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compare: raj_mathe:9134ebcff6a339211c913a5cd0757cfbdd15ad65
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Author SHA1 Message Date
raj_mathe
9134ebcff6 main > main: justfile - include clean output 2022-10-08 10:56:44 +02:00
raj_mathe
6d16f668c8 main > main: nb - corrected sorting of outputs 2022-10-08 10:56:22 +02:00
2 changed files with 10 additions and 65 deletions
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73
docs/examples_dilations.ipynb
View File

@ -22,7 +22,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 16, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -43,7 +43,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 17, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -64,25 +64,9 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 18, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"The marginal semigroups T_i and their generators A_i:\n",
"\n",
" i spec bound of A_i A_i dissipative (<==> T_i contractive)?\n",
"--- ------------------- -----------------------------------------\n",
" 1 -1.000000 True\n",
" 2 -1.000000 True\n",
" 3 -1.000000 True\n",
" 4 -1.000000 True\n"
]
}
],
"source": [ "source": [
"# create the generators `A_i` of the marginal semigroups `T_i`:`\n", "# create the generators `A_i` of the marginal semigroups `T_i`:`\n",
"A = [\n", "A = [\n",
@ -114,37 +98,9 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 19, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Dissipation operators:\n",
"\n",
" K min σ(S_{T,K}) S_{T,K} >= 0?\n",
"------------ ---------------- ---------------\n",
" [] 1.000000 True\n",
" [3] 0.465478 True\n",
" [2] 0.465478 True\n",
" [1] 0.465478 True\n",
" [0] 0.465478 True\n",
" [2, 3] 0.207789 True\n",
" [1, 3] 0.179513 True\n",
" [1, 2] 0.179239 True\n",
" [0, 3] 0.315586 True\n",
" [0, 2] 0.205222 True\n",
" [0, 1] 0.327619 True\n",
" [1, 2, 3] 0.049226 True\n",
" [0, 2, 3] 0.088339 True\n",
" [0, 1, 3] 0.098730 True\n",
" [0, 1, 2] 0.081731 True\n",
"[0, 1, 2, 3] -0.133914 False\n"
]
}
],
"source": [ "source": [
"# compute the dissipation operators `S_TK` for each `K ⊆ {1,2,...,d}``:\n", "# compute the dissipation operators `S_TK` for each `K ⊆ {1,2,...,d}``:\n",
"S, beta_T = dissipation_operators(shape=[N, N], A=A);\n", "S, beta_T = dissipation_operators(shape=[N, N], A=A);\n",
@ -152,7 +108,7 @@
"repr = tabulate(\n", "repr = tabulate(\n",
" tabular_data = [\n", " tabular_data = [\n",
" (K, b, True if b >= -MACHINE_EPS else False)\n", " (K, b, True if b >= -MACHINE_EPS else False)\n",
" for K, S_TK, b in sorted(S, key=lambda x: len(x[0]))\n", " for K, S_TK, b in sorted(S, key=lambda x: (len(x[0]), x[0]) )\n",
" ],\n", " ],\n",
" headers = ['K', 'min σ(S_{T,K})', 'S_{T,K} >= 0?'],\n", " headers = ['K', 'min σ(S_{T,K})', 'S_{T,K} >= 0?'],\n",
" showindex = False,\n", " showindex = False,\n",
@ -165,20 +121,9 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 20, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"β_T = min_K min σ(S_{T,K}) = -0.133914\n",
"⟹ T is not compeletely dissipative.\n",
"⟹ (by Thm 1.1) T does not have a regular unitary dilation.\n"
]
}
],
"source": [ "source": [
"# Display summary:\n", "# Display summary:\n",
"print('')\n", "print('')\n",

2
justfile
View File

@ -89,7 +89,7 @@ clean:
@just clean-notebooks @just clean-notebooks
clean-notebooks: clean-notebooks:
@echo "Clean python notebooks." @echo "Clean python notebooks."
@#{{PYTHON}} -m jupyter nbconvert --clear-output --inplace docs/*.ipynb @{{PYTHON}} -m jupyter nbconvert --clear-output --inplace docs/*.ipynb
@- {{PYTHON}} -m jupytext --update-metadata '{"vscode":""}' docs/*.ipynb 2> /dev/null @- {{PYTHON}} -m jupytext --update-metadata '{"vscode":""}' docs/*.ipynb 2> /dev/null
@- {{PYTHON}} -m jupytext --update-metadata '{"vscode":null}' docs/*.ipynb 2> /dev/null @- {{PYTHON}} -m jupytext --update-metadata '{"vscode":null}' docs/*.ipynb 2> /dev/null
clean-basic: clean-basic: