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Lambda Lambda Lambda
-
<function <lambda> at 0x7feda8eee480>
+
<function <lambda> at 0x7f89a03ae480>
 4
 

 

@@ -1112,7 +1112,7 @@ 
Lambda Lambda Lambda
-
<function <lambda> at 0x7feda8e82160>
+
<function <lambda> at 0x7f89a03ae020>
 5
 

 

@@ -1129,7 +1129,7 @@ 
Lambda Lambda Lambda
-
<function <lambda> at 0x7feda8eedf80>
+
<function <lambda> at 0x7f89a03adf80>
 5
 5
 

@@ -1150,7 +1150,7 @@ 
Lambda Lambda Lambda
 

 

-
<function <lambda> at 0x7feda8eedd00>
+
<function <lambda> at 0x7f89a03ae2a0>
 1
 3
 6
@@ -1326,7 +1326,7 @@ 
Creating arrays in python
/tmp/ipykernel_1843/3002503601.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1854/3002503601.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   print(np.row_stack([a, b]))
 

 

@@ -1779,7 +1779,7 @@ 
Indexing vectors and arrays in Python
-1.7950016288086892
 

 

-
/tmp/ipykernel_1843/518394352.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1854/518394352.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz( x[x > 2], y[x > 2]))
 

 

@@ -1876,17 +1876,17 @@ 
3D arrays#
 

 

-
[[[0.80321106 0.44641335 0.61280867]
-  [0.08561714 0.48916264 0.12148204]
-  [0.67663477 0.08682434 0.75214321]]
+
[[[0.48002794 0.97868829 0.88642924]
+  [0.51873709 0.59485089 0.46198812]
+  [0.20065208 0.80558278 0.40429193]]
 
- [[0.05188889 0.83731674 0.53269215]
-  [0.68939332 0.41800378 0.9449533 ]
-  [0.37003968 0.94434034 0.18078264]]
+ [[0.77306348 0.02738732 0.3228694 ]
+  [0.43175158 0.1070621  0.56649795]
+  [0.82474244 0.29901801 0.1160524 ]]
 
- [[0.6152774  0.34896826 0.39407928]
-  [0.56752324 0.35240605 0.32444222]
-  [0.30024248 0.49098965 0.78413294]]]
+ [[0.47549009 0.34115665 0.90873334]
+  [0.66160365 0.46052865 0.0972723 ]
+  [0.54247246 0.39699709 0.24047473]]]
 

 

 

@@ -1900,11 +1900,11 @@ 
3D arrays#
 

 

-
[[0.80321106 0.08561714 0.67663477]
- [0.05188889 0.68939332 0.37003968]
- [0.6152774  0.56752324 0.30024248]]
-[0.80321106 0.05188889 0.6152774 ]
-[0.53269215 0.9449533  0.18078264]
+
[[0.48002794 0.51873709 0.20065208]
+ [0.77306348 0.43175158 0.82474244]
+ [0.47549009 0.66160365 0.54247246]]
+[0.48002794 0.77306348 0.47549009]
+[0.3228694  0.56649795 0.1160524 ]
 

 

 

diff --git a/blog/data-analysis.html b/blog/data-analysis.html
index 94f584a2..20aa13a2 100644
--- a/blog/data-analysis.html
+++ b/blog/data-analysis.html
@@ -697,11 +697,33 @@ 
Linear regression with confidence intervals (updated)
 

 

-
[[ 4.90747573e-02  5.09057619e-02]
- [-3.49867290e-04 -2.45825350e-04]
- [ 5.40268319e-07  2.14670135e-06]
- [-7.67338629e-09  7.03689494e-10]
- [-3.23368759e-12  1.06276267e-11]]
+
---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[5], line 1
+----> 1 from pycse import regress
+      2 import numpy as np
+      3 time = np.array([0.0, 50.0, 100.0, 150.0, 200.0, 250.0, 300.0])
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/__init__.py:24
+     12 from .PYCSE import (
+     13     polyfit,
+     14     regress,
+   (...)
+     20     lbic,
+     21 )
+     22 from .utils import feq, flt, fgt, fle, fge, read_gsheet
+---> 24 from .hashcache import hashcache
+     26 # from .beginner import *
+     29 from IPython import get_ipython
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/hashcache.py:84
+     82 import inspect
+     83 import joblib
+---> 84 import orjson
+     85 import os
+     86 from pathlib import Path
+
+ModuleNotFoundError: No module named 'orjson'
 

 

 

diff --git a/blog/differential-equations.html b/blog/differential-equations.html
index 8cd56b7f..12dd5e5f 100644
--- a/blog/differential-equations.html
+++ b/blog/differential-equations.html
@@ -1618,7 +1618,7 @@ 
Linear algebra approaches to solving systems of constant coefficient ODEs
 

 

-
/tmp/ipykernel_1898/2289625004.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1913/2289625004.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   T = np.row_stack([t, t])
 

 

diff --git a/blog/interpolation.html b/blog/interpolation.html
index c11af49a..6266a113 100644
--- a/blog/interpolation.html
+++ b/blog/interpolation.html
@@ -916,9 +916,9 @@ 
Interpolation with splines
/tmp/ipykernel_1928/1138919460.py:26: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+
/tmp/ipykernel_1943/1138919460.py:26: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   plt.title('Max point = ({0:1.2f}, {1:1.2f})'.format(float(xmax),
-/tmp/ipykernel_1928/1138919460.py:27: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+/tmp/ipykernel_1943/1138919460.py:27: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   float(f(xmax))));
 

 

diff --git a/blog/linear-algebra.html b/blog/linear-algebra.html
index 9a8e3faa..2926c0f6 100644
--- a/blog/linear-algebra.html
+++ b/blog/linear-algebra.html
@@ -1178,7 +1178,7 @@ 
Determining linear independence of a set of vectors

 

-
/tmp/ipykernel_1955/3718588497.py:6: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1968/3718588497.py:6: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   A = np.row_stack([v1, v2, v3])
 

 

@@ -1231,7 +1231,7 @@ 
Another example
[7.57773162 5.99149259]
 

 

-
/tmp/ipykernel_1955/73961882.py:7: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1968/73961882.py:7: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   A = np.row_stack([v1, v2])
 

 

diff --git a/blog/math.html b/blog/math.html
index f1b5f5de..0476c99f 100644
--- a/blog/math.html
+++ b/blog/math.html
@@ -673,9 +673,9 @@ 
Numeric derivatives by differences
-
 Forward difference took 0.000212 seconds
- Backward difference took 0.000192 seconds
- Centered difference took 0.000257 seconds
+
 Forward difference took 0.000217 seconds
+ Backward difference took 0.000194 seconds
+ Centered difference took 0.000227 seconds
 

 

 ../_images/e82a955efa2e01fb55f09524ce9405030516d0ae15614c934dfaf2d14380e228.png
@@ -775,7 +775,7 @@ 
2-point vs. 4-point numerical derivatives
-../_images/febe8044aff6c82265e93d6936dbfe613fb32264c62ab9e7a955d067cca78544.png
+../_images/56940aa8a6ba338315884ca81f0b9a6c87e6e0a6b9bed5722dcee49df000045d.png
 

 

 
@@ -900,7 +900,7 @@ 
Derivatives by FFT
-../_images/19b1bad9149f971c41765c8986180ad3b4859e57c2cffc893a77a06c66bca260.png
+../_images/fc153836ecdee39e685d038c59b7fbed2b3c8a368ada50cec3168750bf981f1f.png
 

 

 
@@ -1280,7 +1280,7 @@ 
Numerical data integration
4.25 0.0625
 

 

-
/tmp/ipykernel_1980/1388173814.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1994/1388173814.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   i2 = np.trapz(y, x)
 

 

@@ -1323,7 +1323,7 @@ 
Numerical data integration
4.000408121620243
 

 

-
/tmp/ipykernel_1980/1343167527.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1994/1343167527.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz(y2, x2))
 

 

@@ -1363,7 +1363,7 @@ 
Combining numerical data with quad
/tmp/ipykernel_1980/1681875887.py:13: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1994/1681875887.py:13: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz(yfine, xfine))
 

 

@@ -1774,7 +1774,7 @@ 
The trapezoidal method of integration
-
time elapsed = 0.0007123947143554688 sec
+
time elapsed = 0.0006909370422363281 sec
 1.9999983517708524
 

 

@@ -1795,7 +1795,7 @@ 
The trapezoidal method of integration
-
time elapsed = 0.00017595291137695312 sec
+
time elapsed = 0.0002090930938720703 sec
 1.9999934070923728
 

 

@@ -1814,7 +1814,7 @@ 
The trapezoidal method of integration
-
time elapsed = 7.295608520507812e-05 sec
+
time elapsed = 0.00010180473327636719 sec
 1.999993407092373
 

 

@@ -2009,7 +2009,7 @@ 
Function integration by the Romberg method
/tmp/ipykernel_1980/1760157840.py:9: DeprecationWarning: `scipy.integrate.romberg` is deprecated as of SciPy 1.12.0and will be removed in SciPy 1.15.0. Please use`scipy.integrate.quad` instead.
+
/tmp/ipykernel_1994/1760157840.py:9: DeprecationWarning: `scipy.integrate.romberg` is deprecated as of SciPy 1.12.0and will be removed in SciPy 1.15.0. Please use`scipy.integrate.quad` instead.
   print(romberg(np.sin, a, b))
 

 

@@ -2038,7 +2038,9 @@ 
Solve the quadratic equation
 
[(-b - sqrt(-4*a*c + b**2))/(2*a), (-b + sqrt(-4*a*c + b**2))/(2*a)]
-⎡        _____________          _____________⎤
+

+

+
⎡        _____________          _____________⎤
 ⎢       ╱           2          ╱           2 ⎥
 ⎢-b - ╲╱  -4⋅a⋅c + b    -b + ╲╱  -4⋅a⋅c + b  ⎥
 ⎢─────────────────────, ─────────────────────⎥
diff --git a/blog/nonlinear-algebra.html b/blog/nonlinear-algebra.html
index 45ba220e..162b3cea 100644
--- a/blog/nonlinear-algebra.html
+++ b/blog/nonlinear-algebra.html
@@ -765,10 +765,10 @@ 
Method of continuity for nonlinear equation solving
 

 

-
/tmp/ipykernel_2009/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2022/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   y1, = fsolve(tmp, x0)
-/tmp/ipykernel_2009/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
+/tmp/ipykernel_2022/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last five Jacobian evaluations.
   y1, = fsolve(tmp, x0)
 

@@ -1086,7 +1086,35 @@ 
Finding the nth root of a periodic function
-../_images/7e64bf53667d43e52a048719d67ed4b13e0d77573e83f1b983e1552a3326c7c7.png
+
---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[18], line 1
+----> 1 from pycse import *  # contains the ode integrator with events
+      3 from scipy.special import jn, jn_zeros
+      4 import matplotlib.pyplot as plt
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/__init__.py:24
+     12 from .PYCSE import (
+     13     polyfit,
+     14     regress,
+   (...)
+     20     lbic,
+     21 )
+     22 from .utils import feq, flt, fgt, fle, fge, read_gsheet
+---> 24 from .hashcache import hashcache
+     26 # from .beginner import *
+     29 from IPython import get_ipython
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/hashcache.py:84
+     82 import inspect
+     83 import joblib
+---> 84 import orjson
+     85 import os
+     86 from pathlib import Path
+
+ModuleNotFoundError: No module named 'orjson'
+

+

 

 

 
You can work this out once, and then you have all the roots in the interval and you can select the one you want.

diff --git a/blog/plotting.html b/blog/plotting.html
index 4b91c0ee..99c4bb28 100644
--- a/blog/plotting.html
+++ b/blog/plotting.html
@@ -1173,7 +1173,7 @@ 
Peak annotation in matplotlib
-
/tmp/ipykernel_2066/256016704.py:19: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2078/256016704.py:19: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   area = np.trapz(i[ind], w[ind])
 

 

diff --git a/blog/programming.html b/blog/programming.html
index 312dc75d..f60d329b 100644
--- a/blog/programming.html
+++ b/blog/programming.html
@@ -795,7 +795,7 @@ 
Unique entries in a vector
-
['a', 'b', 'c', 'abracadabra', 'd']
+
['d', 'b', 'a', 'abracadabra', 'c']
 

 

 

@@ -838,6 +838,9 @@ 
Lather, rinse and repeat
120.0
 

 

+

+

+

 

 

 

@@ -1168,11 +1171,11 @@ 
About your python
-
uname_result(system='Linux', node='fv-az525-184', release='6.5.0-1022-azure', version='#23~22.04.1-Ubuntu SMP Thu May  9 17:59:24 UTC 2024', machine='x86_64')
+
uname_result(system='Linux', node='fv-az1108-758', release='6.5.0-1022-azure', version='#23~22.04.1-Ubuntu SMP Thu May  9 17:59:24 UTC 2024', machine='x86_64')
 Linux
 ('64bit', 'ELF')
 x86_64
-fv-az525-184
+fv-az1108-758
 Linux-6.5.0-1022-azure-x86_64-with-glibc2.35
 x86_64
 ('main', 'Jun 25 2024 18:25:01')
diff --git a/blog/statistics.html b/blog/statistics.html
index 8fce90e3..051a7da6 100644
--- a/blog/statistics.html
+++ b/blog/statistics.html
@@ -1124,9 +1124,9 @@ 
Addition and subtraction
-../_images/0d72ed916725b1fd980ad2f3a8b1ed421dac2ef273e28b47f184fa4de649056b.png
-
0.5030084431650822
-0.5012543690981847
+../_images/4cd7e432e54cd36aae7abd887e4f2f616996a3fb8f3411321d335eff1691e6a5.png
+
0.5018059331088555
+0.5007770515598653
 0.5
 

 

@@ -1150,7 +1150,7 @@ 
Multiplication
-
11.976179880469868
+
11.924546427120736
 11.872657663724665
 

 

@@ -1169,7 +1169,7 @@ 
Division
 

 

 

-
0.2972693963735536
+
0.2948085873640377
 0.2898598062432779
 

 

@@ -1194,7 +1194,7 @@ 
exponents
-
1.7232989683907753
+
1.717020860390297
 1.7236544062149992
 

 

@@ -1208,7 +1208,7 @@ 
exponents
-
0.007487385769720177
+
0.007394231676488066
 0.007483647387490024
 

 

@@ -1236,7 +1236,7 @@ 
the chain rule in error propagation
-
3.5699388683256155
+
3.6174393755793153
 3.6180105030251086
 

 

@@ -1494,7 +1494,7 @@ 
Another approach to error propagation
-
Ca(exit) = 0.005011876359460245+/-0.00017254908730403556
+
Ca(exit) = 0.0050087201108168725+/-0.0001701923887459706
 

 

 

@@ -1526,7 +1526,7 @@ 
Random thoughts
-
n = 0.7399837089084849
+
n = 0.8910371801565335
 You win!
 

 

@@ -1551,10 +1551,10 @@ 
Random thoughts
-
You won 5050 times (50.500000%)
+
You won 5148 times (51.480000%)
 

 

-../_images/1254d65e58659f6ec2f8b2f0289528024b6e03f1f9aebb8b9d19cc4461dece02.png
+../_images/302a8d146c3ecca8cb0ba6a592cd1afe4498728f633cf872a749d74154a6d979.png
 

 

 
As you can see you win slightly more than you lost.

@@ -1570,10 +1570,10 @@ 
Random thoughts
-
25
-[84 87 35]
-[[36 70]
- [16 94]]
+
5
+[84 82 16]
+[[49 31]
+ [37  7]]
 

 

 

@@ -1591,8 +1591,8 @@ 
Random thoughts
-
1.5946225628388502
-[0.83509644 0.73464142]
+
1.2593831279907737
+[2.00619763 1.32975997]
 

 

 

@@ -1615,7 +1615,7 @@ 
Random thoughts
-../_images/d0465d4c01634e4054d20362cc71ea11e5a45544ed45a2a6874e0910b96846cd.png
+../_images/7e98df2e587773feef87914d268c988909fdcf8450fe1a47eb6e77285c106ed5.png
 

 

 
What fraction of points lie between plus and minus one standard deviation of the mean?

@@ -1638,8 +1638,8 @@ 
Random thoughts
-
67.760000% of samples are within +- 1 standard deviations of the mean
-95.380000% of samples are within +- 2 standard deviations of the mean
+
68.300000% of samples are within +- 1 standard deviations of the mean
+95.300000% of samples are within +- 2 standard deviations of the mean
 

 

 

diff --git a/blog/worked-examples.html b/blog/worked-examples.html
index 01555269..17e82a58 100644
--- a/blog/worked-examples.html
+++ b/blog/worked-examples.html
@@ -1432,7 +1432,7 @@ 
Linear equality constraints for atomic mass conservation
/tmp/ipykernel_2158/1892264215.py:6: RuntimeWarning: invalid value encountered in log
+
/tmp/ipykernel_2170/1892264215.py:6: RuntimeWarning: invalid value encountered in log
   G = np.sum(nj * (Gjo / R / T + np.log(nj / Enj)))
 

 

@@ -1548,9 +1548,9 @@ 
The Gibbs free energy of a reacting mixture and the equilibrium composition<
 

 

 

-
/tmp/ipykernel_2158/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
+
/tmp/ipykernel_2170/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
   diffg += R * T * x1 * np.log(x2 * P / P0)
-/tmp/ipykernel_2158/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
+/tmp/ipykernel_2170/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
   diffg += R * T * x1 * np.log(x2 * P / P0)
 

 

@@ -1576,9 +1576,9 @@ 
The Gibbs free energy of a reacting mixture and the equilibrium composition<
 
0.46959618248998036
 

 

-
/tmp/ipykernel_2158/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
+
/tmp/ipykernel_2170/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
   diffg += R * T * x1 * np.log(x2 * P / P0)
-/tmp/ipykernel_2158/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
+/tmp/ipykernel_2170/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
   diffg += R * T * x1 * np.log(x2 * P / P0)
 

 

@@ -2019,9 +2019,9 @@ 
Constrained minimization to find equilibrium compositions
/tmp/ipykernel_2158/1928982228.py:17: RuntimeWarning: invalid value encountered in log
+
/tmp/ipykernel_2170/1928982228.py:17: RuntimeWarning: invalid value encountered in log
   d * np.log(P) + yI * d * np.log(yI) +
-/tmp/ipykernel_2158/1928982228.py:18: RuntimeWarning: invalid value encountered in log
+/tmp/ipykernel_2170/1928982228.py:18: RuntimeWarning: invalid value encountered in log
   yB * d * np.log(yB) + yP1 * d * np.log(yP1) + yP2 * d * np.log(yP2))
 

 

@@ -2373,9 +2373,9 @@ 
Numerically calculating an effectiveness factor for a porous catalyst bead

 

-
/tmp/ipykernel_2158/4291268947.py:40: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2170/4291268947.py:40: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   eta_numerical = (np.trapz(k * Ca * 4 * np.pi * (r**2), r)
-/tmp/ipykernel_2158/4291268947.py:41: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+/tmp/ipykernel_2170/4291268947.py:41: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   / np.trapz(k * CAs * 4 * np.pi * (r**2), r))
 

 

@@ -3698,9 +3698,9 @@ 
What region is a point in
-
/tmp/ipykernel_2158/339476128.py:64: RuntimeWarning: invalid value encountered in scalar divide
+
/tmp/ipykernel_2170/339476128.py:64: RuntimeWarning: invalid value encountered in scalar divide
   m1 = y1 / x1
-/tmp/ipykernel_2158/339476128.py:64: RuntimeWarning: divide by zero encountered in scalar divide
+/tmp/ipykernel_2170/339476128.py:64: RuntimeWarning: divide by zero encountered in scalar divide
   m1 = y1 / x1
 

 

diff --git a/book/00-intro.html b/book/00-intro.html
index 2e89230f..7bec08de 100644
--- a/book/00-intro.html
+++ b/book/00-intro.html
@@ -816,7 +816,7 @@ 
scipy#<
           906177281,  1325485569,  1443712780,  1963025921, -2063369727,
             6098177,   553716061,   856765187,   588325653,    53813521,
            16973318,  -704760322,  1593690581,  -470014715,   872205571,
-           27328168,       50016,       32557,   756342280,       32557],
+           27328168,       50016,       32720,         208,           0],
        dtype=int32),
  'alist': array([0.00000000e+00, 2.25000000e+00, 7.67216743e-04, 2.10783652e-03,
         4.30872995e-03, 7.48622952e-03, 1.17307690e-02, 1.71108947e-02,
@@ -844,19 +844,19 @@ 
scipy#<
         2.01589600e-312, 2.33419537e-312, 2.22809558e-312, 2.14321575e-312,
         2.41907520e-312, 2.33419537e-312, 9.97338022e-313, 2.35541533e-312,
         2.27053550e-312, 1.64726287e+265]),
- 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.90861902e-310, 6.90861874e-310,
-        6.90861855e-310, 6.90861902e-310, 6.90861874e-310, 6.90861855e-310,
-        6.90861902e-310, 6.90861874e-310, 6.90861855e-310, 6.90861902e-310,
-        6.90861874e-310, 6.90861855e-310, 6.90861902e-310, 6.90861874e-310,
-        6.90861855e-310, 6.90861902e-310, 6.90861874e-310, 6.90861855e-310,
-        6.90861902e-310, 6.90861874e-310, 6.90861855e-310, 6.90861902e-310,
-        6.90861874e-310, 6.90861855e-310, 6.90861902e-310, 6.90861874e-310,
-        6.90861855e-310, 6.90861902e-310, 6.90861874e-310, 6.90861855e-310,
-        6.90861902e-310, 6.90861874e-310, 6.90861855e-310, 6.90861902e-310,
-        6.90861874e-310, 6.90861855e-310, 6.90861902e-310, 6.90861874e-310,
-        6.90861855e-310, 6.90861902e-310, 6.90861874e-310, 6.90861855e-310,
-        6.90861902e-310, 6.90861874e-310, 6.90861855e-310, 6.90861902e-310,
-        6.90861874e-310, 6.90861855e-310]),
+ 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.94332722e-310, 6.94332695e-310,
+        6.94332675e-310, 6.94332722e-310, 6.94332695e-310, 6.94332675e-310,
+        6.94332722e-310, 6.94332695e-310, 6.94332676e-310, 6.94332722e-310,
+        6.94332695e-310, 6.94332676e-310, 6.94332722e-310, 6.94332695e-310,
+        6.94332676e-310, 6.94332722e-310, 6.94332695e-310, 6.94332676e-310,
+        6.94332722e-310, 6.94332695e-310, 6.94332676e-310, 6.94332722e-310,
+        6.94332695e-310, 6.94332676e-310, 6.94332722e-310, 6.94332695e-310,
+        6.94332676e-310, 6.94332722e-310, 6.94332695e-310, 6.94332676e-310,
+        6.94332722e-310, 6.94332695e-310, 6.94332676e-310, 6.94332722e-310,
+        6.94332695e-310, 6.94332676e-310, 6.94332722e-310, 6.94332695e-310,
+        6.94332676e-310, 6.94332722e-310, 6.94332695e-310, 6.94332676e-310,
+        6.94332722e-310, 6.94332695e-310, 6.94332676e-310, 6.94332722e-310,
+        6.94332695e-310, 6.94332676e-310]),
  'elist': array([7.86630709e-09, 1.01263339e-14, 0.00000000e+00, 0.00000000e+00,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
@@ -882,7 +882,7 @@ 
scipy#<
 

 

 

-
/tmp/ipykernel_2191/843280888.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2202/843280888.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   (np.trapz(integrand(x1), x1) - I) / I
 

 

diff --git a/book/02-integration-1.html b/book/02-integration-1.html
index 07dceeb8..46bb550e 100644
--- a/book/02-integration-1.html
+++ b/book/02-integration-1.html
@@ -727,7 +727,7 @@ 
numpy.trapz
-
/tmp/ipykernel_2239/3604360318.py:4: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2249/3604360318.py:4: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   np.trapz(y, x)
 

 

@@ -953,7 +953,7 @@ 
Estimating the volume of a plug flow reactor
/tmp/ipykernel_2239/4086341036.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2249/4086341036.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   vol = np.trapz(y[0:i+1], X[0:i+1])
 

 

@@ -990,7 +990,7 @@ 
Estimating the volume of a plug flow reactor
/tmp/ipykernel_2239/427682055.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2249/427682055.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   vol = np.trapz(y[0:i+1], X[0:i+1])
 

 

@@ -1162,7 +1162,7 @@ 
Numerical quadrature - or integration of functions
 

 

-
/tmp/ipykernel_2239/36719416.py:4: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
+
/tmp/ipykernel_2249/36719416.py:4: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
   If increasing the limit yields no improvement it is advised to analyze 
   the integrand in order to determine the difficulties.  If the position of a 
   local difficulty can be determined (singularity, discontinuity) one will 
diff --git a/book/03-fode-1.html b/book/03-fode-1.html
index ce7bbd86..9d818e87 100644
--- a/book/03-fode-1.html
+++ b/book/03-fode-1.html
@@ -631,7 +631,7 @@ 
Homogeneous, first-order linear differential equations
 
(array([0., 0., 0., 0.]),
  array([1., 1., 1., 1.]),
- array([4.66267157e-310, 0.00000000e+000, 4.66166781e-310, 4.66166780e-310]))
+ array([4.68882412e-310, 0.00000000e+000, 4.68986134e-310, 4.68986136e-310]))
 

 

 

@@ -775,7 +775,7 @@ 
Homogeneous, first-order linear differential equations
 

 

-
<matplotlib.legend.Legend at 0x7f6ce689e4d0>
+
<matplotlib.legend.Legend at 0x7f22a8a9edd0>
 

 

 ../_images/0d992e05e05f92dc53b78d747da1fa725f1cb6fc66247847be3c6e338ba12bc2.png
@@ -1114,7 +1114,7 @@ 
scipy.integrate.solve_ivp
-
<matplotlib.legend.Legend at 0x7f6ce45c4810>
+
<matplotlib.legend.Legend at 0x7f22a67a9a10>
 

 

 ../_images/0f3cb0f20de8a66563583063f2afeb51738e8b0db5b5ace82e7cb68a5289387e.png
diff --git a/book/07-nla-1.html b/book/07-nla-1.html
index 21648f25..f8624ddd 100644
--- a/book/07-nla-1.html
+++ b/book/07-nla-1.html
@@ -854,7 +854,7 @@ 
Derivatives of functions
-
/tmp/ipykernel_2356/1845505028.py:6: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2364/1845505028.py:6: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   derivative(f, x0, dx=1e-6), 3 * x0**2  # the numerical and analytical derivative
 

 

@@ -899,9 +899,9 @@ 
Derivatives of functions
-
/tmp/ipykernel_2356/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2364/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   d0 = derivative(func, x0, dx=dx)
-/tmp/ipykernel_2356/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+/tmp/ipykernel_2364/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   dnew = derivative(func, x0, dx=dx)
 

 

@@ -937,9 +937,9 @@ 
Derivatives of functions
-
/tmp/ipykernel_2356/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2364/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   d0 = derivative(func, x0, dx=dx)
-/tmp/ipykernel_2356/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+/tmp/ipykernel_2364/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   dnew = derivative(func, x0, dx=dx)
 

 

@@ -982,7 +982,7 @@ 
fsolve#

 

-
/tmp/ipykernel_2356/1619064557.py:9: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+
/tmp/ipykernel_2364/1619064557.py:9: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   print(f'{float(ans):1.2f}')
 

 

@@ -1212,7 +1212,7 @@ 
Parameterized objective functions
-
/tmp/ipykernel_2356/2335501430.py:17: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+
/tmp/ipykernel_2364/2335501430.py:17: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   fa_exit[i] = ans
 

 

diff --git a/book/08-nla-2.html b/book/08-nla-2.html
index 4ca1b8ba..8b3bf259 100644
--- a/book/08-nla-2.html
+++ b/book/08-nla-2.html
@@ -721,7 +721,7 @@ 
Cubic equations of state
-
/tmp/ipykernel_2382/406724879.py:1: ComplexWarning: Casting complex values to real discards the imaginary part
+
/tmp/ipykernel_2390/406724879.py:1: ComplexWarning: Casting complex values to real discards the imaginary part
   float(R[0])
 

 

@@ -799,7 +799,7 @@ 
Other useful things to remember about polynomials
 

 

-
/tmp/ipykernel_2382/174692805.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2390/174692805.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   np.trapz(Y, X)
 

 

@@ -836,7 +836,7 @@ 
Other useful things to remember about polynomials
 

 

-
133 μs ± 399 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
+
130 μs ± 1.38 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
 

 

 

@@ -853,7 +853,7 @@ 
Other useful things to remember about polynomials
 

 

-
6.17 μs ± 14.2 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
+
6.26 μs ± 33 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
 

 

 

@@ -885,7 +885,7 @@ 
Other useful things to remember about polynomials
 

 

-
<function integrand at 0x7f47d0b13100>
+
<function integrand at 0x7f07721377e0>
 

 

 

@@ -1077,12 +1077,12 @@ 
Systems of nonlinear equations
-
Failed at guess [-2.4534185062140668, 6.954500081345638].
+
Failed at guess [-3.930484856676675, -0.5487466790617823].
 The iteration is not making good progress, as measured by the 
-  improvement from the last ten iterations.
+  improvement from the last five Jacobian evaluations.
 

 

-../_images/117ad6838a8ba47f3deb26f01d5bcc17d7824d39fa7ad4a5d8bb9f4467979785.png
+../_images/a650748df3cab2fe2c16f5f130bae44ce8852a4d6b41f4e734f8b4f885b560f8.png
 

 

 

@@ -1100,12 +1100,12 @@ 
Systems of nonlinear equations
-
Failed at guess [1.8824145352753363, -3.774484773749196].
+
Failed at guess [-9.253508275936262, -3.555979658767028].
 The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
 

 

-
array([2.14009532e-12, 6.51838208e-12])
+
array([1.05623848e-11, 2.48866106e-11])
 

 

 

diff --git a/book/09-bvp.html b/book/09-bvp.html
index c3a1118c..e2e8dad6 100644
--- a/book/09-bvp.html
+++ b/book/09-bvp.html
@@ -1076,7 +1076,7 @@ 
Concentration profile in a particle
0.008249311811255714
 

 

-
/tmp/ipykernel_2412/1627362779.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2423/1627362779.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz(c**2, sol.x))
 

 

diff --git a/book/10-min-max.html b/book/10-min-max.html
index 643b049d..7a53a992 100644
--- a/book/10-min-max.html
+++ b/book/10-min-max.html
@@ -664,7 +664,7 @@ 
Find the derivative, and solve for where it is zero
 

 

-
/tmp/ipykernel_2438/2917585576.py:4: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2449/2917585576.py:4: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   return derivative(f, x, dx=1e-6)
 

 

@@ -707,9 +707,9 @@ 
Newton-Raphson method of minima finding
-
/tmp/ipykernel_2438/4103338182.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2449/4103338182.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   yp = derivative(f, x0, dx=1e-6, n=1)
-/tmp/ipykernel_2438/4103338182.py:8: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+/tmp/ipykernel_2449/4103338182.py:8: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   ypp = derivative(f, x0, dx=1e-6, n=2)
 

 

diff --git a/book/11-regression.html b/book/11-regression.html
index 8771b452..2c256b88 100644
--- a/book/11-regression.html
+++ b/book/11-regression.html
@@ -818,7 +818,7 @@ 
Regression of data is a form of function minimization
 

 

-
/tmp/ipykernel_2464/3278399195.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2474/3278399195.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   dEdV = derivative(proxy, V, args=(pars,), dx=1e-6)
 

 

@@ -1055,6 +1055,35 @@ 
Uncertainty estimation

 

 

+

+
---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[23], line 1
+----> 1 from pycse import nlinfit
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/__init__.py:24
+     12 from .PYCSE import (
+     13     polyfit,
+     14     regress,
+   (...)
+     20     lbic,
+     21 )
+     22 from .utils import feq, flt, fgt, fle, fge, read_gsheet
+---> 24 from .hashcache import hashcache
+     26 # from .beginner import *
+     29 from IPython import get_ipython
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/hashcache.py:84
+     82 import inspect
+     83 import joblib
+---> 84 import orjson
+     85 import os
+     86 from pathlib import Path
+
+ModuleNotFoundError: No module named 'orjson'
+

+

+

 

 

 

@@ -1066,8 +1095,14 @@ 
Uncertainty estimation
 

 

-
1.328, [1.058 1.598], 0.0097
-0.026, [-0.002  0.055], 0.0010
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[24], line 1
+----> 1 pars, pars_ci, se = nlinfit(func, x, y, [a0, b0], alpha=0.00001)
+      3 for i, par in enumerate(pars):
+      4     print(f'{par:1.3f}, {np.round(pars_ci[i], 3)}, {se[i]:1.4f}')
+
+NameError: name 'nlinfit' is not defined
 

 

 

@@ -1112,7 +1147,17 @@ 
What about uncertainty on the predictions?
-../_images/8246e3ea35dc3b717992cad6318e9cb67ee0e12a9d548af14cd58aa4a1f631c8.png
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[26], line 2
+      1 p0_mean = pars[0]
+----> 2 p0_se = se[0]
+      4 p0_dist = np.random.normal(p0_mean, p0_se, 5000)
+      5 plt.hist(p0_dist, bins=20);
+
+NameError: name 'se' is not defined
+

+

 

 

 
So the idea is we can generate a distribution of the parameters

@@ -1128,12 +1173,16 @@ 
What about uncertainty on the predictions?
-
(np.float64(1.3206429192279479),
- np.float64(0.009663809666266444),
- np.float64(0.001027904909551584))
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[27], line 1
+----> 1 p1_dist = np.random.normal(pars[1], se[1], 5000)
+      3 y5 = [func(5, p0, p1) for p0, p1 in zip(p0_dist, p1_dist)]
+      4 plt.hist(y5)
+
+NameError: name 'se' is not defined
 

 

-../_images/76ea686970c415a6eb4adc4eff0a80794a05448692cf5f336963a88eded53c24.png
 

 

 
Well, in 20/20 hindsight, we might have guessed the uncertainty in the asymptote would be just like the uncertainty in the \(a\) parameter. In this case, it is appropriate to use three significant figures given the uncertainty on the answer. A useful guideline is that the 95% confidence interval is about ± 2 σ. At ± 1 σ you only have about a 60% confidence interval.

@@ -1144,7 +1193,12 @@ 
What about uncertainty on the predictions?
-
At x=5, y=1.321 +- 0.019 at about the 95% confidence level.
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[28], line 1
+----> 1 print(f'At x=5, y={np.mean(y5):1.3f} +- {2 * np.std(y5):1.3f} at about the 95% confidence level.')
+
+NameError: name 'y5' is not defined
 

 

 

diff --git a/book/12-nonlinear-regression-2.html b/book/12-nonlinear-regression-2.html
index 86a987a5..46c8f539 100644
--- a/book/12-nonlinear-regression-2.html
+++ b/book/12-nonlinear-regression-2.html
@@ -842,6 +842,9 @@ 
Least Median regression
[0.26804924 1.18981534]
 

 

+

+

+

 ../_images/a1e50f72bc5e3e5c0bb353a9d1e93896ed929fda57d1248d914ac7ea47485f81.png
 

 

diff --git a/book/15-intro-linear-algebra.html b/book/15-intro-linear-algebra.html
index 2a943707..44da04d8 100644
--- a/book/15-intro-linear-algebra.html
+++ b/book/15-intro-linear-algebra.html
@@ -1257,7 +1257,7 @@ 
The determinant
-
np.float64(-0.8251799537299618)
+
np.float64(2.5948136423134778)
 

 

 

@@ -1276,9 +1276,9 @@ 
The inverse
-
array([[-0.08237548, -2.40516951,  2.27997091],
-       [ 1.7355912 ,  1.11772446, -1.36649086],
-       [-1.30650852,  1.23851417,  0.86025868]])
+
array([[-2.99709528,  0.58568287,  1.82496278],
+       [-0.79958809, -3.82120149,  5.02490251],
+       [ 3.80901144,  2.59474342, -3.52230933]])
 

 

 

@@ -1569,7 +1569,7 @@ 
Solving linear algebraic equations
-../_images/73fc8eb196dc5a69b67632f01b5ede5c59566458ebb0f3ae0a94f7e8eea96af3.png
+../_images/2970fd15cd8404f793111c2bb1242cd323eb58f631cb8a6bee963292099f7e0f.png
 

 

 
As usual, there is a function we can use to solve this.

@@ -1604,7 +1604,7 @@ 
Solving linear algebraic equations
-../_images/686a8c88a0f5767bd016f1a21ca7ddd897daf783768c94e205f3218ea2199428.png
+../_images/86729e9c0d3a2485d8b401bd43a042f1c013a9033f2b2c9541cdfab3b0ed2f6c.png
 

 

 
You can see by inspection that solve must not be using an inverse to solve these equations; if it did, it would take much longer to solve them. It is remarkable that we can solve ~5000 simultaneous equations here in about 1 second!

diff --git a/book/17-linear-algebra-2.html b/book/17-linear-algebra-2.html
index d8e6a284..876006f7 100644
--- a/book/17-linear-algebra-2.html
+++ b/book/17-linear-algebra-2.html
@@ -721,7 +721,7 @@ 
Interpolation libraries
 

 

-
/tmp/ipykernel_2613/3098855599.py:5: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2627/3098855599.py:5: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   fsolve(obj, 7)
 

@@ -817,9 +817,9 @@ 
Eigenvalues
-
array([[1.34046424, 0.86178149, 0.91189138],
-       [0.86178149, 1.22461304, 0.99286913],
-       [0.91189138, 0.99286913, 0.25113406]])
+
array([[0.56691387, 1.02949137, 0.80383786],
+       [1.02949137, 0.4757645 , 1.1845114 ],
+       [0.80383786, 1.1845114 , 0.13820279]])
 

 

 

@@ -834,7 +834,7 @@ 
Eigenvalues
-
array([ 3.6173277 ,  0.84262328, -0.14924254])
+
array([ 3.0464552 ,  0.46997778, -0.96316615])
 

 

 

@@ -846,7 +846,8 @@ 
Eigenvalues
-
array([ 1.56234425, -0.69920381,  0.37382497])
+
array([ 1.29838691+0.j        , -0.06554573+0.29593574j,
+       -0.06554573-0.29593574j])
 

 

 

@@ -860,7 +861,7 @@ 
Eigenvalues
-
(np.float64(4.310708443232259), np.float64(4.310708443232259))
+
(np.float64(2.5532668319609813), np.float64(2.5532668319609813))
 

 

 

@@ -874,7 +875,7 @@ 
Eigenvalues
-
np.float64(4.310708443232257)
+
np.float64(2.553266831960977)
 

 

 

@@ -888,7 +889,7 @@ 
Eigenvalues
-
(np.float64(-0.4548979121642612), np.float64(-0.4548979121642611))
+
(np.float64(-1.3790288019796235), np.float64(-1.3790288019796262))
 

 

 

@@ -902,10 +903,10 @@ 
Eigenvalues
-
(array([ 3.6173277 ,  0.84262328, -0.14924254]),
- array([[-0.43844358, -0.75946759, -0.48059983],
-        [-0.63020869,  0.64103856, -0.43807143],
-        [-0.64078407, -0.11080858,  0.75968232]]))
+
(array([ 3.0464552 ,  0.46997778, -0.96316615]),
+ array([[-0.72637632, -0.49412408, -0.47772255],
+        [-0.44232072,  0.86808605, -0.22534192],
+        [-0.52605115, -0.04762355,  0.84911847]]))
 

 

 

@@ -919,7 +920,7 @@ 
Eigenvalues
-
(np.float64(1.0), np.float64(0.9999999999999999))
+
(np.float64(1.0), np.float64(1.0))
 

 

 

@@ -931,8 +932,8 @@ 
Eigenvalues
-
(array([-1.4752229 , -2.2740669 , -2.27964711]),
- array([-1.58599412, -2.74724317, -1.73848708]))
+
(array([-2.17208843, -1.35197405, -1.64061995]),
+ array([-2.21287293, -1.50532686, -1.45536035]))
 

 

 

@@ -945,8 +946,8 @@ 
Eigenvalues
-
(array([-1.58599412, -2.27967136, -2.31792598]),
- array([-1.58599412, -2.27967136, -2.31792598]))
+
(array([-2.21287293, -1.34751027, -1.60259127]),
+ array([-2.21287293, -1.34751027, -1.60259127]))
 

 

 

@@ -958,9 +959,7 @@ 
Eigenvalues
-
[np.float64(0.9999999999999999),
- np.float64(0.9999999999999999),
- np.float64(1.0)]
+
[np.float64(1.0), np.float64(0.9999999999999999), np.float64(1.0)]
 

 

 

@@ -1007,10 +1006,10 @@ 
Eigenvalues
-
(array([-0.14924254,  0.84262328,  3.6173277 ]),
- array([[-0.48059983, -0.75946759, -0.43844358],
-        [-0.43807143,  0.64103856, -0.63020869],
-        [ 0.75968232, -0.11080858, -0.64078407]]))
+
(array([-0.96316615,  0.46997778,  3.0464552 ]),
+ array([[-0.47772255, -0.49412408, -0.72637632],
+        [-0.22534192,  0.86808605, -0.44232072],
+        [ 0.84911847, -0.04762355, -0.52605115]]))
 

 

 

diff --git a/book/23-gp.html b/book/23-gp.html
index 3e1d0408..da6ea4f2 100644
--- a/book/23-gp.html
+++ b/book/23-gp.html
@@ -780,7 +780,7 @@ 
GPR by example
-
array([0.74444415, 0.75450807])
+
array([0.75609433, 0.76611267])
 

 

 

@@ -796,7 +796,7 @@ 
GPR by example
-../_images/0050a61f7d72cf69e6ba28f3af534427aa0f17ca475714e7147b1ce665e02212.png
+../_images/185561ef13d978ff02890cddf31411df4bd1f9044852321c3a1144851bca73f8.png
 

 

 
That is not bad, but clearly not great. With a \(\lambda=0.15\), only one data point is contributing to the estimate, the other points have only small contributions because they are far from points we are estimating. This is a feature of the assumption we made about the covariance with \(\lambda\). This means we do not have enough data to make a very good estimate. We can see this if we try this with a much more dense data set.

@@ -830,7 +830,7 @@ 
GPR by example
Known data step size is 0.05
 

 

-../_images/f70b860ecbaf3196c207c1de16b6f6492491fb9b9bf8b35251ffd3155e9499ac.png
+../_images/64a85faa861ef2b909927bff019a5b87108b18719b847a6d4a5c36b760f76c3c.png
 

 

 
Now you can see that we do very well in estimating the values. The length scale here might even be considered too short, since it is evident we are fitting trends in the noise.

@@ -861,7 +861,7 @@ 
GPR by example
Known data step size is 0.05
 

 

-../_images/037d8bf942fa415fef4d530efbba91d44bb1c62f60843951caba1dfde2ef1dac.png
+../_images/932e36ccb4fc9307d745dfa906ca69c9f4022015d6febb5f4e29b6bc480247d6.png
 

 

 

@@ -925,7 +925,7 @@ 
Underfitting in GPR
-../_images/780183c7d0a825258379cd4fd821b87f2d486b41cc7caefc42a2f2bbea57c2c7.png
+../_images/9b555ddfca7c3891152df39fcf4236132b527664918fa0dd833c9b8ec32a30dd.png
 

 

 

@@ -950,7 +950,7 @@ 
Overfitting in GPR
-../_images/45fcb0d8809b129b1fc26187a3f14355274421639381fe50f66a1d1bb25f756e.png
+../_images/3420945fa0b573f7f9cc57cf98f771d699f6cf2624e8390d00baec6f9f584031.png
 

 

 
@@ -991,10 +991,10 @@ 
Finding the hyperparameters in GPR
-
array([1.        , 0.07753928])
+
array([1.       , 0.0722918])
 

 

-../_images/2e4be142effefc99f7236016d9a9a94fcf83d80d474e0c6d9147ada8a76dd827.png
+../_images/1e6c276e86414d288392ac50a0a3e58e0f86835ad9256e1b1df23a6608f47f68.png
 

 

 

@@ -1029,10 +1029,10 @@ 
Finding the hyperparameters in GPR
-
array([1.        , 0.22035713, 0.19674719])
+
array([1.        , 0.20479533, 0.18792282])
 

 

-../_images/036066088c58366f99c2e70766900577ff7860f454fc0be1d0701e00c27695aa.png
+../_images/6147093732edfb87bc36961f6baaa1c79364b5b93ffdeefb0054c3009fbeb8e9.png
 

 

 
Note that we still see some wiggles in the fit, indicating some minor degree of overfitting with the optimal hyperparameters. That is happening because we fit to all the data, and do not use any to estimate how good our fits are. You can use train/test data splits for GPR for this purpose as well, but it is out of the scope of the lecture today.

@@ -1067,7 +1067,7 @@ 
An example with a linear kernel
-../_images/f47779dae16e5588780456870c7b09159430fd005841a9ccae3339048728ad35.png
+../_images/d45fc63f45e9dbae3589ad7d6fbf443bf9e87756f35bd94644a2fcb370eaa06e.png
 

 

 
As before, we setup a log likelihood function and maximize it to get estimates for the parameters.

@@ -1090,15 +1090,15 @@ 
An example with a linear kernel
  message: Desired error not necessarily achieved due to precision loss.
   success: False
    status: 2
-      fun: 7.522897839901731
-        x: [-1.695e-05  6.406e-01 -1.498e+00]
-      nit: 32
-      jac: [ 1.490e-06  2.503e-05 -1.490e-05]
- hess_inv: [[ 2.296e-03  8.492e-04 -1.171e-03]
-            [ 8.492e-04  3.212e-04 -4.340e-04]
-            [-1.171e-03 -4.340e-04  5.991e-04]]
-     nfev: 336
-     njev: 81
+      fun: 7.459536243764161
+        x: [-6.473e-06  6.249e-01 -1.555e+00]
+      nit: 29
+      jac: [ 3.576e-07  1.204e-05  2.384e-06]
+ hess_inv: [[ 5.631e-02  2.903e-02  4.855e-02]
+            [ 2.903e-02  2.535e-02  1.529e-02]
+            [ 4.855e-02  1.529e-02  5.101e-02]]
+     nfev: 240
+     njev: 60
 

 

 

@@ -1126,7 +1126,7 @@ 
An example with a linear kernel
-../_images/1d5499692d000aab584dda64cb4a1aea993be76ca8f7b9c0feb903ddacdb445f.png
+../_images/72f8c4d252cd90ced8d7e15b87b8d7a7f25e73a34b498b168bb104ff6873d4db.png
 

 

 
Note that now, we get linear extrapolation, because we are using a linear kernel. Note also that the hyperparameters do not mean anything in particular to us. They do not include the slope or intercept. We can work those out pretty easily though. The intercept is just a prediction at \(x=0\):

@@ -1139,7 +1139,7 @@ 
An example with a linear kernel
-
array([2.98505269])
+
array([3.02382035])
 

 

 

@@ -1152,7 +1152,7 @@ 
An example with a linear kernel
-
np.float64(1.993244807139879)
+
np.float64(1.9445415617297417)
 

 

 

@@ -1186,7 +1186,7 @@ 
Uncertainty quantification in GPR
-../_images/506272a3ca79da105aad4872aa9a7baaec4e4253661d8d29d249e7cd514463b3.png
+../_images/44a5bac709afcfda9028a109328c17f6782fb489aad3cec5b73438c82e7f889a.png
 

 

 
@@ -1204,7 +1204,7 @@ 
Combining kernels
-../_images/f145097bc618bd6b50b22ac8ef080f643ace3a1fdbaafb1554ef1a1509ff5c4c.png
+../_images/591301230d76a46d78025b5eb226f1c0abcefa7ac662e0ea380186a6e7632804.png
 

 

 
This looks like a sin wave superimposed on a line. A periodic kernel is defined as

@@ -1229,19 +1229,19 @@ 
Combining kernels
  message: Desired error not necessarily achieved due to precision loss.
   success: False
    status: 2
-      fun: 21.176278999791734
-        x: [-1.252e-06  3.975e-01 -1.443e+00  6.508e-01  9.330e-01
-            -3.468e-01]
-      nit: 40
-      jac: [ 2.146e-06  1.407e-05 -1.192e-05  6.437e-06  8.178e-05
-            -1.407e-05]
- hess_inv: [[ 3.545e+01  8.521e-01 ...  2.805e-01 -7.937e-01]
-            [ 8.521e-01  2.491e-02 ...  7.136e-03 -2.049e-02]
+      fun: 21.498555183755244
+        x: [-1.435e-07  4.091e-01 -1.399e+00  6.617e-01  9.343e-01
+            -3.425e-01]
+      nit: 45
+      jac: [ 5.960e-06  1.335e-05  9.537e-06  1.144e-05  6.914e-06
+             1.287e-05]
+ hess_inv: [[ 2.073e-02 -1.787e-04 ...  7.153e-04  5.799e-03]
+            [-1.787e-04  4.242e-03 ...  7.165e-04  2.181e-04]
             ...
-            [ 2.805e-01  7.136e-03 ...  2.405e-03 -6.535e-03]
-            [-7.937e-01 -2.049e-02 ... -6.535e-03  2.461e-02]]
-     nfev: 504
-     njev: 72
+            [ 7.153e-04  7.165e-04 ...  3.366e-04  5.197e-04]
+            [ 5.799e-03  2.181e-04 ...  5.197e-04  5.535e-03]]
+     nfev: 1044
+     njev: 147
 

 

 

@@ -1268,7 +1268,7 @@ 
Combining kernels
-../_images/ea211fe3fa37e9bf3f862e7caa0c530221eb515e137fedfe2b9f6f11c187fbc5.png
+../_images/ed76276891751cd4035e534c1ade5f12b571f896377a444b5c8625207c6b9eec.png
 

 

 
Note that we get oscillatory + linear extrapolation behavior!

diff --git a/docs/about.html b/docs/about.html
index 5cd47228..082a2bc3 100644
--- a/docs/about.html
+++ b/docs/about.html
@@ -582,11 +582,11 @@ 
About pycse
-
uname_result(system='Linux', node='fv-az525-184', release='6.5.0-1022-azure', version='#23~22.04.1-Ubuntu SMP Thu May  9 17:59:24 UTC 2024', machine='x86_64')
+
uname_result(system='Linux', node='fv-az1108-758', release='6.5.0-1022-azure', version='#23~22.04.1-Ubuntu SMP Thu May  9 17:59:24 UTC 2024', machine='x86_64')
 Linux
 ('64bit', 'ELF')
 x86_64
-fv-az525-184
+fv-az1108-758
 Linux-6.5.0-1022-azure-x86_64-with-glibc2.35
 x86_64
 ('main', 'Jun 25 2024 18:25:01')
@@ -629,7 +629,32 @@ 
About the Python packages
-
'2.2.1'
+
---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[3], line 1
+----> 1 import pycse
+      2 pycse.__version__
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/__init__.py:24
+     12 from .PYCSE import (
+     13     polyfit,
+     14     regress,
+   (...)
+     20     lbic,
+     21 )
+     22 from .utils import feq, flt, fgt, fle, fge, read_gsheet
+---> 24 from .hashcache import hashcache
+     26 # from .beginner import *
+     29 from IPython import get_ipython
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/hashcache.py:84
+     82 import inspect
+     83 import joblib
+---> 84 import orjson
+     85 import os
+     86 from pathlib import Path
+
+ModuleNotFoundError: No module named 'orjson'
 

 

 

diff --git a/docs/beginner.html b/docs/beginner.html
index afe4ae93..52277724 100644
--- a/docs/beginner.html
+++ b/docs/beginner.html
@@ -580,6 +580,35 @@ 
pycse - Beginner mode

 

 

+

+
---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[1], line 1
+----> 1 from pycse.beginner import *
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/__init__.py:24
+     12 from .PYCSE import (
+     13     polyfit,
+     14     regress,
+   (...)
+     20     lbic,
+     21 )
+     22 from .utils import feq, flt, fgt, fle, fge, read_gsheet
+---> 24 from .hashcache import hashcache
+     26 # from .beginner import *
+     29 from IPython import get_ipython
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/hashcache.py:84
+     82 import inspect
+     83 import joblib
+---> 84 import orjson
+     85 import os
+     86 from pathlib import Path
+
+ModuleNotFoundError: No module named 'orjson'
+

+

+

 

 
 

@@ -601,7 +630,12 @@ 
Avoiding indexing in lists
-
1
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[3], line 1
+----> 1 first(a)
+
+NameError: name 'first' is not defined
 

 

 

@@ -613,7 +647,12 @@ 
Avoiding indexing in lists
-
2
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[4], line 1
+----> 1 second(a)
+
+NameError: name 'second' is not defined
 

 

 

@@ -625,7 +664,12 @@ 
Avoiding indexing in lists
-
3
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[5], line 1
+----> 1 third(a)
+
+NameError: name 'third' is not defined
 

 

 

@@ -637,7 +681,12 @@ 
Avoiding indexing in lists
-
4
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[6], line 1
+----> 1 fourth(a)
+
+NameError: name 'fourth' is not defined
 

 

 

@@ -649,7 +698,12 @@ 
Avoiding indexing in lists
-
5
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[7], line 1
+----> 1 fifth(a)
+
+NameError: name 'fifth' is not defined
 

 

 

@@ -662,7 +716,12 @@ 
Avoiding indexing in lists
-
9
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[8], line 1
+----> 1 nth(a, 8)
+
+NameError: name 'nth' is not defined
 

 

 

@@ -678,7 +737,12 @@ 
functional approach to slicing
-
[6, 7, 8, 9]
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[9], line 1
+----> 1 cut(a, 5)
+
+NameError: name 'cut' is not defined
 

 

 

@@ -692,7 +756,14 @@ 
functional approach to slicing
-
[6, 7]
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[10], line 3
+      1 # get index 5..7
+      2 # as with Python, the stop position is not inclusive. It means up to but not including the stop.
+----> 3 cut(a, start=5, stop=7)
+
+NameError: name 'cut' is not defined
 

 

 

@@ -705,7 +776,13 @@ 
functional approach to slicing
-
[1, 3, 5, 7, 9]
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[11], line 2
+      1 # get every other element starting at index=0
+----> 2 cut(a, step=2)
+
+NameError: name 'cut' is not defined
 

 

 

@@ -721,7 +798,12 @@ 
Other pieces of a list
 

 

-
9
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[12], line 1
+----> 1 last(a)
+
+NameError: name 'last' is not defined
 

 

 

@@ -734,7 +816,13 @@ 
Other pieces of a list
 

 

-
[2, 3, 4, 5, 6, 7, 8, 9]
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[13], line 2
+      1 # everything past the first element
+----> 2 rest(a)
+
+NameError: name 'rest' is not defined
 

 

 

@@ -747,7 +835,13 @@ 
Other pieces of a list
 

 

-
[1, 2, 3, 4, 5, 6, 7, 8]
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[14], line 2
+      1 # everything but the last element
+----> 2 butlast(a)
+
+NameError: name 'butlast' is not defined
 

 

 

@@ -776,7 +870,7 @@ 
A better fsolve
-
/tmp/ipykernel_2783/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2798/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   fsolve(f, 2.5)
 

@@ -799,7 +893,7 @@ 
A better fsolveCell In[17], line 1
 ----> 1 nsolve(f, np.sqrt(2.5))
 
-NameError: name 'np' is not defined
+NameError: name 'nsolve' is not defined
 

 

 

@@ -820,7 +914,14 @@ 
Simpler integration
-
0.33333333333333337
+
---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Cell In[18], line 4
+      1 def f(x):
+      2     return x**2
+----> 4 integrate(f, 0, 1)
+
+NameError: name 'integrate' is not defined
 

 

 

diff --git a/docs/execution-statistics.html b/docs/execution-statistics.html
index 61811742..5ec5ddc7 100644
--- a/docs/execution-statistics.html
+++ b/docs/execution-statistics.html
@@ -513,225 +513,225 @@ 
Build statistics
blog/basic-python

-
2024-07-06 18:26

+
2024-07-07 18:12

 
force

-
2.83

+
3.8

 
✅

 
 
blog/data-analysis

-
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+
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3.52

+
3.86

 
✅

 
 
blog/differential-equations

-
2024-07-06 18:26

+
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9.98

+
10.13

 
✅

 
 
blog/interpolation

-
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force

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+
2.03

 
✅

 
 
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force

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+
1.68

 
✅

 
 
blog/math

-
2024-07-06 18:26

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force

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+
4.71

 
✅

 
 
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-
2024-07-06 18:26

+
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force

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2.94

+
3.13

 
✅

 
 
blog/optimization

-
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2.23

 
✅

 
 
blog/plotting

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3.05

+
3.16

 
✅

 
 
blog/programming

-
2024-07-06 18:27

+
2024-07-07 18:12

 
force

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1.45

+
1.47

 
✅

 
 
blog/statistics

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4.23

+
4.26

 
✅

 
 
blog/units

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+
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1.2

 
✅

 
 
blog/worked-examples

-
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+
11.36

 
✅

 
 
book/00-intro

-
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+
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✅

 
 
book/01-jupyter

-
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+
1.71

 
✅

 
 
book/02-integration-1

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+
2.65

 
✅

 
 
book/03-fode-1

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+
2.35

 
✅

 
 
book/04-fode-2

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+
5.3

 
✅

 
 
book/05-nth-odes

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✅

 
 
book/07-nla-1

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2.27

 
✅

 
 
book/08-nla-2

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18.09

 
✅

 
 
book/09-bvp

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2.89

 
✅

 
 
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+
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book/12-nonlinear-regression-2

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102.26

 
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book/21-machine-learning

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2024-07-06 18:30

+
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force

-
2.46

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2.71

 
✅

 
 
book/23-gp

-
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force

-
3.1

+
3.15

 
✅

 
 
docs/about

-
2024-07-06 18:30

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force

-
2.2

+
2.4

 
✅

 
 
docs/beginner

-
2024-07-06 18:30

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force

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2.04

+
1.95

 
✅

 
 
docs/utils

-
2024-07-06 18:30

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force

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2.15

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2.54

 
✅

 
 
diff --git a/docs/pycse.html b/docs/pycse.html
index e03addc9..fa32e73b 100644
--- a/docs/pycse.html
+++ b/docs/pycse.html
@@ -521,20 +521,8 @@ 
 Contents 

 
  • read_gsheet()
    • 
 
 
-
  • pycse.plotly
-
    • 
-
  • pycse.hashcache
-
    • 
+
  • pycse.plotly
    • 
+
  • pycse.hashcache
    • 
 
             
         
    
@@ -679,6 +667,7 @@ 
    Documentationupper bound for smallest allowed Hessian eigenvalue
    
 
    efeigenvalue factor for scaling Hessian
    
 
    This function uses numdifftools for the Hessian and Jacobian.
    
+
    See https://en.wikipedia.org/wiki/Prediction_interval#Unknown_mean,_unknown_variance
    
 
 
 
    Returns:
    
@@ -736,10 +725,12 @@ 
    Documentationconfidence level, 95% = 0.05
    
 
    ubupper bound for smallest allowed Hessian eigenvalue
    
 
    efeigenvalue factor for scaling Hessian
    
+
    See See https://en.wikipedia.org/wiki/Prediction_interval#Unknown_mean,_unknown_variance
    
 
    Returns
    
 
    y, yint, pred_se
    
 
    ythe predicted values
    
-
    yintan array of predicted confidence intervals
    
+
    yint: confidence interval
    
+
    pred_se: std error on predictions.
    
 
 
 
@@ -763,14 +754,14 @@ 
    Documentationa vector of values you want to fit
    
 
    alpha100*(1 - alpha) confidence level
    
-
    ags and kwargs are passed to np.linalg.lstsq
    
+
    args and kwargs are passed to np.linalg.lstsq
    
 
 
 
    Returns:
    
 
    
 
    [b, bint, se]
    
 
    b is a vector of the fitted parameters
    
-
    bint is a 2D array of confidence intervals
    
+
    bint is an array of confidence intervals bint[0] is the lower, bint[1] is the upper level.
    
 
    se is an array of standard error for each parameter.
    
 
    
 
    
@@ -840,127 +831,11 @@ 
    Documentation
-
    pycse.plotly#
    
-
    Module for using plotly with orgmode.
    
-
    This monkey-patches go.Figure.show to provide a png image for org-mode, and an
-html file that is saved that you can click on in org-mode to see the interactive
-version.
    
-
    
-
    
-pycse.plotly.myshow(self, *args, **kwargs)#
    
-
    Make a PNG image to display for plotly.
    
-
    
-
-
    
-
    
-
    pycse.hashcache#
    
-
    hashcache - a decorator for persistent, file/hash-based cache
    
-
    I found some features of joblib were unsuitable for how I want to use a cache.
    
-
    1. The “file” Python thinks the function is in is used to save the results in
-joblib, which leads to repeated runs if you run the same code in Python,
-notebook or stdin, and means the cache is not portable to other machines, and
-maybe not even in time since temp directories and kernel parameters are
-involved. I could not figure out how to change those in joblib.
    
-
    2. joblib uses the function source code in the hash, so inconsequential changes
-like whitespace, docstrings and comments change the hash.
    
-
    This library aims to provide a simpler version of what I wish joblib did for me.
    
-
    Results are cached based on a hash of the function name, argnames, bytecode, arg
-values and kwarg values. I use joblib.hash for this. This means any two
-functions with the same bytecode, even if they have different names, will cache
-to the same result.
    
-
    The cache location is set as a function attribute:
    
-
    
-
    hashcache.cache = ‘./cache’
    
-
    
-
    This is alpha, proof of concept code. Test it a lot for your use case. The API
-is not stable, and subject to change.
    
-
    Some things to do:
    
-
    1. the function attributes are kind of weird, maybe these should be decorator
-arguments.
    
-
    Pros:
    
-
    1. File-based cache which means many functions can run in parallel reading and
-writing, and you are limited only by file io speeds, and disk space.
    
-
    2. semi-portability. The cache could be synced across machines, and caches
-can be merged with little risk of conflict.
    
-
      
-
    1. No server is required. Everything is done at the OS level.
      2. 
-
    
-
    4. Extendability. You can define your own functions for loading and dumping
-data.
    
-
    Cons:
    
-
    1. hashes are fragile and not robust. They are fragile with respect to any
-changes in how byte-code is made, or via mutable arguments, etc. The hashes are
-not robust to system level changes like library versions, or global variables.
-The only advantage of hashes is you can compute them.
    
-
    2. File-based cache which means if you generate thousands of files, it can be
-slow to delete them. Although it should be fast to access the results since you
-access them directly by path, it will not be fast to iterate over all the
-results, e.g. if you want to implement some kind of search or reporting.
    
-
    3. No server. You have to roll your own update strategy if you run things on
-multiple machines that should all cache to a common location.
    
-
    
-
    Changelog#
    
-
    [2023-09-23 Sat] Changed hash signature (breaking change). It is too difficult
-to figure out how to capture global state, and the use of internal variable
-names is not consistent with using the bytecode to be insensitive to
-unimportant variable name changes.
    
-
    Pulled out some functions for loading and dumping data. This is a precursor to
-enabling other backends like lmdb or sqlite instead of files. You can then
-simply provide new functions for this.
    
+
    
+
    pycse.plotly#
    
 
    
-
    
-
    
-pycse.hashcache.dump_data(hsh, data, verbose)#
    
-
    Dump DATA into HSH.
    
-
    
-
-
    
-
    
-pycse.hashcache.get_hash(func, args, kwargs)#
    
-
    Get a hash for running FUNC(ARGS, KWARGS).
    
-
    This is the most critical feature of hashcache as it provides a key to store
-and look up results later. You should think carefully before changing this
-function, it breaks past caches.
    
-
    FUNC should be as pure as reasonable. This hash is insensitive to global
-variables.
    
-
    The hash is on the function name, bytecode, and a standardized kwargs
-including defaults. We use bytecode because it is insensitive to things like
-whitespace, comments, docstrings, and variable name changes that don’t
-affect results. It is assumed that two functions with the same name and
-bytecode will evaluate to the same result.
    
-
    
-
-
    
-
    
-pycse.hashcache.get_hashpath(hsh)#
    
-
    Return path to file for HSH.
    
-
    
-
-
    
-
    
-pycse.hashcache.get_standardized_args(func, args, kwargs)#
    
-
    Returns a standardized dictionary of kwargs for func(args, kwargs)
    
-
    This dictionary includes default values, even if they were not called.
    
-
    
-
-
    
-
    
-pycse.hashcache.hashcache(verbose=False, loader=<function load_data>, dumper=<function dump_data>)#
    
-
    Cache results by hash of the function, arguments and kwargs.
    
-
    Set hashcache.cache to the directory you want the cache saved in.
-Default = cache
    
-
    
-
-
    
-
    
-pycse.hashcache.load_data(hsh, verbose=False)#
    
-
    Load data for HSH.
    
-
    HSH is a string for the hash associated with the data you want.
    
-
    Returns success, data. If it succeeds, success with be True. If the data
-does not exist yet, sucess will be False, and data will be None.
    
-
    
-
+
    
+
    pycse.hashcache#
    
 
    
 
    
 
@@ -1050,20 +925,8 @@ 
    Changelogread_gsheet()
 
 
-
  • pycse.plotly
-
    • 
-
  • pycse.hashcache
-
    • 
+
  • pycse.plotly
    • 
+
  • pycse.hashcache
    • 
 
   
    
 
diff --git a/docs/utils.html b/docs/utils.html
index f5ed515d..98c05727 100644
--- a/docs/utils.html
+++ b/docs/utils.html
@@ -600,7 +600,32 @@ 
    Float comparisons
-
    True
+
    ---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[2], line 1
+----> 1 from pycse.utils import feq
+      3 feq(0.3, 0.1 + 0.2)
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/__init__.py:24
+     12 from .PYCSE import (
+     13     polyfit,
+     14     regress,
+   (...)
+     20     lbic,
+     21 )
+     22 from .utils import feq, flt, fgt, fle, fge, read_gsheet
+---> 24 from .hashcache import hashcache
+     26 # from .beginner import *
+     29 from IPython import get_ipython
+
+File /opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/pycse/hashcache.py:84
+     82 import inspect
+     83 import joblib
+---> 84 import orjson
+     85 import os
+     86 from pathlib import Path
+
+ModuleNotFoundError: No module named 'orjson'
 
    
 
    
 
    
diff --git a/genindex.html b/genindex.html
index a0621f2e..dfcc33a6 100644
--- a/genindex.html
+++ b/genindex.html
@@ -440,10 +440,7 @@ 
    Index
    
 
 
    
  B
- | D
  | F
- | G
- | H
  | I
  | L
  | M
@@ -460,14 +457,6 @@ 
    B
    
   
 
 
-
    D
    
-
-  
-
    
-
 
    F
    
 
    
   
      
@@ -486,28 +475,6 @@ 
      F
      
   
    		
 
    
 
-
    G
    
-
-  
-  
-
    
-
-
    H
    
-
-  
-
    
-
 
    I
    
 
-  
    
   
 
    
 
 
    N
    
@@ -575,28 +530,14 @@ 
    P
    
       
  • predict() (in module pycse.PYCSE)
 
    • 
       
  • 
-    pycse.hashcache
-
-      
    • 
-      
  • 
-    pycse.plotly
-
-      
    • 
-  
-  
+  
      
       
    • 
     pycse.utils
 
diff --git a/objects.inv b/objects.inv
index 8a2ffcc42b4577acb93d252018aca5b47f164b88..c697dbda19ba19ac62dd2dc14c744f9c09dffb0f 100644
GIT binary patch
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aF*CNqjwudvBH7}-gz($`UG*P7$td}nI4xZO

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z^@aisAnNSR`?v%)4k6D<jk&c{n
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zkf!!sY7X{7g!~0hXsEP$z-3~A6o2>PsbdYPSc|XuxQ&&_^3OD$bT=FnSq`GT#~%u{2DvW59)^j<>X
z5Wn3}s5n})`-Edq_szw>L|Z76GPR2Cp8eKZWOnd!$=eu~akw6F;W
z%_?lhIQ~YUK^l`d7z7w1_Pi2GO~>m*fjD$T$?M)6et9ATzvo38CS`tEIcpR;@zEpptTXdDjw*PCPUuVe@W{-&%d4)BuW
z)R1h?rAPGAK5^l3m0afN9^Z3W=$iYi?xP&Hp(|ZCt&6n@`FdLj4xKz~NpBTg1n0)5
wE!;)s98E`iMZX}0-&Z`*Nc#XR9v5bUwooy}aSB9P+)Ge@?fPython Module Index
    
        
        pycse
        
-     
-       
-          
-       pycse.hashcache
-       
-     
-       
-          
-       pycse.plotly
-       
      
        
           
diff --git a/searchindex.js b/searchindex.js
index df464e8e..47483bf4 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"2-point vs. 4-point numerical derivatives": [[6, "point-vs-4-point-numerical-derivatives"]], "2d arrays": [[0, "d-arrays"]], "3D arrays": [[0, "id2"]], "A better fsolve": [[38, "a-better-fsolve"]], "A harder problem": [[3, "a-harder-problem"]], "A nonlinear BVP": [[2, "a-nonlinear-bvp"]], "A novel way to numerically estimate the derivative of a function - complex-step derivative approximation": [[6, "a-novel-way-to-numerically-estimate-the-derivative-of-a-function-complex-step-derivative-approximation"]], "A simple first order ode evaluated at specific points": [[2, "a-simple-first-order-ode-evaluated-at-specific-points"]], "A worked bvp problem": [[22, "a-worked-bvp-problem"]], "A worked example": [[20, "a-worked-example"]], "About pycse": [[37, "about-pycse"]], "About the Python packages": [[37, "about-the-python-packages"]], "About your python": [[10, "about-your-python"]], "Addition and subtraction": [[11, "addition-and-subtraction"], [27, "addition-and-subtraction"]], "Advanced function creation": [[0, "advanced-function-creation"]], "Advanced mathematical operators": [[0, "advanced-mathematical-operators"]], "Advanced selection of \u03bb": [[30, "advanced-selection-of"]], "Advanced string formatting": [[0, "advanced-string-formatting"]], "An application": [[26, "an-application"]], "An example of polynomial fitting": [[30, "an-example-of-polynomial-fitting"]], "An example with a linear kernel": [[34, "an-example-with-a-linear-kernel"]], "An example with curve_fit": [[24, "an-example-with-curve-fit"]], "Analytically solve a simple ODE": [[6, "analytically-solve-a-simple-ode"]], "Another approach to error propagation": [[11, "another-approach-to-error-propagation"]], "Another example": [[5, "another-example"], [5, "id2"]], "Another interpretation of neural networks": [[32, "another-interpretation-of-neural-networks"]], "Another way to parameterize an ODE - nested function": [[2, "another-way-to-parameterize-an-ode-nested-function"]], "Application in linear boundary value problems": [[28, "application-in-linear-boundary-value-problems"]], "Application in reaction engineering - Steady state CSTR": [[28, "application-in-reaction-engineering-steady-state-cstr"]], "Application to independent chemical reactions.": [[5, "application-to-independent-chemical-reactions"]], "Application to maximizing profit in a PFR": [[23, "application-to-maximizing-profit-in-a-pfr"]], "Application to roots of a polynomial": [[29, "application-to-roots-of-a-polynomial"]], "Applications": [[16, "applications"]], "Applications of lambda functions": [[0, "applications-of-lambda-functions"]], "Applications of linear algebra": [[28, "applications-of-linear-algebra"]], "Applications to optimization": [[29, "applications-to-optimization"]], "Are averages different": [[11, "are-averages-different"]], "Avoiding indexing in lists": [[38, "avoiding-indexing-in-lists"]], "Basic math": [[0, "basic-math"]], "Basic python usage": [[0, "basic-python-usage"]], "Basic statistics": [[11, "basic-statistics"]], "Better interpolate than never": [[3, "better-interpolate-than-never"]], "Boundary value equations": [[2, "boundary-value-equations"]], "Boundary value problem in heat conduction": [[2, "boundary-value-problem-in-heat-conduction"]], "Boundary value problems": [[22, "boundary-value-problems"]], "Brief comparison of GPR and NN": [[34, "brief-comparison-of-gpr-and-nn"]], "Brief intro to regular expressions": [[10, "brief-intro-to-regular-expressions"]], "Brief review": [[18, "brief-review"]], "Build statistics": [[39, "build-statistics"]], "CO": [[13, "co"]], "CO2": [[13, "co2"]], "Calculating a bubble point pressure of a mixture": [[13, "calculating-a-bubble-point-pressure-of-a-mixture"]], "Calling lapack directly from scipy": [[5, "calling-lapack-directly-from-scipy"]], "Changelog": [[40, "changelog"]], "Choice of activation functions in neural networks": [[33, "choice-of-activation-functions-in-neural-networks"]], "Combining kernels": [[34, "combining-kernels"]], "Combining numerical data with quad": [[6, "combining-numerical-data-with-quad"]], "Compare the equilibrium constants": [[13, "compare-the-equilibrium-constants"]], "Compare to a loop solution": [[10, "compare-to-a-loop-solution"]], "Compressibility variation from an implicit equation of state": [[31, "compressibility-variation-from-an-implicit-equation-of-state"]], "Compute areas": [[13, "compute-areas"]], "Compute gas phase pressures of each species": [[13, "compute-gas-phase-pressures-of-each-species"]], "Compute mole fractions and partial pressures": [[13, "compute-mole-fractions-and-partial-pressures"]], "Compute the t-score for our data": [[11, "compute-the-t-score-for-our-data"]], "Computing a pipe diameter": [[13, "computing-a-pipe-diameter"]], "Computing determinants from matrix decompositions": [[5, "computing-determinants-from-matrix-decompositions"]], "Computing equilibrium constants": [[13, "computing-equilibrium-constants"]], "Computing the pressure from a solid equation of state": [[31, "computing-the-pressure-from-a-solid-equation-of-state"]], "Concentration profile in a particle": [[22, "concentration-profile-in-a-particle"]], "Concluding remarks": [[35, "concluding-remarks"]], "Conclusions": [[10, "conclusions"]], "Confidence interval on an average": [[11, "confidence-interval-on-an-average"]], "Confidence intervals on the parameters": [[30, "confidence-intervals-on-the-parameters"]], "Conservation of mass in chemical reactions": [[13, "conservation-of-mass-in-chemical-reactions"]], "Constrained minimization": [[26, "constrained-minimization"]], "Constrained minimization to find equilibrium compositions": [[13, "constrained-minimization-to-find-equilibrium-compositions"]], "Constrained optimization": [[8, "constrained-optimization"], [26, "constrained-optimization"]], "Constrained optimization with Lagrange multipliers and autograd": [[31, "constrained-optimization-with-lagrange-multipliers-and-autograd"]], "Construct the Lagrange multiplier augmented function": [[8, "construct-the-lagrange-multiplier-augmented-function"]], "Constructing arrays": [[27, "constructing-arrays"]], "Controlling the format of printed variables": [[0, "controlling-the-format-of-printed-variables"]], "Counting roots": [[7, "counting-roots"]], "Coupled nonlinear equations": [[7, "coupled-nonlinear-equations"]], "Creating arrays in python": [[0, "creating-arrays-in-python"]], "Creating your own functions": [[0, "creating-your-own-functions"]], "Cubic equations of state": [[21, "cubic-equations-of-state"]], "Curve fitting to get overlapping peak areas": [[13, "curve-fitting-to-get-overlapping-peak-areas"]], "Customizing plots after the fact": [[9, "customizing-plots-after-the-fact"]], "Data analysis": [[1, "data-analysis"]], "Debugging/getting help": [[15, "debugging-getting-help"]], "Defining functions in python": [[0, "defining-functions-in-python"]], "Delay Differential Equations": [[2, "delay-differential-equations"]], "Derivatives by FFT": [[6, "derivatives-by-fft"]], "Derivatives by fitting a function and taking the analytical derivative": [[6, "derivatives-by-fitting-a-function-and-taking-the-analytical-derivative"]], "Derivatives by polynomial fitting": [[6, "derivatives-by-polynomial-fitting"]], "Derivatives of functions": [[20, "derivatives-of-functions"]], "Determining linear independence of a set of vectors": [[5, "determining-linear-independence-of-a-set-of-vectors"]], "Differential algebraic systems of equations": [[2, "differential-algebraic-systems-of-equations"]], "Differential equations": [[2, "differential-equations"]], "Diffusion": [[16, "diffusion"]], "Discussion": [[3, "discussion"]], "Division": [[11, "division"]], "Docker": [[41, "docker"]], "Documentation": [[40, "documentation"]], "Double-y axis plot": [[9, "double-y-axis-plot"]], "Effects of outliers on regression": [[25, "effects-of-outliers-on-regression"]], "Efficiency": [[13, "efficiency"]], "Eigenvalues": [[29, "eigenvalues"]], "Entropy-temperature chart": [[13, "entropy-temperature-chart"]], "Equality constraints": [[26, "equality-constraints"]], "Equilibrium constant based on mole numbers": [[13, "equilibrium-constant-based-on-mole-numbers"]], "Equilibrium constant calculation": [[13, "equilibrium-constant-calculation"]], "Equilibrium yield of WGS": [[13, "equilibrium-yield-of-wgs"]], "Error tolerance in numerical solutions to ODEs": [[2, "error-tolerance-in-numerical-solutions-to-odes"]], "Estimate the value of f at t=2.": [[3, "estimate-the-value-of-f-at-t-2"]], "Estimating the boiling point of water": [[13, "estimating-the-boiling-point-of-water"]], "Estimating the volume of a plug flow reactor": [[16, "estimating-the-volume-of-a-plug-flow-reactor"]], "Estimating the volume of a solid": [[16, "estimating-the-volume-of-a-solid"]], "Euler\u2019s method": [[17, "euler-s-method"]], "Evaluating line integrals": [[31, "evaluating-line-integrals"]], "Exponential and logarithmic functions": [[0, "exponential-and-logarithmic-functions"]], "Families of solutions to FODEs": [[18, "families-of-solutions-to-fodes"]], "Fancy, built-in colors in Python": [[9, "fancy-built-in-colors-in-python"]], "Find the derivative, and solve for where it is zero": [[23, "find-the-derivative-and-solve-for-where-it-is-zero"]], "Find the minimum distance from a point to a curve.": [[8, "find-the-minimum-distance-from-a-point-to-a-curve"]], "Find the volume of a PFR": [[16, "find-the-volume-of-a-pfr"]], "Finding equilibrium composition by direct minimization of Gibbs free energy on mole numbers": [[13, "finding-equilibrium-composition-by-direct-minimization-of-gibbs-free-energy-on-mole-numbers"]], "Finding equilibrium conversion": [[13, "finding-equilibrium-conversion"]], "Finding independent reactions": [[28, "finding-independent-reactions"]], "Finding maxima": [[23, "finding-maxima"]], "Finding the 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\ No newline at end of file

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