91 lines
2.9 KiB
Python
91 lines
2.9 KiB
Python
"""
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Routines for computing eigenvectors with DomainMatrix.
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"""
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from sympy.core.symbol import Dummy
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from ..agca.extensions import FiniteExtension
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from ..factortools import dup_factor_list
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from ..polyroots import roots
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from ..polytools import Poly
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from ..rootoftools import CRootOf
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from .domainmatrix import DomainMatrix
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def dom_eigenvects(A, l=Dummy('lambda')):
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charpoly = A.charpoly()
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rows, cols = A.shape
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domain = A.domain
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_, factors = dup_factor_list(charpoly, domain)
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rational_eigenvects = []
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algebraic_eigenvects = []
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for base, exp in factors:
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if len(base) == 2:
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field = domain
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eigenval = -base[1] / base[0]
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EE_items = [
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[eigenval if i == j else field.zero for j in range(cols)]
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for i in range(rows)]
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EE = DomainMatrix(EE_items, (rows, cols), field)
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basis = (A - EE).nullspace()
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rational_eigenvects.append((field, eigenval, exp, basis))
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else:
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minpoly = Poly.from_list(base, l, domain=domain)
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field = FiniteExtension(minpoly)
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eigenval = field(l)
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AA_items = [
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[Poly.from_list([item], l, domain=domain).rep for item in row]
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for row in A.rep.to_ddm()]
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AA_items = [[field(item) for item in row] for row in AA_items]
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AA = DomainMatrix(AA_items, (rows, cols), field)
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EE_items = [
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[eigenval if i == j else field.zero for j in range(cols)]
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for i in range(rows)]
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EE = DomainMatrix(EE_items, (rows, cols), field)
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basis = (AA - EE).nullspace()
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algebraic_eigenvects.append((field, minpoly, exp, basis))
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return rational_eigenvects, algebraic_eigenvects
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def dom_eigenvects_to_sympy(
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rational_eigenvects, algebraic_eigenvects,
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Matrix, **kwargs
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):
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result = []
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for field, eigenvalue, multiplicity, eigenvects in rational_eigenvects:
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eigenvects = eigenvects.rep.to_ddm()
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eigenvalue = field.to_sympy(eigenvalue)
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new_eigenvects = [
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Matrix([field.to_sympy(x) for x in vect])
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for vect in eigenvects]
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result.append((eigenvalue, multiplicity, new_eigenvects))
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for field, minpoly, multiplicity, eigenvects in algebraic_eigenvects:
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eigenvects = eigenvects.rep.to_ddm()
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l = minpoly.gens[0]
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eigenvects = [[field.to_sympy(x) for x in vect] for vect in eigenvects]
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degree = minpoly.degree()
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minpoly = minpoly.as_expr()
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eigenvals = roots(minpoly, l, **kwargs)
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if len(eigenvals) != degree:
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eigenvals = [CRootOf(minpoly, l, idx) for idx in range(degree)]
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for eigenvalue in eigenvals:
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new_eigenvects = [
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Matrix([x.subs(l, eigenvalue) for x in vect])
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for vect in eigenvects]
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result.append((eigenvalue, multiplicity, new_eigenvects))
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return result
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