演習本にデコンボリューション法が載っていたのだけど、実装までは載ってなかったので、調べたら、論文が見つかった。
ファーマコキネティクス―演習による理解GOTOとIFの組み合わせがwhileなのかforなのか悩むとこが幾つかあったが、pythonで書きなおした。結構、fortranっぽさが残っている気もするが。
#!/usr/bin/env python
def calc_eps():
eps = 1.0
while eps + 1.0 > 1.0: eps = eps/2.0
return eps
def sign(a1,a2):
if a2 >= 0: return abs(a1)
else: return -abs(a1)
def deconv(a,div,b,dose):
n = len(a); m = len(b); l = n + m -1
eps = calc_eps()
u = [0.0 for i in range(l)]
v = [0.0 for i in range(l)]
gamma = [0.0 for i in range(20)]
g = [0.0 for i in range(20)]
a.sort(lambda x,y:cmp(x[1],y[1]))
for II in range(n-1):
x1 = a[II][1] * -1
x2 = a[II+1][1] * -1
qx1 = 0.0
qx2 = 0.0
for i in range(n):
s1 = 1.0
s2 = 1.0
for j in range(n):
if j != i:
s1 = s1*(a[j][1] + x1)
s2 = s2*(a[j][1] + x2)
qx1 = qx1 + a[i][0] * s1
qx2 = qx2 + a[i][0] * s2
x3 = x1
qx3 = qx1
d = x2 -x1
e = d
while(1):
if abs(qx3) < abs(qx2):
x1 = x2; x2 = x3; x3 = x1
qx1 = qx2; qx2 = qx3; qx3 = qx1
tol = 4.0*eps*abs(x2)
xm = 0.5*(x3-x2)
if abs(xm) <= tol or qx2 == 0.0: break
if abs(e) >= tol and abs(qx1) > abs(qx2):
if x1 == x3:
s = qx2/qx1; p = 2.0*xm*s; q = 1.0-s
else:
q = qx1/qx3; r = qx2/qx3; s = qx2/qx1
p = s*(2.0*xm*q*(q-r) - (x2-x1)*(r-1.0))
q = (q-1.0)*(r-1.0)*(s-1.0)
if p > 0.0: q = -q
p = abs(p)
if 2.0*p < 3.0*xm*q - abs(tol*q) and p < abs(0.5*e*q):
e = d
d = p/q
else:
d = xm
e = d
else:
d = xm
e = d
x1 = x2
qx1 =qx2
x2 = x2 + d
if abs(d) <= tol: x2 = x2 - d + sign(tol,xm)
qx2 = 0.0
for i in range(n):
s2 = 1.0
for j in range(n):
if j != i: s2 = s2*(a[j][1] +x2)
qx2 = qx2 + a[i][0] * s2
if qx2*(qx3/abs(qx3)) > 0.0:
x3 = x1
qx3 = qx1
d = x2 - x1
e = d
gamma[II] = x2
s2 = 0.0
for j in range(n):
s1 = 0.0
for k in range(n):
if k != j:
s1 = s1 + 1.0/(gamma[II] + a[k][1])
s2 = s2 + a[j][0]*s1/(gamma[II] + a[j][1])
g[II] = 1.0/s2
ak1 = 0.0
ak2 = 0.0
ak3 = 0.0
for i in range(n):
ak1 = ak1 + a[i][0];
ak2 = ak2 + a[i][0]*a[i][1]
if n > 1 and i != n-1: ak3 = ak3 + g[i]/gamma[i]
ak1 = 1.0/ak1
ak2 = ak1*ak1*ak2
ak3 = ak2 - ak3
ak4 = 100.0*div/dose
uz = 0.0
for i in range(l):
s = 0.0
if i > m-1:
v[i] = -gamma[i-m]
for j in range(m):
s = s + b[j][0]/(gamma[i-m] + b[j][1])
u[i] = ak4*g[i-m]*s/gamma[i-m]
else:
v[i] = b[i][1]
u[i] = ak4*b[i][0]*(ak1 - ak3/b[i][1])
if n != 1:
for j in range(n-1):
s = s + g[j]/(gamma[j]*(gamma[j] + b[i][1]))
u[i] = u[i] - ak4*b[i][0]*s
uz = uz - u[i]
return uz,u,v
if __name__ =='__main__':
print "=== Data set 1 ==="
a = [[1.0427,5.0526],[0.97617,0.97567]]
div = 1.0
b = [[-0.80547,3.6373],[0.80547,0.83033]]
dose = 0.6
print deconv(a,div,b,dose)
print "=== Data set 2 ==="
a = [[1.3377,3.1851],[0.52381,0.61065]]
div = 1.0
b = [[-2.2637,2.0800],[2.2637,1.2513]]
dose = 0.6
print deconv(a,div,b,dose)
print "=== Data set 3 ==="
a = [[1.0308,5.9131],[1.0487,1.0262]]
div = 1.0
b = [[-1.6103,3.3563],[1.6103,1.3917]]
dose = 0.6
print deconv(a,div,b,dose)
print "=== Data set 4 ==="
a = [[1.3377,3.1851],[0.52381,0.61065]]
div = 1.0
b = [[-5.5440,2.2488],[5.5440,1.7521]]
dose = 0.6
print deconv(a,div,b,dose)
Table.1 のテスト計算を実行。論文のデータセット4のa2はタイポでしょう。
=== Data set 1 ===
(103.38116460095375,
[99.756988719460651, -23.218031509886707, -179.92012181052769],
[3.6373000000000002, 0.83033000000000001, 2.9469592648362699])
=== Data set 2 ===
(94.012343334076377,
[212.39909284817011, 2395.320119577972, -2701.7315557602187],
[2.0800000000000001, 1.2513000000000001, 1.3350740721242431])
=== Data set 3 ===
(94.362883301636657,
[-1704.7606134762168, 73.013373899587776, 1537.3843562749923],
[3.3563000000000001, 1.3916999999999999, 3.4906828227939406])
=== Data set 4 ===
(91.15932635164495,
[370.51731307178676, -1111.1884882257646, 649.51184880233291],
[2.2488000000000001, 1.7521, 1.3350740721242431])