def test_hs28():
# Hock-Schittkowski problem 28 (linearly constrained)
def func(p):
y = np.empty(3)
t1 = p[0] + p[1]
t2 = p[1] + p[2]
y[:] = t1*t1 + t2*t2
return y
def jacf(p):
j = np.empty((3, 3))
t1 = p[0] + p[1]
t2 = p[1] + p[2]
j[:, 0] = 2.0 * t1
j[:, 1] = 2.0 * (t1 + t2)
j[:, 2] = 2.0 * t2
return j
y = np.zeros(3)
p0 = [-4.0, 1.0, 1.0]
pt = [ 0.5, -0.5, 0.5]
A = np.asarray([1.0, 2.0, 3.0])
b = np.asarray([1.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=3)
def test_hs48():
# Hock-Schittkowski problem 48 (linearly constrained)
def func(p):
y = np.empty(5)
t1 = p[0] - 1.0
t2 = p[1] - p[2]
t3 = p[3] - p[4]
y[:] = t1*t1 + t2*t2 + t3*t3
return y
def jacf(p):
j = np.empty((5, 5))
t1 = p[0] - 1.0
t2 = p[1] - p[2]
t3 = p[3] - p[4]
j[:, 0] = 2.0*t1
j[:, 1] = 2.0*t2
j[:, 2] = -2.0*t2
j[:, 3] = 2.0*t3
j[:, 4] = -2.0*t3
return j
y = np.zeros(5, np.float64)
p0 = [3.0, 5.0, -3.0, 2.0, -2.0]
pt = [1.0, 1.0, 1.0, 1.0, 1.0]
A = np.asarray([[1.0, 1.0, 1.0, 1.0, 1.0],
[0.0, 0.0, 1.0, -2.0, -2.0]])
b = np.asarray([5.0, -3.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
def test_hs48():
# Hock-Schittkowski problem 48 (linearly constrained)
def func(p):
y = np.empty(5)
t1 = p[0] - 1.0
t2 = p[1] - p[2]
t3 = p[3] - p[4]
y[:] = t1 * t1 + t2 * t2 + t3 * t3
return y
def jacf(p):
j = np.empty((5, 5))
t1 = p[0] - 1.0
t2 = p[1] - p[2]
t3 = p[3] - p[4]
j[:, 0] = 2.0 * t1
j[:, 1] = 2.0 * t2
j[:, 2] = -2.0 * t2
j[:, 3] = 2.0 * t3
j[:, 4] = -2.0 * t3
return j
y = np.zeros(5, np.float64)
p0 = [3.0, 5.0, -3.0, 2.0, -2.0]
pt = [1.0, 1.0, 1.0, 1.0, 1.0]
A = np.asarray([[1.0, 1.0, 1.0, 1.0, 1.0], [0.0, 0.0, 1.0, -2.0, -2.0]])
b = np.asarray([5.0, -3.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
def test_hs28():
# Hock-Schittkowski problem 28 (linearly constrained)
def func(p):
y = np.empty(3)
t1 = p[0] + p[1]
t2 = p[1] + p[2]
y[:] = t1 * t1 + t2 * t2
return y
def jacf(p):
j = np.empty((3, 3))
t1 = p[0] + p[1]
t2 = p[1] + p[2]
j[:, 0] = 2.0 * t1
j[:, 1] = 2.0 * (t1 + t2)
j[:, 2] = 2.0 * t2
return j
y = np.zeros(3)
p0 = [-4.0, 1.0, 1.0]
pt = [0.5, -0.5, 0.5]
A = np.asarray([1.0, 2.0, 3.0])
b = np.asarray([1.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=5)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=3)
def test_hs51():
# Hock-Schittkowski problem 51 (linearly constrained)
def func(p):
y = np.empty(5)
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
y[:] = t1*t1 + t2*t2 + t3*t3 + t4*t4
return y
def jacf(p):
j = np.empty((5,5))
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
j[:,0] = 2.0*t1
j[:,1] = 2.0*(t2-t1)
j[:,2] = 2.0*t2
j[:,3] = 2.0*t3
j[:,4] = 2.0*t4
return j
y = np.zeros(5, np.float64)
p0 = [2.5, 0.5, 2.0, -1.0, 0.5]
pt = [1.0, 1.0, 1.0, 1.0, 1.0]
A = np.asarray([[1.0, 3.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 1.0, -2.0],
[0.0, 1.0, 0.0, 0.0, -1.0]])
b = np.asarray([4.0, 0.0, 0.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=3)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=3)
def test_bt3():
# Boggs-Tolle problem 3 (linearly constrained)
def func(p):
y = np.empty(5)
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
y[:] = t1*t1 + t2*t2 + t3*t3 + t4*t4
return y
def jacf(p):
j = np.empty((5, 5))
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
j[:, 0] = 2.0 * t1
j[:, 1] = 2.0 * (t2 - t1)
j[:, 2] = 2.0 * t2
j[:, 3] = 2.0 * t3
j[:, 4] = 2.0 * t4
return j
y = np.zeros(5)
p0 = [2.0, 2.0, 2.0, 2.0, 2.0]
pt = [-0.76744, 0.25581, 0.62791, -0.11628, 0.25581]
A = np.asarray([[1.0, 3.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 1.0, -2.0],
[0.0, 1.0, 0.0, 0.0, -1.0]])
b = np.asarray([0.0, 0.0, 0.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
def test_hs51():
# Hock-Schittkowski problem 51 (linearly constrained)
def func(p):
y = np.empty(5)
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
y[:] = t1 * t1 + t2 * t2 + t3 * t3 + t4 * t4
return y
def jacf(p):
j = np.empty((5, 5))
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
j[:, 0] = 2.0 * t1
j[:, 1] = 2.0 * (t2 - t1)
j[:, 2] = 2.0 * t2
j[:, 3] = 2.0 * t3
j[:, 4] = 2.0 * t4
return j
y = np.zeros(5, np.float64)
p0 = [2.5, 0.5, 2.0, -1.0, 0.5]
pt = [1.0, 1.0, 1.0, 1.0, 1.0]
A = np.asarray([[1.0, 3.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 1.0, -2.0],
[0.0, 1.0, 0.0, 0.0, -1.0]])
b = np.asarray([4.0, 0.0, 0.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=3)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=3)
def test_bt3():
# Boggs-Tolle problem 3 (linearly constrained)
def func(p):
y = np.empty(5)
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
y[:] = t1 * t1 + t2 * t2 + t3 * t3 + t4 * t4
return y
def jacf(p):
j = np.empty((5, 5))
t1 = p[0] - p[1]
t2 = p[1] + p[2] - 2.0
t3 = p[3] - 1.0
t4 = p[4] - 1.0
j[:, 0] = 2.0 * t1
j[:, 1] = 2.0 * (t2 - t1)
j[:, 2] = 2.0 * t2
j[:, 3] = 2.0 * t3
j[:, 4] = 2.0 * t4
return j
y = np.zeros(5)
p0 = [2.0, 2.0, 2.0, 2.0, 2.0]
pt = [-0.76744, 0.25581, 0.62791, -0.11628, 0.25581]
A = np.asarray([[1.0, 3.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 1.0, -2.0],
[0.0, 1.0, 0.0, 0.0, -1.0]])
b = np.asarray([0.0, 0.0, 0.0])
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), jacf=jacf, **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
p, pcov, info = levmar.levmar_lec(func, p0, y, (A, b), cdiff=True, **OPTS)
assert_array_almost_equal(p, pt, decimal=4)
