from dcprogs.likelihood import eig
from dcprogs.likelihood import find_upper_bound_for_roots, find_lower_bound_for_roots, \
find_root_intervals, brentq, find_roots, QMatrix, DeterminantEq
qmatrix = QMatrix([ [-3050, 50, 3000, 0, 0],
[2./3., -1502./3., 0, 500, 0],
[ 15, 0, -2065, 50, 2000],
[ 0, 15000, 4000, -19000, 0],
[ 0, 0, 10, 0, -10] ], 2)
det = DeterminantEq(qmatrix, 1e-4);
upper_bound = find_upper_bound_for_roots(det);
lower_bound = find_lower_bound_for_roots(det);
get_eigenvalues = lambda s: eig(det.H(s))[0].T
assert all(get_eigenvalues(lower_bound) > lower_bound)
assert all(get_eigenvalues(upper_bound) < upper_bound)
print("Root Determination\n" \
"==================\n\n" \
" * Interval containing roots: {lower}, {upper}\n" \
" * Eigenvalues of H at lower bound: {eiglow}\n" \
" * Eigenvalues of H at upper bound: {eigup}\n" \
.format( lower=lower_bound, upper=upper_bound,
eiglow = get_eigenvalues(lower_bound),
eigup = get_eigenvalues(upper_bound) ))
intervals = find_root_intervals(det, lower_bound, upper_bound)
for (start, end), multiplicity in intervals:
from dcprogs.likelihood import DeterminantEq, QMatrix
# Define parameters.
matrix = [[-3050, 50, 3000, 0, 0], [2. / 3., -1502. / 3., 0, 500, 0],
[15, 0, -2065, 50, 2000], [0, 15000, 4000, -19000, 0],
[0, 0, 10, 0, -10]]
qmatrix = QMatrix(matrix, 2)
tau = 1e-4
det0 = DeterminantEq(qmatrix, 1e-4)
det1 = DeterminantEq(matrix, 2, 1e-4)
print("{0!s}\n\n{1!s}".format(det0, det1))
x = [0, -1, -1e2]
assert all(abs(det0(x) - det1(x)) < 1e-8)
roots = array([-3045.285776037674, -162.92946543451328])
assert all(abs(det0(roots)) < 1e-6 * abs(roots))
transpose = det0.transpose()
roots = array([-17090.192769236815, -2058.0812921673496, -0.24356535498785126],
dtype=internal_dtype)
assert all(abs(transpose(roots)) < 1e-6 * abs(roots))
print(" * H({0}):\n{1}\n".format(0, det0.H(0)))
print(" * H({0}):\n{1}\n".format(-1e2, det0.H(-1e2)))
print(" * d[sI-H(s)]/ds for s={0}:\n{1}\n".format(0, det0.s_derivative(0)))
print(" * d[sI-H(s)]/ds for s={0}:\n{1}\n".format(-1e2,
det0.s_derivative(-1e2)))
