Multivariate least squares"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The text.latex.preview rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The mathtext.fallback_to_cm rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: Support for setting the 'mathtext.fallback_to_cm' rcParam is deprecated since 3.3 and will be removed two minor releases later; use 'mathtext.fallback : 'cm' instead.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The validate_bool_maybe_none function was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The savefig.jpeg_quality rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The keymap.all_axes rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The animation.avconv_path rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
"In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
"The animation.avconv_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n"
]
}
],
"source": [
"import numpy as np\n",
"import matplotlib\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's do a simple multivariate fit: a fit of a plane to some data. We can use the simple form for least squares:\n",
"$${A^T\\over \\sigma} {A\\over \\sigma} par = {A^T\\over \\sigma} {y\\over \\sigma}$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def model(x,y,par) :\n",
" \"\"\" Function of two variables, linear in parameters\n",
" \"\"\"\n",
" return par[0] + par[1]*x +par[2]*y \n",
"\n",
"def deriv(x,y) :\n",
" \"\"\" Derivative with respect to each parameter\n",
" \"\"\"\n",
" return [np.ones(len(x)), x, y]\n",
" \n",
"# simulate some data \n",
"x=np.random.uniform(size=500)\n",
"y=np.random.uniform(size=500)\n",
"truepar=[3,4,8]\n",
"sig=0.001\n",
"z=model(x,y,truepar)+np.random.normal(0.,sig,size=len(x))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"par: [2.99981733 3.99995974 8.00025013]\n",
"[2.99981733 3.99995974 8.00025013]\n",
"[[ 1.37963671e-08 -1.18205573e-08 -1.14877577e-08]\n",
" [-1.18205573e-08 2.46205607e-08 -1.55756384e-09]\n",
" [-1.14877577e-08 -1.55756384e-09 2.45559416e-08]]\n"
]
}
],
"source": [
"# design matrix\n",
"design=np.array(deriv(x,y)).T/sig\n",
"\n",
"# solve for best fitting parameters in least squares sense\n",
"data=np.array(z)/sig\n",
"ATA=np.dot(design.T,design)\n",
"par=np.linalg.solve(ATA,np.dot(design.T,data))\n",
"print('par: ',par)\n",
"#use inverse matrix to get uncertainties\n",
"inv=np.linalg.inv(ATA)\n",
"print(np.dot(inv,np.dot(design.T,data)))\n",
"print(inv)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are some possibilities for visualizing the results"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.4.3\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
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