range(len(df)): res = __find_linear_relation(df[k], g); if(not (res is None)): - __dprint("Found relation:\n\t(%s) == [%s]*(%s) + [%s]" %(repr(g),repr(res[0]), repr(res[1]), repr(df[k]), _debug); + __dprint("Found relation:\n\t(%s) == [%s]*(%s) + [%s]" %(repr(g),repr(res[0]), repr(df[k]), repr(res[1])), _debug); return (k,res); return None; @@ -367,8 +370,9 @@ def __find_linear_relation(f,g): raise TypeError("find_linear_relation: The functions are not DDFunctions"); try: - of = 1; while(f.getSequenceElement(of) == 0): of += 1; - og = 1; while(g.getSequenceElement(og) == 0): og += 1; + of = 1; og = 1; + while(f.getSequenceElement(of) == 0): of += 1; + while(g.getSequenceElement(og) == 0): og += 1; if(of == og): c = f.getSequenceElement(of)/g.getSequenceElement(og); @@ -387,11 +391,96 @@ def __find_linear_relation(f,g): elif(g.is_constant): return None; -def __build_derivation_matrix(coeffs, drelations, _debug=False): - ## TODO: Implement this - raise NotImplementedError("__build_derivation_matrix: method not implemented"); +def __build_derivation_matrix(gens, coeffs, drelations, _debug=False): + ''' + Method to build a derivation matrix 'C' for the vector of generators 'gen'. + + All the information about the coefficients and their relations are given + by the arguments 'coeffs' (list of basic elements for 'gens') and + 'drelations' (relations between elements in 'coeffs' and the last derivative + on 'gens'). + + It could be that gens[0] == 1. This element must be treated in a specific + way collecting all the relations on 'drelations'. + ''' + __dprint("Building derivation matrix for %s" %gens, _debug); + + rows = []; # Variable for the rows of the matrix M + + constant = (gens[0] == 1); # Flag variable for gens[0] == 1 + coeff_order = []; # Collecting the real order of each coefficient in the vector space + for i in range(len(coeffs)): + if(drelations[i][0] is None): + coeff_order += [coeffs[i].getOrder()]; + else: + coeff_order += [drelations[i][0]]; + coeff_index = [0]; # Variable for the index of coeff[i] in gens + if(constant): coeff_index[0] = 1; + for i in range(1, len(coeffs)): coeff_index += [coeff_index[-1]+coeff_order[i-1]]; + + __dprint("Is there constant: %s" %constant, _debug); + __dprint("Orders: %s\nIndices: %s" %(coeff_order, coeff_index), _debug); + + ## Considering the case that gens[0] == -1 + if(constant): + new_row = [0]; + for i in range(len(coeffs)): + new_row += [0 for j in range(coeff_order[i])]; + if(not (drelations[i][1] is None)): + new_row[-1] = drelations[i][1][1][1]; + rows += [new_row]; + + ## Now we loop through all the coefficients in coeffs + for i in range(len(coeffs)): + com = coeffs[i].equation.companion(); + for j in range(coeff_order[i]): + ## Building the jth row for coeff[i] + new_row = [0 for k in range(coeff_index[i])]; # First columns for the row + + ## Middle columns for the row + new_row += [com[j][k] for k in range(coeff_order[i]-1)]; + if((not (drelations[i][0] is None)) and (drelations[i][1][0] == j)): + new_row += [drelations[i][1][1][0]]; + else: + new_row += [com[j][coeff_order[i]-1]]; + + new_row += [0 for k in range(coeff_index[i]+coeff_order[i], len(gens))]; # Last columns for the row + + ## Adding the resulting row + rows += [new_row]; + + if(_debug): + print "Matrix:"; + for row in rows: + print row; + + return Matrix(rows); + +def __build_vector(coeffs, monomials, poset, relations, drelations, gens, _debug=False): + ''' + This method builds a vector that represent the polynomial generated by + 'coeffs' and 'monomials' using the relations contained in 'poset', 'relations' + and 'drelations' w.r.t. the vector 'gens'. + + The output vector v satisfies: + sum(coeff[i]*monomials[i]) == sum(v[j]*gens[j]) + ''' -def __build_vector(coeffs, monomials, poset, relation, drelation, _debug=False): + ## Getting the minimal chain for each coefficient up to a maximal coefficient + maximal_elements = poset.maximal_elements(); + chains = {i : [el for el in poset.chains() if (len(el) > 0 and el[0] == i and (el[-1] in maximal_elements)] for i in range(len(coeffs))}; + min_chains = []; + for i in range(len(coeffs)): + current = chains[i]; + shortest = current[0]; + for j in range(1,len(current)): + if(len(shortest) > len(current[j])): + shortest = current[j]; + min_chains += [shortest]; + + ## For each coefficient, compute the representation in gens + ## We must follow the shortest chain to a maximal element to know where and + ## how put the coefficients in the final vector. ## TODO: Implement this raise NotImplementedError("__build_vector: method not implemented"); @@ -892,11 +981,11 @@ def __dprint(obj, _debug): #################################################################################################### #### PACKAGE ENVIRONMENT VARIABLES #################################################################################################### -__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg", "inverse_DA", "func_inverse_DA", "guess_DA_DDfinite", "guess_homogeneous_DNfinite", "FaaDiBruno_polynomials", "Exponential_polynomials"]; - +__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "diffalg_reduction", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg", "inverse_DA", "func_inverse_DA", "guess_DA_DDfinite", "guess_homogeneous_DNfinite", "FaaDiBruno_polynomials", "Exponential_polynomials"]; -def simplify_coefficients(R, coeffs, derivatives, _debug=True): - return __simplify_coefficients(R,coeffs,derivatives,_debug); +# Extra functions for debugging +def simplify_coefficients(base, coeffs, derivatives, _debug=True): + return __simplify_coefficients(base,coeffs,derivatives,_debug); def simplify_derivatives(derivatives, _debug=True): return __simplify_derivatives(derivatives, _debug) @@ -907,10 +996,10 @@ def find_relation(g,df, _debug=True): def find_linear_relation(f,g): return __find_linear_relation(g,df); -def build_derivation_matrix(coeffs, drelations, _debug=True): - return __build_derivation_matrix(coeffs, drelations, _debug); +def build_derivation_matrix(gens, coeffs, drelations, _debug=True): + return __build_derivation_matrix(gens, coeffs, drelations, _debug); + +def build_vector(coeffs, monomials, poset, relations, drelations, gens, _debug=True): + return 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