{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear Operators\n",
"\n",
"Finite dimensional linear operators allow matrix algebra without explicitly constructing a full matrix representation. Instead it suffices to define a matrix-vector product and a shape attribute. This avoids unnecessary memory usage and can often be more convenient to derive."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Make inline plots vector graphics instead of raster graphics\n",
"%matplotlib inline\n",
"from IPython.display import set_matplotlib_formats\n",
"set_matplotlib_formats('pdf', 'svg')\n",
"\n",
"# Plotting\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('../probnum.mplstyle')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sparsity and Operator Arithmetic\n",
"\n",
"We begin by sampling a random sparse matrix, represent it as a `LinearOperator` and perform some simple arithmetic."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.sparse\n",
"from probnum.linalg.linops import MatrixMult, Identity\n",
"\n",
"# Linear operator from sparse matrix\n",
"n = 50\n",
"mat = scipy.sparse.rand(m=n, n=n, density=0.05, random_state=42)\n",
"A = MatrixMult(A=mat)\n",
"\n",
"# Linear operator arithmetic\n",
"Id = Identity(shape=n)\n",
"B = A ** 4 + 1.5 * Id"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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