switching to high quality piper tts and added label translations

2026-01-29 23:48:19 +01:00
commit d80c619df9
3934 changed files with 1451600 additions and 0 deletions
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+"""
+
+Routines for computing eigenvectors with DomainMatrix.
+
+"""
+from sympy.core.symbol import Dummy
+
+from ..agca.extensions import FiniteExtension
+from ..factortools import dup_factor_list
+from ..polyroots import roots
+from ..polytools import Poly
+from ..rootoftools import CRootOf
+
+from .domainmatrix import DomainMatrix
+
+
+def dom_eigenvects(A, l=Dummy('lambda')):
+    charpoly = A.charpoly()
+    rows, cols = A.shape
+    domain = A.domain
+    _, factors = dup_factor_list(charpoly, domain)
+
+    rational_eigenvects = []
+    algebraic_eigenvects = []
+    for base, exp in factors:
+        if len(base) == 2:
+            field = domain
+            eigenval = -base[1] / base[0]
+
+            EE_items = [
+                [eigenval if i == j else field.zero for j in range(cols)]
+                for i in range(rows)]
+            EE = DomainMatrix(EE_items, (rows, cols), field)
+
+            basis = (A - EE).nullspace(divide_last=True)
+            rational_eigenvects.append((field, eigenval, exp, basis))
+        else:
+            minpoly = Poly.from_list(base, l, domain=domain)
+            field = FiniteExtension(minpoly)
+            eigenval = field(l)
+
+            AA_items = [
+                [Poly.from_list([item], l, domain=domain).rep for item in row]
+                for row in A.rep.to_ddm()]
+            AA_items = [[field(item) for item in row] for row in AA_items]
+            AA = DomainMatrix(AA_items, (rows, cols), field)
+            EE_items = [
+                [eigenval if i == j else field.zero for j in range(cols)]
+                for i in range(rows)]
+            EE = DomainMatrix(EE_items, (rows, cols), field)
+
+            basis = (AA - EE).nullspace(divide_last=True)
+            algebraic_eigenvects.append((field, minpoly, exp, basis))
+
+    return rational_eigenvects, algebraic_eigenvects
+
+
+def dom_eigenvects_to_sympy(
+    rational_eigenvects, algebraic_eigenvects,
+    Matrix, **kwargs
+):
+    result = []
+
+    for field, eigenvalue, multiplicity, eigenvects in rational_eigenvects:
+        eigenvects = eigenvects.rep.to_ddm()
+        eigenvalue = field.to_sympy(eigenvalue)
+        new_eigenvects = [
+            Matrix([field.to_sympy(x) for x in vect])
+            for vect in eigenvects]
+        result.append((eigenvalue, multiplicity, new_eigenvects))
+
+    for field, minpoly, multiplicity, eigenvects in algebraic_eigenvects:
+        eigenvects = eigenvects.rep.to_ddm()
+        l = minpoly.gens[0]
+
+        eigenvects = [[field.to_sympy(x) for x in vect] for vect in eigenvects]
+
+        degree = minpoly.degree()
+        minpoly = minpoly.as_expr()
+        eigenvals = roots(minpoly, l, **kwargs)
+        if len(eigenvals) != degree:
+            eigenvals = [CRootOf(minpoly, l, idx) for idx in range(degree)]
+
+        for eigenvalue in eigenvals:
+            new_eigenvects = [
+                Matrix([x.subs(l, eigenvalue) for x in vect])
+                for vect in eigenvects]
+            result.append((eigenvalue, multiplicity, new_eigenvects))
+
+    return result