From b9a8c9bbc01f0af88c46be2ed82d19892e6ed17f Mon Sep 17 00:00:00 2001 From: Saad Jbabdi <saad@SJMBPr2016.local> Date: Fri, 20 Mar 2020 14:04:19 +0000 Subject: [PATCH] inserted comments and what each section introduces --- .../matlab_vs_python/fitting/fit_model.ipynb | 233 +++++++++++++++--- talks/matlab_vs_python/rbf/play_rbf.ipynb | 21 +- 2 files changed, 208 insertions(+), 46 deletions(-) diff --git a/talks/matlab_vs_python/fitting/fit_model.ipynb b/talks/matlab_vs_python/fitting/fit_model.ipynb index 04fc8f1..2db8ef3 100644 --- a/talks/matlab_vs_python/fitting/fit_model.ipynb +++ b/talks/matlab_vs_python/fitting/fit_model.ipynb @@ -1,23 +1,86 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Short example of Model fitting\n", + "\n", + "Here we fit a MRI-style model to some simulated data.\n", + "\n", + "The model is: $\\textrm{Signal} = M_0\\exp\\left[-R_2\\textrm{TE}\\right]\\left(1-\\exp\\left[-R_1\\textrm{TI}\\right]\\right)$ \n", + "\n", + "The parameters that we will be fitting are $(M_0,R_1,R_2)$. \n", + "\n", + "Basic imports:\n" + ] + }, { "cell_type": "code", - "execution_count": 223, + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.optimize import minimize\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this section:\n", + "\n", + "- defining a numpy array\n", + "- double list comprehension\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "TEs = np.array([10,40,50,60,80]) # TE values in ms\n", + "TRs = np.array([.8,1,1.5,2]) # TR in seconds (I know this is bad)\n", + "\n", + "# All combinations of TEs/TRs\n", + "comb = np.array([(x,y) for x in TEs for y in TRs])\n", + "TEs,TRs = comb[:,0],comb[:,1]\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Now we define our forward model\n", + "\n", + "In this section:\n", + "\n", + "- inline function definition\n", + "- random number generation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[<matplotlib.lines.Line2D at 0x125da2160>]" + "[<matplotlib.lines.Line2D at 0x121b13978>]" ] }, - "execution_count": 223, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -27,23 +90,6 @@ } ], "source": [ - "# Fit a model to some data\n", - "# Model is:\n", - "# prediction = M0 * exp(-R2*TE)*(1-exp(-R1*TR))\n", - "# where M0,R1,R2 are unknown parameters and TE/TR are experimental parameters\n", - "\n", - "\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy.optimize import minimize\n", - "\n", - "\n", - "TEs = np.array([10,40,50,60,80]) # TE values in ms\n", - "TRs = np.array([.8,1,1.5,2]) # TR in seconds (I know this is bad)\n", - "\n", - "# All combinations of TEs/TRs\n", - "comb = np.array([(x,y) for x in TEs for y in TRs])\n", - "TEs,TRs = comb[:,0],comb[:,1]\n", "\n", "# function for our model\n", "def forward(p):\n", @@ -51,27 +97,136 @@ " return M0*np.exp(-R2*TEs)*(1-np.exp(-R1*TRs))\n", "\n", "# simulate data using model \n", - "true_p = [100,1/.8,1/50]\n", + "true_p = [100,1/.8,1/50] # M0, R1=1/T1,R2=1/T2\n", "data = forward(true_p)\n", "snr = 50\n", - "noise_std = 100/snr\n", + "noise_std = true_p[0]/snr\n", "noise = np.random.randn(data.size)*noise_std\n", "data = data + noise\n", "\n", + "# quick plot of the data\n", + "plt.figure()\n", "plt.plot(data)\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have the data and our forward model we are almost ready to begin fitting.\n", + "\n", + "We need a cost function to optimise. We will use mean squared error. \n", + "\n", + "In this section:\n", + "\n", + "- '**' operation\n", + "- np.mean" + ] + }, { "cell_type": "code", - "execution_count": 224, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ - "# Now for the fitting\n", - "# we need a cost function:\n", + "# cost function is mean square error divided by 2\n", + "def cf(p):\n", + " pred = forward(p)\n", + " return np.mean((pred-data)**2)/2.0\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can set up our optimisation.\n", "\n", - " \n", - "# always a good idea to calculate gradient\n", + "In this section:\n", + "\n", + "- scipy minimize\n", + "- dictionary\n", + "- keyword arguments\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# get ready to minimize\n", + "p0 = [200,1/1,1/70] # some random initial guess\n", + "method = 'powell' # pick a method. scipy has loads!\n", + "\n", + "\n", + "kw_args = {'x0':p0,'method':method}\n", + "result = minimize(cf,**kw_args)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot the data with the model prediction.\n", + "\n", + "In this section\n", + "\n", + "- printing\n", + "- text formatting\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fitted = [1.02562035e+02 1.16194491e+00 1.98071179e-02]\n", + "true = [100, 1.25, 0.02]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(data,'o')\n", + "plt.plot(forward(result.x))\n", + "print('fitted = {}'.format(result.x))\n", + "print('true = {}'.format(true_p))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optional: use gradients and hessians to help with the optimisation\n", + "\n", + "In this example the forward model is simple enough that calculating the derivatives of the cost function is relatively easy to do analytically. Below is an example of how you could define these and use them in the fitting\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# gradient of the forward model\n", "def forward_deriv(p):\n", " M0,R1,R2 = p\n", " E1,E2 = np.exp(-R1*TRs),np.exp(-R2*TEs)\n", @@ -84,6 +239,7 @@ " dfdR2 = M0*dE2*(1-E1)\n", " return np.array([dfdM0,dfdR1,dfdR2])\n", "\n", + "# hessian of the forward model\n", "def forward_deriv2(p):\n", " M0,R1,R2 = p\n", " E1,E2 = np.exp(-R1*TRs),np.exp(-R2*TEs)\n", @@ -92,17 +248,14 @@ " ddE1 = (TRs**2)*E1\n", " ddE2 = (TEs**2)*E2\n", " \n", - " #dfdM0 = E2*(1-E1)\n", " dfdM0dM0 = np.zeros(E1.shape)\n", " dfdM0dR1 = E2*(-dE1)\n", " dfdM0dR2 = dE2*(1-E1)\n", "\n", - " #dfdR1 = M0*E2*(-dE1)\n", " dfdR1dM0 = E2*(-dE1)\n", " dfdR1dR1 = M0*E2*(-ddE1)\n", " dfdR1dR2 = M0*(dE2)*(-dE1)\n", " \n", - " #dfdR2 = M0*dE2*(1-E1)\n", " dfdR2dM0 = dE2*(1-E1)\n", " dfdR2dR1 = M0*dE2*(-dE1)\n", " dfdR2dR2 = M0*ddE2*(1-E1)\n", @@ -139,20 +292,20 @@ }, { "cell_type": "code", - "execution_count": 226, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "fitted = [9.90012687e+01 1.28692542e+00 1.97590584e-02]\n", + "fitted = [1.02576306e+02 1.16153921e+00 1.98044006e-02]\n", "true = [100, 1.25, 0.02]\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -162,6 +315,8 @@ } ], "source": [ + "\n", + "\n", "# get ready to minimize\n", "p0 = [200,1/1,1/70] # some random guess\n", "method = 'trust-ncg'\n", @@ -177,17 +332,15 @@ "print('fitted = {}'.format(result.x))\n", "print('true = {}'.format(true_p))\n", "\n", - "\n", - "\n", "\n" ] }, { - "cell_type": "code", - "execution_count": 200, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "## The end." + ] }, { "cell_type": "code", diff --git a/talks/matlab_vs_python/rbf/play_rbf.ipynb b/talks/matlab_vs_python/rbf/play_rbf.ipynb index 41c3914..793afa4 100644 --- a/talks/matlab_vs_python/rbf/play_rbf.ipynb +++ b/talks/matlab_vs_python/rbf/play_rbf.ipynb @@ -10,18 +10,17 @@ "\n", "In this section\n", "\n", - "- matplotlib\n", + "- numpy\n", "- matlab-like functions like np.linspace\n" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", - "import matplotlib.pyplot as plt\n", "\n", "# Generate noisy sine wave\n", "x = np.linspace(0,10,100)\n", @@ -46,7 +45,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -87,12 +86,12 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -106,6 +105,9 @@ "# invert model\n", "beta = np.linalg.pinv(desmat)@y.T\n", "\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", "# plot data, RBFs, and fitted model\n", "plt.figure()\n", "plt.plot(x,y,'.')\n", @@ -121,6 +123,13 @@ "\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The end." + ] + }, { "cell_type": "code", "execution_count": null, -- GitLab