def get_fixation_unconstrained_kb_fquad(
S, d, log_kb, x, w, codon_neighbor_mask):
"""
This uses the Kacser and Burns effect instead of the sign function.
"""
#TODO: possibly use a mirror symmetry to double the speed
soft_sign_S = algopy.tanh(algopy.exp(log_kb)*S)
D = d * soft_sign_S
H = algopy.zeros_like(S)
for i in range(H.shape[0]):
for j in range(H.shape[1]):
if codon_neighbor_mask[i, j]:
H[i, j] = 1. / kimrecessive.denom_fixed_quad(
0.5*S[i, j], D[i, j], x, w)
return H
def get_fixation_unconstrained_kb_fquad(
S, d, log_kb, x, w, codon_neighbor_mask):
"""
This uses the Kacser and Burns effect instead of the sign function.
"""
#TODO: possibly use a mirror symmetry to double the speed
soft_sign_S = algopy.tanh(algopy.exp(log_kb)*S)
D = d * soft_sign_S
H = algopy.zeros_like(S)
for i in range(H.shape[0]):
for j in range(H.shape[1]):
if codon_neighbor_mask[i, j]:
H[i, j] = 1. / kimrecessive.denom_fixed_quad(
0.5*S[i, j], D[i, j], x, w)
return H
def get_fixation_unconstrained_fquad(S, d, x, w, codon_neighbor_mask):
"""
In this function name, fquad means "fixed quadrature."
The S ndarray with ndim=2 depends on free parameters.
The d parameter is itself a free parameter.
So both of those things are algopy objects carrying Taylor information.
On the other hand, x and w are precomputed ndim=1 ndarrays
which are not carrying around extra Taylor information.
@param S: array of selection differences
@param d: parameter that controls dominance vs. recessivity
@param x: precomputed roots for quadrature
@param w: precomputed weights for quadrature
@param codon_neighbor_mask: only compute entries neighboring pairs
"""
#TODO: possibly use a mirror symmetry to double the speed
sign_S = algopy.sign(S)
D = d * sign_S
H = algopy.zeros_like(S)
for i in range(H.shape[0]):
for j in range(H.shape[1]):
if codon_neighbor_mask[i, j]:
H[i, j] = 1. / kimrecessive.denom_fixed_quad(
0.5*S[i, j], D[i, j], x, w)
return H
def get_fixation_unconstrained_fquad(S, d, x, w, codon_neighbor_mask):
"""
In this function name, fquad means "fixed quadrature."
The S ndarray with ndim=2 depends on free parameters.
The d parameter is itself a free parameter.
So both of those things are algopy objects carrying Taylor information.
On the other hand, x and w are precomputed ndim=1 ndarrays
which are not carrying around extra Taylor information.
@param S: array of selection differences
@param d: parameter that controls dominance vs. recessivity
@param x: precomputed roots for quadrature
@param w: precomputed weights for quadrature
@param codon_neighbor_mask: only compute entries of neighboring codon pairs
"""
#TODO: possibly use a mirror symmetry to double the speed
sign_S = algopy.sign(S)
D = d * sign_S
H = algopy.zeros_like(S)
for i in range(H.shape[0]):
for j in range(H.shape[1]):
if codon_neighbor_mask[i, j]:
H[i, j] = 1. / kimrecessive.denom_fixed_quad(
0.5*S[i, j], D[i, j], x, w)
return H
def do_integration_demo():
N = 101
#d = np.linspace(-5, 5, N) / 10000.
#c = np.linspace(-100, 100, N) / 10.
#d = np.linspace(-5, 5, N) / 3.
#c = np.linspace(-100, 100, N) / 3.
d = np.linspace(-5, 5, N)
c = np.linspace(-100, 100, N)
#d = np.linspace(-1, 1, N) * 0.25
#c = np.linspace(-1, 1, N) * 0.02
#d = np.linspace(-3, 3, N) / 10.
#c = np.linspace(-30, 30, N) / 10.
#d = np.linspace(-3, 3, N) / 10000.
#c = np.linspace(-30, 30, N) / 10000.
#d = np.linspace(-3, 3, N)
#c = np.linspace(-30, 30, N)
#d = np.linspace(-4, 4, N)
#c = np.linspace(-40, 40, N)
#c = np.linspace(-20, 20, N)
#d = np.linspace(-.2, .2, N)
#c = np.linspace(-100, 100, N)
#c = np.linspace(-200, 200, N)
#dc, dd = 0.001, 0.001
#c = np.arange(1.-0.05, 1.+0.05, dc)
#d = np.arange(1.-0.05, 1.+0.05, dd)
##dc, dd = 0.005, 0.005
##c = np.arange(0, 0.3, dc)
##d = np.arange(-0.2, 0.2, dd)
"""
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_a(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
"""
"""
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_b(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
"""
"""
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_c(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
"""
"""
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_d(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
"""
"""
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_e1(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_e2(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_e3(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_e4(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
Z = np.zeros((len(d), len(c)))
for j, dj in enumerate(d):
for i, ci in enumerate(c):
Z[j, i] = get_relative_error_e6(ci, dj)
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()
"""
Z = np.zeros((len(d), len(c)))
W = np.zeros((len(d), len(c)))
quad_x, quad_w = kimrecessive.precompute_quadrature(0, 1, 101)
for j, dj in enumerate(d):
for i, ci in enumerate(c):
x = kimrecessive.denom_quad(ci, dj)
#y = kimrecessive.denom_poly_b(ci, dj)
#y = kimengine.denom_poly(ci, dj)
#y = kimrecessive.denom_hyperu_b(ci, dj)
#y = kimrecessive.denom_erfcx_b(ci, dj)
y = kimrecessive.denom_fixed_quad(ci, dj, quad_x, quad_w)
#y = kimrecessive.denom_combo_b(ci, dj)
w = abs(y - x) / abs(x)
W[j, i] = w
Z[j, i] = refilter(w)
print numpy.max(W)
import matplotlib.pyplot as plt
fig = plt.figure()
im = plt.imshow(Z, cmap=plt.cm.jet)
plt.show()