mirror of
https://github.com/fjosw/pyerrors.git
synced 2025-05-15 12:03:42 +02:00
Merge branch 'develop' into documentation
This commit is contained in:
fjosw
commit
61a9e124f6
6 changed files with 196 additions and 646 deletions
|
|
@ -3,7 +3,7 @@
|
|||
`pyerrors` is a python package for error computation and propagation of Markov chain Monte Carlo data.
|
||||
|
||||
- **Documentation:** https://fjosw.github.io/pyerrors/pyerrors.html
|
||||
- **Examples**: https://github.com/fjosw/pyerrors/tree/develop/examples (Do not work properly at the moment)
|
||||
- **Examples**: https://github.com/fjosw/pyerrors/tree/develop/examples
|
||||
- **Contributing:** https://github.com/fjosw/pyerrors/blob/develop/CONTRIBUTING.md
|
||||
- **Bug reports:** https://github.com/fjosw/pyerrors/issues
|
||||
|
||||
|
|
|
|||
File diff suppressed because one or more lines are too long
File diff suppressed because one or more lines are too long
File diff suppressed because one or more lines are too long
|
|
@ -51,7 +51,7 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The standard matrix product can be performed with @"
|
||||
"The standard matrix product can be performed with `@`"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -101,13 +101,38 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Mathematical functions work elementwise"
|
||||
"For large matrices overloading the standard operator `@` can become inefficient as pyerrors has to perform a large number of elementary opeations. For these situations pyerrors provides the function `linalg.matmul` which optimizes the required automatic differentiation. The function can take an arbitray number of operands."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[[Obs[78.12099999999998] Obs[-22.909999999999997]]\n",
|
||||
" [Obs[-22.909999999999997] Obs[7.1]]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"print(pe.linalg.matmul(matrix, matrix, matrix)) # Equivalent to matrix @ matrix @ matrix but faster for large matrices"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Mathematical functions work elementwise"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
|
|
@ -126,12 +151,12 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"For a vector of `Obs`, we again use np.asarray to end up with the correct object"
|
||||
"For a vector of `Obs`, we again use `np.asarray` to end up with the correct object"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -160,14 +185,14 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[Obs[7.2(1.7)] Obs[-1.00(45)]]\n"
|
||||
"[Obs[7.2(1.7)] Obs[-1.00(46)]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -182,40 +207,7 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Matrix to scalar operations\n",
|
||||
"If we want to apply a numpy matrix function with a scalar return value we can use `scalar_mat_op`. __Here we need to use the autograd wrapped version of numpy__ (imported as anp) to use automatic differentiation."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"det \t Obs[3.10(28)]\n",
|
||||
"trace \t Obs[5.10(20)]\n",
|
||||
"norm \t Obs[4.45(19)]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"import autograd.numpy as anp # Thinly-wrapped numpy\n",
|
||||
"funcs = [anp.linalg.det, anp.trace, anp.linalg.norm]\n",
|
||||
"\n",
|
||||
"for i, func in enumerate(funcs):\n",
|
||||
" res = pe.linalg.scalar_mat_op(func, matrix)\n",
|
||||
" res.gamma_method()\n",
|
||||
" print(func.__name__, '\\t', res)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"For matrix operations which are not supported by autograd we can use numerical differentiation"
|
||||
"`pyerrors` provides the user with wrappers to the `numpy.linalg` functions which work on `Obs` valued matrices. We can for example calculate the determinant of the matrix via"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -227,26 +219,21 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"cond \t Obs[6.23(58)]\n",
|
||||
"expm_cond \t Obs[4.45(19)]\n"
|
||||
"3.10(28)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"funcs = [np.linalg.cond, scipy.linalg.expm_cond]\n",
|
||||
"\n",
|
||||
"for i, func in enumerate(funcs):\n",
|
||||
" res = pe.linalg.scalar_mat_op(func, matrix, num_grad=True)\n",
|
||||
" res.gamma_method()\n",
|
||||
" print(func.__name__, ' \\t', res)"
|
||||
"det = pe.linalg.det(matrix)\n",
|
||||
"det.gamma_method()\n",
|
||||
"print(det)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Matrix to matrix operations\n",
|
||||
"For matrix operations with a matrix as return value we can use another wrapper `mat_mat_op`. Take as an example the cholesky decompostion. __Here we need to use the autograd wrapped version of numpy__ (imported as anp) to use automatic differentiation."
|
||||
"The cholesky decomposition can be obtained as follows"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -259,12 +246,12 @@
|
|||
"output_type": "stream",
|
||||
"text": [
|
||||
"[[Obs[2.025(49)] Obs[0.0]]\n",
|
||||
" [Obs[-0.494(51)] Obs[0.870(29)]]]\n"
|
||||
" [Obs[-0.494(50)] Obs[0.870(29)]]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"cholesky = pe.linalg.mat_mat_op(anp.linalg.cholesky, matrix)\n",
|
||||
"cholesky = pe.linalg.cholesky(matrix)\n",
|
||||
"for (i, j), entry in np.ndenumerate(cholesky):\n",
|
||||
" entry.gamma_method()\n",
|
||||
"print(cholesky)"
|
||||
|
|
@ -321,7 +308,7 @@
|
|||
}
|
||||
],
|
||||
"source": [
|
||||
"inv = pe.linalg.mat_mat_op(anp.linalg.inv, cholesky)\n",
|
||||
"inv = pe.linalg.inv(cholesky)\n",
|
||||
"for (i, j), entry in np.ndenumerate(inv):\n",
|
||||
" entry.gamma_method()\n",
|
||||
"print(inv)\n",
|
||||
|
|
@ -334,59 +321,14 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Matrix to matrix operations which are not supported by autograd can also be computed with numeric differentiation"
|
||||
"## Eigenvalues and eigenvectors\n",
|
||||
"We can also compute eigenvalues and eigenvectors of symmetric matrices with a special wrapper `eigh`"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"orth\n",
|
||||
"[[Obs[-0.9592(76)] Obs[0.283(26)]]\n",
|
||||
" [Obs[0.283(26)] Obs[0.9592(76)]]]\n",
|
||||
"expm\n",
|
||||
"[[Obs[75(15)] Obs[-21.4(4.1)]]\n",
|
||||
" [Obs[-21.4(4.1)] Obs[8.3(1.4)]]]\n",
|
||||
"logm\n",
|
||||
"[[Obs[1.334(57)] Obs[-0.496(61)]]\n",
|
||||
" [Obs[-0.496(61)] Obs[-0.203(50)]]]\n",
|
||||
"sinhm\n",
|
||||
"[[Obs[37.3(7.4)] Obs[-10.8(2.1)]]\n",
|
||||
" [Obs[-10.8(2.1)] Obs[3.94(68)]]]\n",
|
||||
"sqrtm\n",
|
||||
"[[Obs[1.996(51)] Obs[-0.341(37)]]\n",
|
||||
" [Obs[-0.341(37)] Obs[0.940(14)]]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"funcs = [scipy.linalg.orth, scipy.linalg.expm, scipy.linalg.logm, scipy.linalg.sinhm, scipy.linalg.sqrtm]\n",
|
||||
"\n",
|
||||
"for i,func in enumerate(funcs):\n",
|
||||
" res = pe.linalg.mat_mat_op(func, matrix, num_grad=True)\n",
|
||||
" for (i, j), entry in np.ndenumerate(res):\n",
|
||||
" entry.gamma_method()\n",
|
||||
" print(func.__name__)\n",
|
||||
" print(res)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Eigenvalues and eigenvectors\n",
|
||||
"We can also compute eigenvalues and eigenvectors of symmetric matrices with a special wrapper `eigh`"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
|
|
@ -395,8 +337,8 @@
|
|||
"Eigenvalues:\n",
|
||||
"[Obs[0.705(57)] Obs[4.39(19)]]\n",
|
||||
"Eigenvectors:\n",
|
||||
"[[Obs[-0.283(26)] Obs[-0.9592(76)]]\n",
|
||||
" [Obs[-0.9592(76)] Obs[0.283(26)]]]\n"
|
||||
"[[Obs[-0.283(26)] Obs[-0.9592(75)]]\n",
|
||||
" [Obs[-0.9592(75)] Obs[0.283(26)]]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -421,7 +363,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -451,7 +393,7 @@
|
|||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"display_name": "Python 3 (ipykernel)",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
|
|
@ -465,7 +407,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.6.9"
|
||||
"version": "3.8.10"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -522,7 +522,7 @@ class Corr:
|
|||
if self.N != 1:
|
||||
raise Exception("Correlator must be projected before plotting")
|
||||
if x_range is None:
|
||||
x_range = [0, self.T]
|
||||
x_range = [0, self.T - 1]
|
||||
|
||||
fig = plt.figure()
|
||||
ax1 = fig.add_subplot(111)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue