def test_integral_3D():
from math import sin, cos, exp, log, pi, e
from ostap.math.integral import genzmalik3, integral3
funcs = [
(lambda x, y, z: x * x + y * abs(y), -1, 2, -1, 2, -1, 2, 48),
(lambda x, y, z: x * x + y * abs(y) + z * z * cos(z), -1, 2, -1, 2, -1,
2, 51.53827020952059001502),
(lambda x, y, z: x * exp(x) + sin(y) * abs(y) + z * z * exp(z), -1, 2,
-1, 2, -1, 2, 202.53557154832049036486),
]
for entry in funcs:
v1 = genzmalik3(*entry[:7], err=True)
v2 = integral3(*entry[:7], err=True)
vv = entry[-1]
print vv, '%.20f' % v2.value()
logger.info('%20s: I %-20s %-20s %-20s ' %
(entry[0], v1, v2, vv))
logger.info('%20s: Delta %-20s %-20s' %
(entry[0], v1 - vv, v2 - vv))
logger.info('%20s: Delta/I %-20s %-20s' % (entry[0], (v1 - vv) / vv,
(v2 - vv) / vv))
logger.info('%20s: Delta/E %-20s %-20s' % (entry[0],
(v1 - vv) / v1.error(),
(v2 - vv) / v2.error()))
def test_models():
xmin = 0
xmax = 2
ymin = xmin
ymax = xmax
zmin = xmin
zmax = xmax
funcs = [
Ostap.Math.Bernstein3D(2, 2, 2, xmin, xmax, ymin, ymax, zmin, zmax),
Ostap.Math.Bernstein3DSym(2, xmin, xmax),
Ostap.Math.Bernstein3DMix(2, 2, xmin, xmax, zmin, zmax),
Ostap.Math.Positive3D(2, 2, 2, xmin, xmax, ymin, ymax, zmin, zmax),
Ostap.Math.Positive3DSym(2, xmin, xmax),
Ostap.Math.Positive3DMix(2, 2, xmin, xmax, zmin, zmax),
]
cnt1 = SE()
cnt2 = SE()
cnt3 = SE()
cnt4 = SE()
cnt5 = SE()
cnt6 = SE()
cnt7 = SE()
for f in funcs:
## print f.xmin() , f.xmax() , f.ymin() , f.ymax(), type(f)
for i in range(f.npars()):
f.setPar(i, random.uniform(1, 5))
for i in range(0, 100):
if 0 == i:
x1, x2, y1, y2, z1, z2 = xmin, xmax, ymin, ymax, zmin, zmax
else:
x1 = random.uniform(xmin, xmax / 2)
x2 = random.uniform(x1, xmax)
y1 = random.uniform(ymin, ymax / 2)
y2 = random.uniform(y1, ymax)
z1 = random.uniform(zmin, zmax / 2)
z2 = random.uniform(z1, zmax)
for f in funcs:
i1 = f.integral(x1, x2, y1, y2, z1, z2)
i2 = integral3(f, x1, x2, y1, y2, z1, z2)
r1 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r1
) < 1.e-5, 'I3:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f,%.2f,%.2f) %s' % (
r1, x1, x2, y1, y2, z1, z2, type(f))
cnt1 += r1
xm = 0.5 * (x1 + x2)
ym = 0.5 * (y1 + y2)
zm = 0.5 * (z1 + z2)
i1 = f.integrateX(ym, zm, x1, x2)
IX = Integrate3D_X(f, x1, x2)
i2 = IX(ym, zm)
r2 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r2
) < 1.e-5, 'IX:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f) %s' % (
r2, x1, x2, ym, zm, type(f))
cnt2 += r2
i1 = f.integrateY(xm, zm, y1, y2)
IY = Integrate3D_Y(f, y1, y2)
i2 = IY(xm, zm)
r3 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r3
) < 1.e-5, 'IY:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f) %s' % (
r2, xm, y1, y2, zm, type(f))
cnt3 += r3
i1 = f.integrateZ(xm, ym, z1, z2)
IZ = Integrate3D_Z(f, z1, z2)
i2 = IZ(xm, ym)
r4 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r4
) < 1.e-5, 'IY:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f) %s' % (
r2, xm, ym, z1, z2, type(f))
cnt4 += r4
i1 = f.integrateXY(zm, x1, x2, y1, y2)
I5 = Integrate3D_XY(f, x1, x2, y1, y2)
i2 = I5(zm)
r5 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r5
) < 1.e-5, 'I5:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f,%.2f) %s' % (
r2, x1, x2, y1, y2, zm, type(f))
cnt5 += r5
i1 = f.integrateXZ(ym, x1, x2, z1, z2)
I6 = Integrate3D_XZ(f, x1, x2, z1, z2)
i2 = I6(ym)
r6 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r6
) < 1.e-5, 'I6:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f,%.2f) %s' % (
r2, x1, x2, ym, z1, z2, type(f))
cnt6 += r6
i1 = f.integrateYZ(xm, y1, y2, z1, z2)
I7 = Integrate3D_YZ(f, y1, y2, z1, z2)
i2 = I7(xm)
r7 = (i1 - i2) / (abs(i1) + abs(i2))
assert abs(
r7
) < 1.e-5, 'I7:ERROR: difference is too large: %s (%.2f,%.2f,%.2f,%.2f,%.2f) %s' % (
r2, xm, y1, y2, z1, z2, type(f))
cnt7 += r7
print 'COUNTER(I3):', cnt1
print 'COUNTER(IX):', cnt2
print 'COUNTER(IY):', cnt3
print 'COUNTER(IZ):', cnt4
print 'COUNTER(I5):', cnt5
print 'COUNTER(I6):', cnt6
print 'COUNTER(I7):', cnt7