Update NB 8.0 with f-strings

Author: jsdodge

notebooks/8.0-Hypothesis-testing.ipynb

@@ -160,7 +160,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Now define a model function based on Ohm's law and choose an initial guess for the resistance. The voltage uncertainty is too small to be appear on the `errorbar` plot, so we switch to the conventional `plot` command."
+    "Now define a model function based on Ohm's law and choose an initial guess for the resistance. The voltage uncertainty is too small to appear on the `errorbar` plot, so we switch to the conventional `plot` command."
    ]
   },
   {
@@ -170,14 +170,14 @@
    "outputs": [],
    "source": [
     "# Define model\n",
-    "def vOhm(current, resistance):\n",
+    "def v_ohm(current, resistance):\n",
     "    return current*resistance\n",
     "\n",
     "# Assign initial guess for resistance and\n",
     "RInit = 100\n",
     "Imodel_mA = np.linspace(0,100)\n",
     "Imodel = 1e-3*Imodel_mA\n",
-    "Vmodel = vOhm(Imodel, RInit)\n",
+    "Vmodel = v_ohm(Imodel, RInit)\n",
     "plt.plot(I_mA, Vm, 'o')\n",
     "plt.plot(Imodel_mA, Vmodel, '-')\n",
     "plt.xlabel(\"Current (mA)\")\n",
@@ -197,10 +197,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "R_fit, R_fit_cov = curve_fit(vOhm, I_mA*1e-3, Vm, p0=[RInit], \n",
+    "R_fit, R_fit_cov = curve_fit(v_ohm, I_mA*1e-3, Vm, p0=[RInit], \n",
     "                             sigma=alphaV*np.ones(np.size(Vm)), absolute_sigma=True)\n",
     "alpha_R = np.sqrt(R_fit_cov[0,0])\n",
-    "print(\"R = {0:.3f} ± {1:.3f} ohms\".format(R_fit[0], alpha_R))"
+    "print(f\"R = {R_fit[0]:.3f} ± {alpha_R:.3f} ohms\")"
    ]
   },
   {
@@ -217,10 +217,10 @@
    "outputs": [],
    "source": [
     "# Compute and display chi-squared\n",
-    "res = Vm - vOhm(I_mA*1e-3, R_fit)\n",
+    "res = Vm - v_ohm(I_mA*1e-3, R_fit)\n",
     "normres = res/alphaV\n",
     "chisq = np.sum(normres**2)\n",
-    "print(\"chisq = {0:.1f}\".format(chisq))"
+    "print(f\"chisq = {chisq:.1f}\")"
    ]
   },
   {
@@ -241,8 +241,8 @@
     "# Compute the probability of getting this fit result\n",
     "dof = 10\n",
     "cdf = chi2.cdf(chisq, dof)\n",
-    "print(\"Cumulative probability = {0:.6f}\".format(cdf))\n",
-    "print(\"Significance: {0:.6f}\".format(1-cdf))"
+    "print(f\"Cumulative probability = {cdf:.6f}\")\n",
+    "print(f\"Significance: {1-cdf:.6f}\")"
    ]
   },
   {
@@ -279,18 +279,18 @@
    "outputs": [],
    "source": [
     "# Define new model\n",
-    "def vOhm_offset(current, resistance, offset):\n",
+    "def v_ohm_offset(current, resistance, offset):\n",
     "    return current*resistance + offset\n",
     "\n",
     "VoffInit = 0\n",
-    "p_fit, p_fit_cov = curve_fit(vOhm_offset, I_mA*1e-3, Vm, p0=[RInit,VoffInit], \n",
+    "p_fit, p_fit_cov = curve_fit(v_ohm_offset, I_mA*1e-3, Vm, p0=[RInit,VoffInit], \n",
     "                             sigma=alphaV*np.ones(np.size(Vm)), absolute_sigma=True)\n",
     "R_fit = p_fit[0]\n",
     "Voff_fit = p_fit[1]\n",
     "alpha_R = np.sqrt(p_fit_cov[0,0])\n",
     "alpha_Voff = np.sqrt(p_fit_cov[1,1])\n",
-    "print(\"R = {0:.3f} ± {1:.3f} ohms\".format(R_fit, alpha_R))\n",
-    "print(\"Voff = {0:.3f} ± {1:.3f} V\".format(Voff_fit, alpha_Voff))"
+    "print(f\"R = {R_fit:.3f} ± {alpha_R:.3f} ohms\")\n",
+    "print(f\"Voff = {Voff_fit:.3f} ± {alpha_Voff:.3f} V\")"
    ]
   },
   {
@@ -307,16 +307,16 @@
    "outputs": [],
    "source": [
     "# Compute and display chi-squared\n",
-    "res_offset = Vm - vOhm_offset(I_mA*1e-3, R_fit, Voff_fit)\n",
+    "res_offset = Vm - v_ohm_offset(I_mA*1e-3, R_fit, Voff_fit)\n",
     "normres_offset = res_offset/alphaV\n",
     "chisq_offset = np.sum(normres_offset**2)\n",
-    "print(\"chisq_offset = {0:.1f}\".format(chisq_offset))\n",
+    "print(f\"chisq_offset = {chisq_offset:.1f}\")\n",
     "\n",
     "# Compute the probability of getting this fit result\n",
     "dof_offset = 9\n",
     "cdf_offset = chi2.cdf(chisq_offset, dof_offset)\n",
-    "print(\"Cumulative probability = {0:.6f}\".format(cdf_offset))\n",
-    "print(\"Significance: {0:.6f}\".format(1-cdf_offset))"
+    "print(f\"Cumulative probability = {cdf_offset:.6f}\")\n",
+    "print(f\"Significance: {1-cdf_offset:.6f}\")"
    ]
   },
   {
@@ -466,7 +466,7 @@
     "g_fit, g_fit_cov = curve_fit(t_fall, d_cm*1e-2, tm, p0=[gInit], \n",
     "                             sigma=alpha_t_est*np.ones(np.size(tm)), absolute_sigma=True)\n",
     "alpha_g = np.sqrt(g_fit_cov[0,0])\n",
-    "print(\"g = {0:.2f} ± {1:.2f} m/s^2\".format(g_fit[0], alpha_g))"
+    "print(f\"g = {g_fit[0]:.2f} ± {alpha_g:.2f} m/s^2\")"
    ]
   },
   {
@@ -486,7 +486,7 @@
     "res = tm - t_fall(d_cm*1e-2, g_fit)\n",
     "normres = res/alpha_t_est\n",
     "chisq = np.sum(normres**2)\n",
-    "print(\"chisq = {0:.1f}\".format(chisq))"
+    "print(f\"chisq = {chisq:.1f}\")"
    ]
   },
   {
@@ -508,9 +508,9 @@
     "dof = 9\n",
     "cdf = chi2.cdf(chisq, dof)\n",
     "sig = chi2.sf(chisq, dof)\n",
-    "print(\"Cumulative probability = {0:.6f}\".format(cdf))\n",
-    "print(\"Significance (1-cdf method): {0:.6f}\".format(1 - cdf))\n",
-    "print(\"Significance (sf method): {0:.6e}\".format(sig))"
+    "print(f\"Cumulative probability = {cdf:.6f}\")\n",
+    "print(f\"Significance (1-cdf method): {1 - cdf:.6f}\")\n",
+    "print(f\"Significance (sf method): {sig:.6e}\")"
    ]
   },
   {
@@ -543,7 +543,7 @@
     "$$\n",
     "S = \\sqrt{\\frac{\\chi^2_\\text{min}}{\\nu}} = \\sqrt{\\chi^2_\\nu},\n",
     "$$\n",
-    "so that the resulting $\\chi'^2_\\text{min} = S\\chi^2_\\text{min}$ matches the number of degrees of freedom exactly. Of course you forfeit the ability to use $\\chi'^2_\\text{min}$ as evidence of fit quality when you do this, so it is usually preferable to just go back and do a more careful measurement of the noise. This is definitely the case in this example, where $\\chi^2_\\text{min}$ indicates such a poor fit.\n",
+    "so that the resulting $\\chi'^2_\\text{min} = S\\chi^2_\\text{min}$ matches the number of degrees of freedom exactly. Of course, you forfeit the ability to use $\\chi'^2_\\text{min}$ as evidence of fit quality when you do this, so it is usually preferable to just go back and do a more careful measurement of the noise. This is definitely the case in this example, where $\\chi^2_\\text{min}$ indicates such a poor fit.\n",
     "\n",
     "When $S\\approx 1$, though, it may be advantageous to scale the residuals to improve the accuracy of the *parameter uncertainty,* since the parameter uncertainty estimate given by `curve_fit` depends on $\\chi^2_\\text{min}$. The following code cell computes the scale factor for our example, then uses this to revise $\\alpha_g$. Another way to achieve the same result is to simply set `absolute_sigma=False` in the `curve_fit` algorithm—this will compute the fit by treating the values assigned to `sigma` as *relative uncertainties*, with an overall scale factor given by $S$ above. The defaults are `absolute_sigma=False` and `sigma` set to a vector of ones with the same size as the `y` data, so that when both `sigma` and `absolute_sigma` are omitted, `curve_fit` minimizes\n",
     "\n",
@@ -560,27 +560,27 @@
    "source": [
     "# Determine the scaling factor\n",
     "S = np.sqrt(chisq/dof)\n",
-    "print(\"Scale factor: {0:.3f}\".format(S))\n",
+    "print(f\"Scale factor: {S:.3f}\")\n",
     "\n",
     "# Scale measurement uncertainty by S\n",
-    "print(\"S*alpha_t_est = {0:.2f} ms\".format(1e3*S*alpha_t_est))\n",
+    "print(f\"S*alpha_t_est = {1e3*S*alpha_t_est:.2f} ms\")\n",
     "\n",
     "# Compare with true measurement uncertainty\n",
-    "print(\"True alpha_t = {0:.2f}\".format(1e3*alpha_t))\n",
+    "print(f\"True alpha_t = {1e3*alpha_t:.2f}\")\n",
     "\n",
     "# Scale parameter uncertainty by S\n",
-    "print(\"g = {0:.2f} ± {1:.2f} m/s^2 (scaled uncertainty)\".format(g_fit[0], S*alpha_g))\n",
+    "print(f\"g = ({g_fit[0]:.2f} ± {S*alpha_g:.2f}) m/s^2 (scaled uncertainty)\")\n",
     "\n",
     "# Repeat fit with absolute_sigma=False\n",
     "g_fit_scaled, g_fit_cov_scaled = curve_fit(t_fall, d_cm*1e-2, tm, p0=[gInit], \n",
     "                             sigma=alpha_t_est*np.ones(np.size(tm)), absolute_sigma=False)\n",
     "alpha_g_scaled = np.sqrt(g_fit_cov_scaled[0,0])\n",
-    "print(\"g = {0:.2f} ± {1:.2f} m/s^2 (absolute_sigma=False)\".format(g_fit_scaled[0], alpha_g_scaled))\n",
+    "print(f\"g = ({g_fit_scaled[0]:.2f} ± {alpha_g_scaled:.2f}) m/s^2 (absolute_sigma=False)\")\n",
     "\n",
     "# Repeat fit without sigma or absolute_sigma keywords\n",
     "g_fit_nosig, g_fit_cov_nosig = curve_fit(t_fall, d_cm*1e-2, tm, p0=[gInit])\n",
     "alpha_g_nosig = np.sqrt(g_fit_cov_nosig[0,0])\n",
-    "print(\"g = {0:.2f} ± {1:.2f} m/s^2 (no sigma)\".format(g_fit_nosig[0], alpha_g_nosig))"
+    "print(f\"g = ({g_fit_nosig[0]:.2f} ± {alpha_g_nosig:.2f}) m/s^2 (no sigma)\")"
    ]
   },
   {