Solve task 1 in HM2
This commit is contained in:
parent
8c8aae635f
commit
97f211fa5e
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# %%
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from IPython.display import display
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from sympy import Matrix, symbols
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[a, b] = symbols("x_1, x_2")
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x0 = Matrix([1.1, 0.9])
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print("x0:")
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display(x0)
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f = Matrix(
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[
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[20.0 - (18.0 * a) - 2.0 * (b ** 2.0)],
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[(-4.0 * b) * (a - (b ** 2.0))]
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])
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Df = Matrix(
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[
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[-18.0, -4.0 * b],
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[-4.0 * b, (-4.0 * a) + 12.0 * (b ** 2.0)]
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])
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Df0 = Df.subs(
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{
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a: x0[0],
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b: x0[1]
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})
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f0 = f.subs(
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{
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a: x0[0],
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b: x0[1]
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})
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print("Df(x0):")
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display(Df0)
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print("f(x0):")
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display(f0)
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print("||f(x0)||_2")
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display(f0.norm(2))
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d0 = Df0.solve(-f0)
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print("d0")
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display(d0)
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print("||d0||_2")
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display(d0.norm(2))
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x1 = x0 + d0
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print("x1:")
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display(x1)
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Df1 = Df.subs(
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{
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a: x1[0],
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b: x1[1]
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})
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f1 = f.subs(
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{
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a: x1[0],
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b: x1[1]
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})
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print("Df(x1)")
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display(Df1)
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print("f(x1)")
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display(f1)
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print("||f(x1)||_2")
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display(f1.norm(2))
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d1 = Df1.solve(-f1)
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print("d1")
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display(d1)
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print("||d1||_2")
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display(d1.norm(2))
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x2 = x1 + d1
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print("x2")
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display(x2)
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# %%
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Pipfile
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Pipfile
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@ -12,6 +12,7 @@ pexpect = "*"
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pandas = "*"
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ipympl = "*"
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sympy = "*"
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autopep8 = "*"
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[dev-packages]
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147
Pipfile.lock
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@ -1,7 +1,7 @@
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{
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"_meta": {
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"sha256": "8c86c6849809fd6594aed0bf17bcfecc16e4e0e68b7949900346649d7b23c60a"
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},
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"pipfile-spec": 6,
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"requires": {
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@ -23,6 +23,14 @@
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],
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"version": "==2.2.1"
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},
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|
||||
"version": "==3.1.0"
|
||||
},
|
||||
"prompt-toolkit": {
|
||||
"hashes": [
|
||||
"sha256:6a2948ec427dfcc7c983027b1044b355db6aaa8be374f54ad2015471f7d81c5b"
|
||||
"sha256:23ac5d50538a9a38c8bde05fecb47d0b403ecd0662857a86f886f798563d5b9b",
|
||||
"sha256:45ea77a2f7c60418850331366c81cf6b5b9cf4c7fd34616f733c5427e6abbb1f"
|
||||
],
|
||||
"markers": "python_full_version >= '3.7.0'",
|
||||
"version": "==3.0.37"
|
||||
"version": "==3.0.38"
|
||||
},
|
||||
"psutil": {
|
||||
"hashes": [
|
||||
|
|
@ -598,6 +607,14 @@
|
|||
],
|
||||
"version": "==0.2.2"
|
||||
},
|
||||
"pycodestyle": {
|
||||
"hashes": [
|
||||
"sha256:347187bdb476329d98f695c213d7295a846d1152ff4fe9bacb8a9590b8ee7053",
|
||||
"sha256:8a4eaf0d0495c7395bdab3589ac2db602797d76207242c17d470186815706610"
|
||||
],
|
||||
"markers": "python_version >= '3.6'",
|
||||
"version": "==2.10.0"
|
||||
},
|
||||
"pygments": {
|
||||
"hashes": [
|
||||
"sha256:b3ed06a9e8ac9a9aae5a6f5dbe78a8a58655d17b43b93c078f094ddc476ae297",
|
||||
|
|
@ -762,6 +779,14 @@
|
|||
"index": "pypi",
|
||||
"version": "==1.11.1"
|
||||
},
|
||||
"tomli": {
|
||||
"hashes": [
|
||||
"sha256:939de3e7a6161af0c887ef91b7d41a53e7c5a1ca976325f429cb46ea9bc30ecc",
|
||||
"sha256:de526c12914f0c550d15924c62d72abc48d6fe7364aa87328337a31007fe8a4f"
|
||||
],
|
||||
"markers": "python_version < '3.11'",
|
||||
"version": "==2.0.1"
|
||||
},
|
||||
"tornado": {
|
||||
"hashes": [
|
||||
"sha256:1d54d13ab8414ed44de07efecb97d4ef7c39f7438cf5e976ccd356bebb1b5fca",
|
||||
|
|
|
|||
Loading…
Reference in a new issue