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Solve task 1 in HM2

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This commit is contained in:
Manuel Thalmann 2023-03-08 15:54:06 +01:00
parent 8c8aae635f
commit 97f211fa5e
5 changed files with 171 additions and 61 deletions
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Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 3/Miguel_S3_Aufg1.pdf Normal file
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Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 3/Miguel_S3_Aufg1.py Normal file
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@ -0,0 +1,84 @@
# %%
from IPython.display import display
from sympy import Matrix, symbols
[a, b] = symbols("x_1, x_2")
x0 = Matrix([1.1, 0.9])
print("x0:")
display(x0)
f = Matrix(
[
[20.0 - (18.0 * a) - 2.0 * (b ** 2.0)],
[(-4.0 * b) * (a - (b ** 2.0))]
])
Df = Matrix(
[
[-18.0, -4.0 * b],
[-4.0 * b, (-4.0 * a) + 12.0 * (b ** 2.0)]
])
Df0 = Df.subs(
{
a: x0[0],
b: x0[1]
})
f0 = f.subs(
{
a: x0[0],
b: x0[1]
})
print("Df(x0):")
display(Df0)
print("f(x0):")
display(f0)
print("||f(x0)||_2")
display(f0.norm(2))
d0 = Df0.solve(-f0)
print("d0")
display(d0)
print("||d0||_2")
display(d0.norm(2))
x1 = x0 + d0
print("x1:")
display(x1)
Df1 = Df.subs(
{
a: x1[0],
b: x1[1]
})
f1 = f.subs(
{
a: x1[0],
b: x1[1]
})
print("Df(x1)")
display(Df1)
print("f(x1)")
display(f1)
print("||f(x1)||_2")
display(f1.norm(2))
d1 = Df1.solve(-f1)
print("d1")
display(d1)
print("||d1||_2")
display(d1.norm(2))
x2 = x1 + d1
print("x2")
display(x2)
# %%

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Notes/Semester 4/HM2 - Höhere Mathematik 2/Week 3/Miguel_S3_Aufg1.rnote Normal file
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@ -12,6 +12,7 @@ pexpect = "*"
pandas = "*" pandas = "*"
ipympl = "*" ipympl = "*"
sympy = "*" sympy = "*"
autopep8 = "*"
[dev-packages] [dev-packages]

147
Pipfile.lock generated
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@ -1,7 +1,7 @@
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"requires": { "requires": {
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