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a/_images/fd1c4dd607192f735e593fedf2e148c1e2e0d8d6627ddc937a5e9bce97dc2680.png b/_images/fd1c4dd607192f735e593fedf2e148c1e2e0d8d6627ddc937a5e9bce97dc2680.png deleted file mode 100644 index cf40654..0000000 Binary files a/_images/fd1c4dd607192f735e593fedf2e148c1e2e0d8d6627ddc937a5e9bce97dc2680.png and /dev/null differ diff --git a/blog/basic-python.html b/blog/basic-python.html index 51b2dbd..a6d26a3 100644 --- a/blog/basic-python.html +++ b/blog/basic-python.html @@ -1096,7 +1096,7 @@

Lambda Lambda Lambda
-
<function <lambda> at 0x7ff543fb6480>
+
<function <lambda> at 0x7efc1ae1b920>
 4
 

 

@@ -1112,7 +1112,7 @@ 
Lambda Lambda Lambda
-
<function <lambda> at 0x7ff543f4a0c0>
+
<function <lambda> at 0x7efc1ae1bce0>
 5
 

 

@@ -1129,7 +1129,7 @@ 
Lambda Lambda Lambda
-
<function <lambda> at 0x7ff543fb62a0>
+
<function <lambda> at 0x7efc1af620c0>
 5
 5
 

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

 

-
<function <lambda> at 0x7ff543fb6200>
+
<function <lambda> at 0x7efc1ae1b920>
 1
 3
 6
@@ -1326,7 +1326,7 @@ 
Creating arrays in python
/tmp/ipykernel_1846/3002503601.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1927/3002503601.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_1846/518394352.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1927/518394352.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#
 

 

-
[[[0.43615886 0.13605706 0.05297671]
-  [0.35305927 0.29357532 0.49733565]
-  [0.38172968 0.07665701 0.5449612 ]]
+
[[[0.38539438 0.11231027 0.40790904]
+  [0.08412152 0.21880168 0.90380847]
+  [0.11389821 0.47825366 0.36913078]]
 
- [[0.49819208 0.5947304  0.5798703 ]
-  [0.08390736 0.36638886 0.81145878]
-  [0.58993414 0.69823151 0.02000972]]
+ [[0.13520422 0.94558297 0.3489036 ]
+  [0.28555128 0.52922711 0.33190157]
+  [0.21311647 0.05928239 0.4696106 ]]
 
- [[0.62070431 0.69793003 0.95113255]
-  [0.60793599 0.23134862 0.79939542]
-  [0.64336982 0.32286496 0.76583464]]]
+ [[0.81299699 0.68237323 0.90055802]
+  [0.07279773 0.92884477 0.54403059]
+  [0.69365596 0.13691994 0.02003016]]]
 

 

 

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

 

-
[[0.43615886 0.35305927 0.38172968]
- [0.49819208 0.08390736 0.58993414]
- [0.62070431 0.60793599 0.64336982]]
-[0.43615886 0.49819208 0.62070431]
-[0.5798703  0.81145878 0.02000972]
+
[[0.38539438 0.08412152 0.11389821]
+ [0.13520422 0.28555128 0.21311647]
+ [0.81299699 0.07279773 0.69365596]]
+[0.38539438 0.13520422 0.81299699]
+[0.3489036  0.33190157 0.4696106 ]
 

 

 

diff --git a/blog/differential-equations.html b/blog/differential-equations.html
index 672b1f3..dfbf93c 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_1899/2289625004.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1982/2289625004.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 840166e..8d95b1b 100644
--- a/blog/interpolation.html
+++ b/blog/interpolation.html
@@ -916,9 +916,9 @@ 
Interpolation with splines
/tmp/ipykernel_1932/1138919460.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_2011/1138919460.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_1932/1138919460.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_2011/1138919460.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 d0561e4..1d07448 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_1957/3718588497.py:6: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_2036/3718588497.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_1957/73961882.py:7: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_2036/73961882.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 7b6511f..83c7d34 100644
--- a/blog/math.html
+++ b/blog/math.html
@@ -673,9 +673,9 @@ 
Numeric derivatives by differences
-
 Forward difference took 0.000218 seconds
- Backward difference took 0.000195 seconds
- Centered difference took 0.000258 seconds
+
 Forward difference took 0.000215 seconds
+ Backward difference took 0.000199 seconds
+ Centered difference took 0.000234 seconds
 

 

 ../_images/e82a955efa2e01fb55f09524ce9405030516d0ae15614c934dfaf2d14380e228.png
@@ -775,7 +775,7 @@ 
2-point vs. 4-point numerical derivatives
-../_images/fd1c4dd607192f735e593fedf2e148c1e2e0d8d6627ddc937a5e9bce97dc2680.png
+../_images/98b5742cbf2a1fd2d1365f69ae04a9b6459adc8c01de2dfebdc1689c8ce54e8d.png
 

 

 
@@ -900,7 +900,7 @@ 
Derivatives by FFT
-../_images/6cbf84e4a4a103ee3949de06e753be27d8a8507dc7a703fe0ff8bb6ec03c5c4d.png
+../_images/7d92bcc8ea06aea71bb368638523605c3e942f43163dbf4a64c0988650bff5db.png
 

 

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

 

-
/tmp/ipykernel_1982/1388173814.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2062/1388173814.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_1982/1343167527.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2062/1343167527.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_1982/1681875887.py:13: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2062/1681875887.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 = 0.0007112026214599609 sec
+
time elapsed = 0.0007185935974121094 sec
 1.9999983517708524
 

 

@@ -1795,7 +1795,7 @@ 
The trapezoidal method of integration
-
time elapsed = 0.00022554397583007812 sec
+
time elapsed = 0.0002205371856689453 sec
 1.9999934070923728
 

 

@@ -1814,7 +1814,7 @@ 
The trapezoidal method of integration
-
time elapsed = 8.726119995117188e-05 sec
+
time elapsed = 8.535385131835938e-05 sec
 1.999993407092373
 

 

@@ -2009,7 +2009,7 @@ 
Function integration by the Romberg method
/tmp/ipykernel_1982/1760157840.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_2062/1760157840.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))
 

 

diff --git a/blog/nonlinear-algebra.html b/blog/nonlinear-algebra.html
index 890f046..9f5a523 100644
--- a/blog/nonlinear-algebra.html
+++ b/blog/nonlinear-algebra.html
@@ -765,10 +765,10 @@ 
Method of continuity for nonlinear equation solving
 

 

-
/tmp/ipykernel_2010/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2091/4022852329.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_2010/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
+/tmp/ipykernel_2091/4022852329.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)
 

diff --git a/blog/plotting.html b/blog/plotting.html
index 4b91c0e..f585e3e 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_2145/256016704.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 0dd3720..68d45fd 100644
--- a/blog/programming.html
+++ b/blog/programming.html
@@ -795,7 +795,7 @@ 
Unique entries in a vector
-
['c', 'a', 'b', 'd', 'abracadabra']
+
['a', 'c', 'd', 'b', 'abracadabra']
 

 

 

@@ -1168,11 +1168,11 @@ 
About your python
-
uname_result(system='Linux', node='fv-az1788-775', 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-az1437-408', 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-az1788-775
+fv-az1437-408
 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 61c6767..932b027 100644
--- a/blog/statistics.html
+++ b/blog/statistics.html
@@ -1124,9 +1124,9 @@ 
Addition and subtraction
-../_images/d3bb7b9ec25aa1c3c907d125c9dea4082afb4610789e613af5a5e6f9a20769a5.png
-
0.5015934623528542
-0.5003768992300748
+../_images/bb8d36cf3af21f04ce35928fab5b18f344dd80cf311a615784ee4d2e2b2f99ac.png
+
0.499377510104839
+0.4988491771507384
 0.5
 

 

@@ -1150,7 +1150,7 @@ 
Multiplication
-
11.846475500268163
+
11.707611729729763
 11.872657663724665
 

 

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

 

 

-
0.2934053728479521
+
0.2914416034580932
 0.2898598062432779
 

 

@@ -1194,7 +1194,7 @@ 
exponents
-
1.7263654373835455
+
1.7165645012576092
 1.7236544062149992
 

 

@@ -1208,7 +1208,7 @@ 
exponents
-
0.007459637666347715
+
0.007490676164880568
 0.007483647387490024
 

 

@@ -1236,7 +1236,7 @@ 
the chain rule in error propagation
-
3.6726434783536566
+
3.618895290045066
 3.6180105030251086
 

 

@@ -1494,7 +1494,7 @@ 
Another approach to error propagation
-
Ca(exit) = 0.005008860140460284+/-0.00017110482885036445
+
Ca(exit) = 0.005009891376171224+/-0.0001706636262175129
 

 

 

@@ -1526,7 +1526,7 @@ 
Random thoughts
-
n = 0.376772255942448
+
n = 0.18217434932547472
 you lose.
 

 

@@ -1551,10 +1551,10 @@ 
Random thoughts
-
You won 5048 times (50.480000%)
+
You won 5031 times (50.310000%)
 

 

-../_images/d5aac764cfc28098e69b26262424edbd71d99399e1576d9387eb2faa2af60ac9.png
+../_images/aa76cce565842ba03a9c81d7544b680668ea425fd4cf8db91d2d0ca831fbc6d6.png
 

 

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

@@ -1570,10 +1570,10 @@ 
Random thoughts
-
31
-[21 37 13]
-[[18 33]
- [71 28]]
+
10
+[88 96 67]
+[[ 9  7]
+ [78 40]]
 

 

 

@@ -1591,8 +1591,8 @@ 
Random thoughts
-
1.6064693055505437
-[1.61262572 1.24087314]
+
1.300725571399232
+[0.72950766 0.74960877]
 

 

 

@@ -1615,7 +1615,7 @@ 
Random thoughts
-../_images/26d76f85130b37955fdee568673029c404f8c4b0bd53d44c8534e575b959422c.png
+../_images/2669cb3aebdc0f049314184b21317eb273b1662e9024af282ac1b59b9563707f.png
 

 

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

@@ -1638,8 +1638,8 @@ 
Random thoughts
-
68.620000% of samples are within +- 1 standard deviations of the mean
-95.420000% of samples are within +- 2 standard deviations of the mean
+
67.440000% of samples are within +- 1 standard deviations of the mean
+95.460000% of samples are within +- 2 standard deviations of the mean
 

 

 

diff --git a/blog/worked-examples.html b/blog/worked-examples.html
index 0155526..657d1ec 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_2236/1892264215.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_2236/2870202885.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_2236/2870202885.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_2236/2870202885.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_2236/2870202885.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_2236/1928982228.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_2236/1928982228.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_2236/4291268947.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_2236/4291268947.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_2236/339476128.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_2236/339476128.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 58f3c21..d938e48 100644
--- a/book/00-intro.html
+++ b/book/00-intro.html
@@ -807,16 +807,16 @@ 
scipy#<
 

 
{'neval': 63,
  'last': 2,
- 'iord': array([          1,           2,           0,           0,   218176832,
-           50334979,     4328707, -1610151165, -2130509563,   168558857,
-          134618112,   269356036,   196103132,   229657428, -1185391788,
-        -1057027072,  1020549432,   288550084,   788541753,  -331557660,
-          809046578,   123229003,   130614288,  1506346256,   708837666,
-            2752523,     5832776,     7798889,   369557642,   637545217,
-          906177281,  1325485569,  1443712780,  1963025921, -2063369727,
-            6098177,   553716061,   856765187,   588325653,    53813521,
-           16973318,  -704760322,  1593690581,  -470014715,   872205571,
-           27328168,       50016,    23789924,           0,   157549938],
+ 'iord': array([          1,           2,           0,           0,           4,
+                547,         413,           0,           0,           0,
+                  0,           0,  -619499072,       21972,  -619499072,
+              21972,           0,           0,           0,           0,
+                  4,        2188,  -874966160,       32520, -2139607952,
+              32520,  -620508304,       21972,           0,           0,
+             903644,           0,           1,           0,           0,
+                  0,           0,           0,           0,           0,
+                  0,           0,           0,           0,           0,
+                  0,           0,           0,           0,           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, 6.90578935e-310, 6.90578886e-310,
-        6.90578867e-310, 6.90578935e-310, 6.90578886e-310, 6.90578867e-310,
-        6.90578935e-310, 6.90578886e-310, 6.90578867e-310, 6.90578935e-310,
-        6.90578886e-310, 6.90578867e-310, 6.90578935e-310, 6.90578886e-310,
-        6.90578867e-310, 6.90578935e-310, 6.90578886e-310, 6.90578867e-310,
-        6.90578935e-310, 6.90578886e-310, 6.90578867e-310, 6.90578935e-310,
-        6.90578886e-310, 6.90578867e-310, 6.90578935e-310, 6.90578886e-310,
-        6.90578867e-310, 6.90578935e-310, 6.90578886e-310, 6.90578867e-310,
-        6.90578935e-310, 6.90578886e-310, 6.90578867e-310, 6.90578935e-310,
-        6.90578886e-310, 6.90578867e-310, 6.90578935e-310, 6.90578886e-310,
-        6.90578867e-310, 6.90578935e-310, 6.90578886e-310, 6.90578867e-310,
-        6.90578935e-310, 6.90578886e-310, 6.90578867e-310, 6.90578935e-310,
-        6.90578886e-310, 6.90578867e-310]),
+ 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.90090130e-310, 6.90090081e-310,
+        6.90090062e-310, 6.90090130e-310, 6.90090081e-310, 6.90090062e-310,
+        6.90090130e-310, 6.90090081e-310, 6.90090062e-310, 6.90090130e-310,
+        6.90090081e-310, 6.90090062e-310, 6.90090130e-310, 6.90090081e-310,
+        6.90090062e-310, 6.90090130e-310, 6.90090081e-310, 6.90090062e-310,
+        6.90090130e-310, 6.90090081e-310, 6.90090062e-310, 6.90090130e-310,
+        6.90090081e-310, 6.90090062e-310, 6.90090130e-310, 6.90090081e-310,
+        6.90090062e-310, 6.90090130e-310, 6.90090081e-310, 6.90090062e-310,
+        6.90090130e-310, 6.90090081e-310, 6.90090062e-310, 6.90090130e-310,
+        6.90090081e-310, 6.90090062e-310, 6.90090130e-310, 6.90090081e-310,
+        6.90090062e-310, 6.90090130e-310, 6.90090081e-310, 6.90090062e-310,
+        6.90090130e-310, 6.90090081e-310, 6.90090062e-310, 6.90090130e-310,
+        6.90090081e-310, 6.90090062e-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_2189/843280888.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2268/843280888.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 c2d52a1..049d39a 100644
--- a/book/02-integration-1.html
+++ b/book/02-integration-1.html
@@ -727,7 +727,7 @@ 
numpy.trapz
-
/tmp/ipykernel_2236/3604360318.py:4: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2314/3604360318.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_2236/4086341036.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2314/4086341036.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_2236/427682055.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2314/427682055.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_2236/36719416.py:4: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
+
/tmp/ipykernel_2314/36719416.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 df5e007..c7ff2c2 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([4.68585503e-310, 0.00000000e+000, 4.68688661e-310, 4.68688662e-310]))
+ array([4.68973099e-310, 0.00000000e+000, 4.68917636e-310, 4.68917638e-310]))
 

 

 

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

 

-
<matplotlib.legend.Legend at 0x7f3d11b838d0>
+
<matplotlib.legend.Legend at 0x7fe040f60650>
 

 

 ../_images/0d992e05e05f92dc53b78d747da1fa725f1cb6fc66247847be3c6e338ba12bc2.png
@@ -1114,7 +1114,7 @@ 
scipy.integrate.solve_ivp
-
<matplotlib.legend.Legend at 0x7f3d0f90f090>
+
<matplotlib.legend.Legend at 0x7fe03ecaad50>
 

 

 ../_images/0f3cb0f20de8a66563583063f2afeb51738e8b0db5b5ace82e7cb68a5289387e.png
diff --git a/book/07-nla-1.html b/book/07-nla-1.html
index 10d30dd..4d2bbdc 100644
--- a/book/07-nla-1.html
+++ b/book/07-nla-1.html
@@ -854,7 +854,7 @@ 
Derivatives of functions
-
/tmp/ipykernel_2345/1845505028.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_2427/1845505028.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_2345/1563071673.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_2427/1563071673.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_2345/1563071673.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_2427/1563071673.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_2345/1563071673.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_2427/1563071673.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_2345/1563071673.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_2427/1563071673.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_2345/1619064557.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_2427/1619064557.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_2345/2335501430.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_2427/2335501430.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 1a3e335..3c668fe 100644
--- a/book/08-nla-2.html
+++ b/book/08-nla-2.html
@@ -721,7 +721,7 @@ 
Cubic equations of state
-
/tmp/ipykernel_2371/406724879.py:1: ComplexWarning: Casting complex values to real discards the imaginary part
+
/tmp/ipykernel_2452/406724879.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_2371/174692805.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2452/174692805.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
 

 

-
128 μs ± 280 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
+
128 μs ± 363 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
 

 

 

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

 

-
6.23 μs ± 9.28 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
+
6.44 μs ± 17.1 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 0x7f0ecc7b36a0>
+
<function integrand at 0x7f10b8d2f380>
 

 

 

@@ -1077,7 +1077,7 @@ 
Systems of nonlinear equations
-../_images/a38ba9d5e66b9995460d5762cf036692c8e112894829d60568b63ddd2b10586e.png
+../_images/71c2351c28a94c99cc9c4a321dd64cd2636801bacf7a5f775bd6eee4d9953460.png
 

 

 

@@ -1095,7 +1095,12 @@ 
Systems of nonlinear equations
-
array([6.11617050e-12, 1.22770081e-11])
+
Failed at guess [-0.15534598444309378, -0.7661123294171879].
+The iteration is not making good progress, as measured by the 
+  improvement from the last ten iterations.
+

+

+
array([1.71845177e-11, 4.35018176e-11])
 

 

 

diff --git a/book/09-bvp.html b/book/09-bvp.html
index 45727f3..28d2136 100644
--- a/book/09-bvp.html
+++ b/book/09-bvp.html
@@ -1076,7 +1076,7 @@ 
Concentration profile in a particle
0.008249311811255714
 

 

-
/tmp/ipykernel_2402/1627362779.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2496/1627362779.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 b6be806..b9e767e 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_2427/2917585576.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_2522/2917585576.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_2427/4103338182.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_2522/4103338182.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_2427/4103338182.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_2522/4103338182.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 1034219..9c78eb4 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_2452/3278399195.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_2547/3278399195.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)
 

 

diff --git a/book/15-intro-linear-algebra.html b/book/15-intro-linear-algebra.html
index 5557ec6..24fa849 100644
--- a/book/15-intro-linear-algebra.html
+++ b/book/15-intro-linear-algebra.html
@@ -1257,7 +1257,7 @@ 
The determinant
-
np.float64(6.042429889740949)
+
np.float64(5.03936975533605)
 

 

 

@@ -1276,9 +1276,9 @@ 
The inverse
-
array([[ 3.05690548, -1.51947922,  1.11461029],
-       [ 2.38390166,  1.34785646, -1.24551064],
-       [-2.77546093,  1.31866119,  0.09791541]])
+
array([[-7.87378426, -6.99555726, 10.99951073],
+       [ 3.89523868,  5.3654205 , -6.2028488 ],
+       [ 1.66229855, -0.7280436 , -0.16899725]])
 

 

 

@@ -1292,9 +1292,9 @@ 
The inverse
-
[[ 1.  0.  0.]
+
[[ 1.  0. -0.]
  [ 0.  1. -0.]
- [ 0.  0.  1.]]
+ [ 0. -0.  1.]]
 

 

 

@@ -1569,7 +1569,7 @@ 
Solving linear algebraic equations
-../_images/7b1e5b20a98c4c50a3fe48ff2e55f5b01c02220f75773371944b7fa3826e3843.png
+../_images/f1fc455bd035e5543326f23acd043e6aa5d63434edf0b1aa19417c850acd95b9.png
 

 

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

@@ -1604,7 +1604,7 @@ 
Solving linear algebraic equations
-../_images/6a0d50ce2169e3caf171b000f00748bae3c5d9ec0c332de0a35abc58cb17330f.png
+../_images/27f9f06aaf2f40039cc16b6b71ae084367ada63d0940fb5c575ceba0e4786416.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 f43fee7..ed77691 100644
--- a/book/17-linear-algebra-2.html
+++ b/book/17-linear-algebra-2.html
@@ -721,7 +721,7 @@ 
Interpolation libraries
 

 

-
/tmp/ipykernel_2605/3098855599.py:5: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2692/3098855599.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([[1.66449548, 1.4937402 , 1.58564427],
-       [1.4937402 , 1.63983854, 0.41286991],
-       [1.58564427, 0.41286991, 0.70594747]])
+
array([[1.12696071, 0.7301827 , 0.99179232],
+       [0.7301827 , 0.00146177, 1.39487429],
+       [0.99179232, 1.39487429, 0.85717957]])
 

 

 

@@ -834,7 +834,7 @@ 
Eigenvalues
-
array([ 2.88850986e+00, -8.91770408e-01, -1.97512519e-04])
+
array([ 2.63321466, -0.02894168, -0.29049999])
 

 

 

@@ -846,8 +846,7 @@ 
Eigenvalues
-
array([1.91481745+0.j       , 0.37018727+0.2031555j,
-       0.37018727-0.2031555j])
+
array([ 1.35869199,  0.13087513, -0.89505778])
 

 

 

@@ -861,7 +860,7 @@ 
Eigenvalues
-
(np.float64(1.9965419394516097), np.float64(1.9965419394516097))
+
(np.float64(2.313772977099295), np.float64(2.313772977099295))
 

 

 

@@ -875,7 +874,7 @@ 
Eigenvalues
-
np.float64(1.9965419394516088)
+
np.float64(2.313772977099296)
 

 

 

@@ -889,7 +888,7 @@ 
Eigenvalues
-
(np.float64(0.0005087700530349978), np.float64(0.0005087700530348564))
+
(np.float64(0.022138908298101622), np.float64(0.02213890829810152))
 

 

 

@@ -903,10 +902,10 @@ 
Eigenvalues
-
(array([ 2.88850986e+00, -8.91770408e-01, -1.97512519e-04]),
- array([[ 0.60631269,  0.78679919, -0.11546409],
-        [ 0.48216489, -0.47918907, -0.73341315],
-        [ 0.632378  , -0.38900498,  0.66990536]]))
+
(array([ 2.63321466, -0.02894168, -0.29049999]),
+ array([[-0.63828507, -0.6808019 , -0.3593062 ],
+        [-0.49117726,  0.71957247, -0.49087713],
+        [-0.59273693,  0.13683651,  0.79368678]]))
 

 

 

@@ -920,7 +919,7 @@ 
Eigenvalues
-
(np.float64(0.9999999999999998), np.float64(0.9999999999999999))
+
(np.float64(1.0000000000000002), np.float64(1.0))
 

 

 

@@ -932,8 +931,8 @@ 
Eigenvalues
-
(array([1.07863149, 1.00048724, 1.28145979]),
- array([ 1.7513402 ,  2.27267721, -0.33351916]))
+
(array([-1.57773731, -1.19301439, -1.55398318]),
+ array([-1.6807416 , -1.79269754, -0.94613034]))
 

 

 

@@ -946,8 +945,8 @@ 
Eigenvalues
-
(array([1.7513402 , 1.39273803, 1.82663009]),
- array([1.7513402 , 1.39273803, 1.82663009]))
+
(array([-1.6807416 , -1.29337516, -1.56080357]),
+ array([-1.6807416 , -1.29337516, -1.56080357]))
 

 

 

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

 

 

@@ -1008,10 +1005,10 @@ 
Eigenvalues
-
(array([-8.91770408e-01, -1.97512519e-04,  2.88850986e+00]),
- array([[ 0.78679919, -0.11546409,  0.60631269],
-        [-0.47918907, -0.73341315,  0.48216489],
-        [-0.38900498,  0.66990536,  0.632378  ]]))
+
(array([-0.29049999, -0.02894168,  2.63321466]),
+ array([[-0.3593062 , -0.6808019 , -0.63828507],
+        [-0.49087713,  0.71957247, -0.49117726],
+        [ 0.79368678,  0.13683651, -0.59273693]]))
 

 

 

diff --git a/book/23-gp.html b/book/23-gp.html
index 352bb1c..263906d 100644
--- a/book/23-gp.html
+++ b/book/23-gp.html
@@ -780,7 +780,7 @@ 
GPR by example
-
array([0.74260194, 0.75221079])
+
array([0.74797836, 0.75786415])
 

 

 

@@ -796,7 +796,7 @@ 
GPR by example
-../_images/9bb942fc401fc8190fd2a68475d8bc7694c22f8a6875e3f4c853dd6ebb36341f.png
+../_images/c91c964e0d1d2c5f985c10a61153861507260de8d5d930ce321a7d72cf50382d.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/9972b14218825004ee7646b9439d8cb3ab17760536508c561137dc9a17433ef6.png
+../_images/d7980c9b7adea63c2d5f5b2c39bbcb034640785f9f885b171908b2d9f4e42272.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/f959ec26bf2da087941b0fea4d2c44ef1c09777708518b31528c595c7ab23369.png
+../_images/174189c883c9ffd228577f46a889043b1dd635be60eff82fb620c8bff7b7f2dc.png
 

 

 

@@ -925,7 +925,7 @@ 
Underfitting in GPR
-../_images/b154b79c48620671e863e8ccf9f42870e56d09dc67cfebb3680d3b88c31ca135.png
+../_images/8d62f0bf53b4a270d19fd1e0958068fdbd2394b85fc1dd74486efb267f6e4a83.png
 

 

 
@@ -950,7 +950,7 @@ 
Overfitting in GPR
-../_images/27c30b74ef2ec755284c2c26261f5f273eec375a0528753468cbf2b90b227ec1.png
+../_images/e6a4021fa9806100792b75546510f220d247d330f6e29b26cf5c8ff0a61015d6.png
 

 

 
@@ -991,10 +991,10 @@ 
Finding the hyperparameters in GPR
-
array([1.        , 0.06958857])
+
array([1.        , 0.07188258])
 

 

-../_images/055d22de8fe6bfa789188957b15f6cfd261a305f69b121d4170a5ead684bca45.png
+../_images/a3da2ea338d8cd78e81665d1f76836c9a031c3b26f618554170b52eaaf1a5bb0.png
 

 

 

@@ -1029,10 +1029,10 @@ 
Finding the hyperparameters in GPR
-
array([1.        , 0.20781083, 0.19952581])
+
array([1.        , 0.21181967, 0.20284237])
 

 

-../_images/202d5aab8fc4f72e941e018c05cb5d8dbdd4270d8707f84ab3b0f6f7fa9a3ac2.png
+../_images/5251557fbd9429ecad331a516a1d6effb907596b1a45a9d8c17f31c8c094a947.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/67cddfe36de9e6e3494c8be0b70a687d176a97e9ad2d365d40ad33f31ed95f07.png
+../_images/6256b4dcd852c5bc577c22b6e48d28a1ca000bf9beeaac04516fcb04f460fbdf.png
 

 

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

@@ -1090,13 +1090,13 @@ 
An example with a linear kernel
  message: Optimization terminated successfully.
   success: True
    status: 0
-      fun: 7.58903161523043
-        x: [-3.618e-05  6.409e-01 -1.497e+00]
+      fun: 7.5940989858352355
+        x: [ 1.767e-05  6.158e-01 -1.584e+00]
       nit: 30
-      jac: [-5.186e-06 -8.345e-06  6.795e-06]
- hess_inv: [[ 3.542e+00 -5.724e-02 -4.603e-02]
-            [-5.724e-02  3.321e-02  2.011e-02]
-            [-4.603e-02  2.011e-02  5.654e-02]]
+      jac: [ 5.066e-06  1.371e-06 -4.709e-06]
+ hess_inv: [[ 6.297e+00  5.103e-05  4.216e-02]
+            [ 5.103e-05  2.069e-02  7.845e-03]
+            [ 4.216e-02  7.845e-03  4.876e-02]]
      nfev: 148
      njev: 37
 

@@ -1126,7 +1126,7 @@ 
An example with a linear kernel
-../_images/f255c552287a09e48df546aa93cdb44f02351a30ec615678f145d99f069e9ade.png
+../_images/0a2f93072fa041ef6984c5fddfbfb9ba83a7d5f82db084372c6fbf6d1344647d.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([2.98596023])
+
array([3.0355338])
 

 

 

@@ -1152,7 +1152,7 @@ 
An example with a linear kernel
-
np.float64(1.9942636446128217)
+
np.float64(1.9163616292745578)
 

 

 

@@ -1186,7 +1186,7 @@ 
Uncertainty quantification in GPR
-../_images/0246b109091b32a6a023d8e20a61866694ab910a8c3508f94cc19c955f20f7e8.png
+../_images/c112b8bb502299f5e2448694f255e30a9fe6002901923d4a11a19b16c5d7baa5.png
 

 

 
@@ -1204,7 +1204,7 @@ 
Combining kernels
-../_images/e52a56bd5dc6d476908251592114c05a3c7e5d3f208ff2e1e2707dcb1fa7c5ec.png
+../_images/3e06098ffe26ee123263241e4279ca6728fd53393ad6bcb506fd27208e78b5a0.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: 22.29128263200922
-        x: [ 5.988e-06  4.474e-01 -1.286e+00  6.704e-01  2.340e+01
-             1.330e-02]
-      nit: 268
-      jac: [ 4.768e-06  7.677e-05 -2.193e-05  1.907e-06  2.623e-06
-             4.463e-04]
- hess_inv: [[ 7.401e-01  5.643e-02 ... -8.424e-01  7.635e-04]
-            [ 5.643e-02  2.612e-02 ... -2.772e-01  2.630e-04]
+      fun: 20.852396565863828
+        x: [-1.480e-06  3.831e-01 -1.515e+00  6.415e-01  9.316e-01
+            -3.409e-01]
+      nit: 39
+      jac: [ 6.676e-06  5.722e-06  1.049e-05 -6.437e-06  6.199e-06
+             4.768e-07]
+ hess_inv: [[ 3.411e+00 -1.477e-01 ... -7.147e-02  1.437e-01]
+            [-1.477e-01  1.020e-02 ...  3.208e-03 -5.237e-03]
             ...
-            [-8.424e-01 -2.772e-01 ...  1.152e+02 -6.659e-02]
-            [ 7.635e-04  2.630e-04 ... -6.659e-02  4.852e-05]]
-     nfev: 2853
-     njev: 406
+            [-7.147e-02  3.208e-03 ...  1.631e-03 -2.894e-03]
+            [ 1.437e-01 -5.237e-03 ... -2.894e-03  1.349e-02]]
+     nfev: 614
+     njev: 86
 

 

 

@@ -1268,7 +1268,7 @@ 
Combining kernels
-../_images/b2708dc85b50097c1daab26de3599fafd5a1b1de3857fcdedb3a77dbf0f1c41a.png
+../_images/866aa6ce4062855aab0fa71ef11c99369f1e7ec7821d1ee7298a49b0d69f2dd9.png
 

 

 
Note that we get oscillatory + linear extrapolation behavior!

diff --git a/docs/about.html b/docs/about.html
index 7f42e71..011b18c 100644
--- a/docs/about.html
+++ b/docs/about.html
@@ -582,11 +582,11 @@ 
About pycse
-
uname_result(system='Linux', node='fv-az1788-775', 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-az1437-408', 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-az1788-775
+fv-az1437-408
 Linux-6.5.0-1022-azure-x86_64-with-glibc2.35
 x86_64
 ('main', 'Jun 25 2024 18:25:01')
diff --git a/docs/beginner.html b/docs/beginner.html
index cab9096..9b47440 100644
--- a/docs/beginner.html
+++ b/docs/beginner.html
@@ -870,7 +870,7 @@ 
A better fsolve
-
/tmp/ipykernel_2777/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2860/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   fsolve(f, 2.5)
 

diff --git a/docs/execution-statistics.html b/docs/execution-statistics.html
index f392402..e056507 100644
--- a/docs/execution-statistics.html
+++ b/docs/execution-statistics.html
@@ -513,225 +513,225 @@ 
Build statistics
blog/basic-python

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2024-07-08 16:43

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2024-07-08 17:20

 
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book/00-intro

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docs/about

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diff --git a/searchindex.js b/searchindex.js
index a9ac5d5..7406088 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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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": 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