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zg%U8=m>^o#1ahV`HZo54r~l8$4uRVL=a+N+&yes`@-J$X-lcvt23|dex_3uewouye G<^Kb_#CG!l diff --git a/_static/searchtools.js b/_static/searchtools.js index 92da3f8..b08d58c 100644 --- a/_static/searchtools.js +++ b/_static/searchtools.js @@ -178,7 +178,7 @@ const Search = { htmlToText: (htmlString, anchor) => { const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); - for (const removalQuery of [".headerlinks", "script", "style"]) { + for (const removalQuery of [".headerlink", "script", "style"]) { htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() }); } if (anchor) { @@ -328,13 +328,14 @@ const Search = { for (const [title, foundTitles] of Object.entries(allTitles)) { if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) { for (const [file, id] of foundTitles) { - let score = Math.round(100 * queryLower.length / title.length) + const score = Math.round(Scorer.title * queryLower.length / title.length); + const boost = titles[file] === title ? 1 : 0; // add a boost for document titles normalResults.push([ docNames[file], titles[file] !== title ? `${titles[file]} > ${title}` : title, id !== null ? "#" + id : "", null, - score, + score + boost, filenames[file], ]); } diff --git a/blog/basic-python.html b/blog/basic-python.html index f838616..cde63ee 100644 --- a/blog/basic-python.html +++ b/blog/basic-python.html @@ -1096,7 +1096,7 @@

    Lambda Lambda Lambda
    -
    -
    -
    <function <lambda> at 0x7fbb647f6340>
    +
     
    -
    <function <lambda> at 0x7fbb647f6020>
    +
    <function <lambda> at 0x7f84d82ba200>
     1
     3
     6
    @@ -1326,7 +1326,7 @@ 

    Creating arrays in python -
    -
    -
    [[0.20114173 0.22052675 0.50508075]
    - [0.43953453 0.70936523 0.39352461]
    - [0.81473398 0.88280938 0.46015632]]
    -[0.20114173 0.43953453 0.81473398]
    -[0.64330352 0.31148072 0.4327842 ]
    +
    [[0.78760796 0.26268852 0.30720658]
    + [0.0620607  0.94771076 0.30794137]
    + [0.77554974 0.80054696 0.4891198 ]]
    +[0.78760796 0.0620607  0.77554974]
    +[0.06928769 0.29094717 0.62386642]
     
    diff --git a/blog/differential-equations.html b/blog/differential-equations.html index adca8b3..e86af7c 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_1896/2289625004.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
    +
    /tmp/ipykernel_1897/2289625004.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 aabcb4d..b81b3b8 100644 --- a/blog/interpolation.html +++ b/blog/interpolation.html @@ -916,9 +916,9 @@

    Interpolation with splines

    - -
    -
    /tmp/ipykernel_1976/1343167527.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_1978/1343167527.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_1976/1681875887.py:13: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_1978/1681875887.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 = 0.0010030269622802734 sec
    +
    time elapsed = 0.0007152557373046875 sec
     1.9999983517708524
     
    @@ -1795,7 +1795,7 @@

    The trapezoidal method of integration -
    time elapsed = 0.00022840499877929688 sec
    +
    time elapsed = 0.00022339820861816406 sec
     1.9999934070923728
     
    @@ -1814,7 +1814,7 @@

    The trapezoidal method of integration -
    time elapsed = 7.390975952148438e-05 sec
    +
    time elapsed = 8.916854858398438e-05 sec
     1.999993407092373
     
    @@ -2009,7 +2009,7 @@

    Function integration by the Romberg method
    /tmp/ipykernel_1976/1760157840.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_1978/1760157840.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))
     
    @@ -2038,9 +2038,7 @@

    Solve the quadratic equation
    [(-b - sqrt(-4*a*c + b**2))/(2*a), (-b + sqrt(-4*a*c + b**2))/(2*a)]
    -
    -
    -
    -
    /tmp/ipykernel_2004/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
    +
    /tmp/ipykernel_2009/4022852329.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_2004/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
    +/tmp/ipykernel_2009/4022852329.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 e7e8391..77a081b 100644 --- a/blog/plotting.html +++ b/blog/plotting.html @@ -1173,7 +1173,7 @@

    Peak annotation in matplotlib -
    /tmp/ipykernel_2059/256016704.py:19: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_2062/256016704.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 dd962d9..dce9025 100644 --- a/blog/programming.html +++ b/blog/programming.html @@ -1168,11 +1168,11 @@

    About your python -
    uname_result(system='Linux', node='fv-az1109-780', release='6.5.0-1023-azure', version='#24~22.04.1-Ubuntu SMP Wed Jun 12 19:55:26 UTC 2024', machine='x86_64')
    +
    uname_result(system='Linux', node='fv-az714-90', release='6.5.0-1023-azure', version='#24~22.04.1-Ubuntu SMP Wed Jun 12 19:55:26 UTC 2024', machine='x86_64')
     Linux
     ('64bit', 'ELF')
     x86_64
    -fv-az1109-780
    +fv-az714-90
     Linux-6.5.0-1023-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 9577662..6f687f6 100644
    --- a/blog/statistics.html
    +++ b/blog/statistics.html
    @@ -1124,9 +1124,9 @@ 

    Addition and subtraction -../_images/5bde168daa4140145b77ff8f26f9188ec2595dca480eb7d4605a76365d0af5cc.png -
    0.5061913303232849
    -0.4953129860305366
    +../_images/a24a040e044851f99acdea7ddb6bb1c9f2be7da04767f92c4de43d250379daf4.png
    +
    0.5027449351425746
    +0.5077536004144549
     0.5
     
    @@ -1150,7 +1150,7 @@

    Multiplication -
    -
    0.29602035868747906
    +
    0.29353463633494103
     0.2898598062432779
     
    @@ -1194,7 +1194,7 @@

    exponents -
    1.7029730713441298
    +
    1.7195996554371908
     1.7236544062149992
     
    @@ -1208,7 +1208,7 @@

    exponents -
    0.007445647369221156
    +
    0.00741915993491057
     0.007483647387490024
     
    @@ -1236,7 +1236,7 @@

    the chain rule in error propagation -
    3.6348443621705666
    +
    3.634080157335256
     3.6180105030251086
     
    @@ -1494,7 +1494,7 @@

    Another approach to error propagation -
    Ca(exit) = 0.005010409261084926+/-0.00016694459925285874
    +
    Ca(exit) = 0.00500803638722034+/-0.00016843874518759807
     
    @@ -1526,7 +1526,7 @@

    Random thoughts -
    n = 0.39944543050232983
    +
    n = 0.21427362538236827
     you lose.
     
    @@ -1551,10 +1551,10 @@

    Random thoughts -
    You won 5057 times (50.570000%)
    +
    You won 5223 times (52.230000%)
     
    -../_images/3d2002be363e512ec01a2e1925e6494a9ba5d7f76271b5cad4a77b1b108e14c2.png +../_images/5ce45208e6981935eb69c8884f1d0d389431b3bcf2df9f58e0ea832c6d13d33b.png

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

    @@ -1570,10 +1570,10 @@

    Random thoughts -

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

    @@ -1638,8 +1638,8 @@

    Random thoughts -
    -
    /tmp/ipykernel_2151/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
    +
    /tmp/ipykernel_2154/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
       diffg += R * T * x1 * np.log(x2 * P / P0)
    -/tmp/ipykernel_2151/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
    +/tmp/ipykernel_2154/2870202885.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_2151/4291268947.py:40: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_2154/4291268947.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_2151/4291268947.py:41: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +/tmp/ipykernel_2154/4291268947.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_2151/339476128.py:64: RuntimeWarning: invalid value encountered in scalar divide
    +
    /tmp/ipykernel_2154/339476128.py:64: RuntimeWarning: invalid value encountered in scalar divide
       m1 = y1 / x1
    -/tmp/ipykernel_2151/339476128.py:64: RuntimeWarning: divide by zero encountered in scalar divide
    +/tmp/ipykernel_2154/339476128.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 508cc58..751515f 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, 92013158, 678, 683], + 27328168, 50016, 654364711, -802750256, 13641472], 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, 5.37710476e+228]), - 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.94724204e-310, 6.94724155e-310, - 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, - 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, - 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, - 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, - 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, - 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, - 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, - 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, - 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, - 6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, - 6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310, - 6.94724155e-310, 6.94724136e-310]), + 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.93253789e-310, 6.93253760e-310, + 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, + 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, + 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, + 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, + 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, + 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, + 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, + 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, + 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, + 6.93253742e-310, 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, + 6.93253789e-310, 6.93253760e-310, 6.93253742e-310, 6.93253789e-310, + 6.93253760e-310, 6.93253742e-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_2182/843280888.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_2185/843280888.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 728e3a5..84c6ac4 100644 --- a/book/02-integration-1.html +++ b/book/02-integration-1.html @@ -727,7 +727,7 @@

    numpy.trapz -
    /tmp/ipykernel_2229/3604360318.py:4: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_2235/3604360318.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_2229/4086341036.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
    +
    /tmp/ipykernel_2235/4086341036.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_2229/36719416.py:4: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
    +
     
    -
    <matplotlib.legend.Legend at 0x7f8db3355710>
    +
    <matplotlib.legend.Legend at 0x7fb91aeae610>
     
    ../_images/0d992e05e05f92dc53b78d747da1fa725f1cb6fc66247847be3c6e338ba12bc2.png @@ -1114,7 +1114,7 @@

    scipy.integrate.solve_ivp -
    <matplotlib.legend.Legend at 0x7f8db10ba0d0>
    +
    <matplotlib.legend.Legend at 0x7fb918c0e0d0>
     
    ../_images/0f3cb0f20de8a66563583063f2afeb51738e8b0db5b5ace82e7cb68a5289387e.png diff --git a/book/07-nla-1.html b/book/07-nla-1.html index 8488a6e..b9fbbc5 100644 --- a/book/07-nla-1.html +++ b/book/07-nla-1.html @@ -854,7 +854,7 @@

    Derivatives of functions -
    /tmp/ipykernel_2342/1845505028.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_2343/1845505028.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_2342/1563071673.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_2343/1563071673.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_2342/1563071673.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_2343/1563071673.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_2342/1619064557.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_2343/1619064557.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_2342/2335501430.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_2343/2335501430.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 451493d..5fd1ed9 100644 --- a/book/08-nla-2.html +++ b/book/08-nla-2.html @@ -721,7 +721,7 @@

    Cubic equations of state -
    -
    -
    -
    @@ -1095,12 +1104,7 @@

    Systems of nonlinear equations -
    Failed at guess [-9.394454424418573, -0.7907650725827731].
    -The iteration is not making good progress, as measured by the 
    -  improvement from the last five Jacobian evaluations.
    -
    -
    -
    -
    -
    /tmp/ipykernel_2425/2917585576.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_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
       return derivative(f, x, dx=1e-6)
     
    @@ -707,9 +707,9 @@

    Newton-Raphson method of minima finding -
    -
    /tmp/ipykernel_2450/3278399195.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_2453/3278399195.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 2f36786..6e1076b 100644 --- a/book/15-intro-linear-algebra.html +++ b/book/15-intro-linear-algebra.html @@ -1257,7 +1257,7 @@

    The determinant -

    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 6fd979a..9e11d68 100644 --- a/book/17-linear-algebra-2.html +++ b/book/17-linear-algebra-2.html @@ -817,9 +817,9 @@

    Eigenvalues -
    array([[1.85294056, 0.3741679 , 1.16139508],
    -       [0.3741679 , 1.40558989, 1.5372893 ],
    -       [1.16139508, 1.5372893 , 0.74941638]])
    +
    array([[1.006998  , 1.05229805, 0.55603374],
    +       [1.05229805, 1.1552348 , 0.69082191],
    +       [0.55603374, 0.69082191, 0.86307225]])
     
    @@ -834,7 +834,7 @@

    Eigenvalues -
    array([ 3.44746413, -0.43591453, -0.89261489])
    +
    array([2.76334155, 0.69550009, 0.03373253])
     
    @@ -846,8 +846,7 @@

    Eigenvalues -
    array([1.55633319+0.j       , 0.09420867+0.2004125j,
    -       0.09420867-0.2004125j])
    +
    array([ 1.6583034 , -0.37742974,  0.11946859])
     
    @@ -861,7 +860,7 @@

    Eigenvalues -
    (np.float64(2.1189347076957206), np.float64(2.1189347076957206))
    +
    (np.float64(3.492574170384824), np.float64(3.492574170384824))
     
    @@ -875,7 +874,7 @@

    Eigenvalues -
    np.float64(2.1189347076957206)
    +
    np.float64(3.4925741703848234)
     
    @@ -889,7 +888,7 @@

    Eigenvalues -
    (np.float64(1.3414213957101666), np.float64(1.3414213957101675))
    +
    (np.float64(0.06483069921628332), np.float64(0.06483069921628344))
     
    @@ -903,10 +902,10 @@

    Eigenvalues -
    (array([ 3.44746413, -0.43591453, -0.89261489]),
    - array([[ 0.36772665,  0.88027133,  0.29983245],
    -        [ 0.53632987,  0.06264024, -0.84168074],
    -        [ 0.759689  , -0.47031754,  0.44908132]]))
    +
    (array([2.76334155, 0.69550009, 0.03373253]),
    + array([[-0.68909527, -0.67872757,  0.25392243],
    +        [-0.5738738 ,  0.29713869, -0.7631366 ],
    +        [-0.44251167,  0.67159325,  0.59426083]]))
     
    @@ -920,7 +919,7 @@

    Eigenvalues -
    (np.float64(1.0000000000000002), np.float64(0.9999999999999999))
    +
    (np.float64(1.0), np.float64(0.9999999999999998))
     
    @@ -932,8 +931,8 @@

    Eigenvalues -
    (array([1.10018882, 1.16497644, 2.43475858]),
    - array([1.26772444, 3.03470383, 1.0336616 ]))
    +
    (array([-1.63380064, -1.11501027, -0.70572824]),
    + array([-1.90420559, -1.87555609,  0.7016744 ]))
     
    @@ -946,8 +945,8 @@

    Eigenvalues -
    (array([1.26772444, 1.84897799, 2.61900058]),
    - array([1.26772444, 1.84897799, 2.61900058]))
    +
    (array([-1.90420559, -1.58580931, -1.22281088]),
    + array([-1.90420559, -1.58580931, -1.22281088]))
     
    @@ -959,9 +958,9 @@

    Eigenvalues -
    [np.float64(0.9999999999999999),
    - np.float64(1.0),
    - np.float64(0.9999999999999999)]
    +
    [np.float64(0.9999999999999998),
    + np.float64(0.9999999999999999),
    + np.float64(1.0)]
     
    @@ -1008,10 +1007,10 @@

    Eigenvalues -
    (array([-0.89261489, -0.43591453,  3.44746413]),
    - array([[ 0.29983245,  0.88027133,  0.36772665],
    -        [-0.84168074,  0.06264024,  0.53632987],
    -        [ 0.44908132, -0.47031754,  0.759689  ]]))
    +
    (array([0.03373253, 0.69550009, 2.76334155]),
    + array([[ 0.25392243, -0.67872757, -0.68909527],
    +        [-0.7631366 ,  0.29713869, -0.5738738 ],
    +        [ 0.59426083,  0.67159325, -0.44251167]]))
     
    diff --git a/book/18-linear-regression.html b/book/18-linear-regression.html index b1ac889..e950097 100644 --- a/book/18-linear-regression.html +++ b/book/18-linear-regression.html @@ -1134,10 +1134,11 @@

    LASSO regression

    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/c291cdf1da7c22fd6b0138dbc39780ad522b7667421e2778c67cdec9ae67dbea.png +../_images/43907df3a9a8182664f72d609a7efd07f68d7bf7b8e083520cf3b8b5ff99b940.png

    @@ -950,7 +950,7 @@

    Overfitting in GPR -../_images/9e803b6dc9401c783cd9fd590de03f3e943b231f8ad868b11532d644df84072a.png +../_images/a78cd84b0ff818f4379579778a5879f48b8f4dbb6f9a0e81e6040e7cd376d02c.png

    @@ -991,10 +991,10 @@

    Finding the hyperparameters in GPR -
    array([1.        , 0.07049851])
    +
    array([1.        , 0.06844819])
     
    -../_images/8f3a7bf246cdc8d2356396ea9d6fb00a2b79ac3bad200af6acc399c384e1e598.png +../_images/e9f828a48c520b6ad1530038ca1eb46f5d9417435763416c5089a0c72b55dca6.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: Optimization terminated successfully.
       success: True
        status: 0
    -      fun: 7.472045608184835
    -        x: [ 2.014e-05  6.449e-01 -1.482e+00]
    -      nit: 30
    -      jac: [-2.861e-06 -5.007e-06  5.841e-06]
    - hess_inv: [[ 3.680e+00  5.002e-03  1.012e-02]
    -            [ 5.002e-03  2.671e-02  1.830e-02]
    -            [ 1.012e-02  1.830e-02  5.557e-02]]
    -     nfev: 152
    -     njev: 38
    +      fun: 7.544479699294113
    +        x: [ 3.536e-05  6.509e-01 -1.475e+00]
    +      nit: 28
    +      jac: [ 6.199e-06 -5.543e-06  2.384e-07]
    + hess_inv: [[ 5.724e+00 -1.382e-03  3.716e-02]
    +            [-1.382e-03  2.573e-02  1.659e-02]
    +            [ 3.716e-02  1.659e-02  5.016e-02]]
    +     nfev: 136
    +     njev: 34
     

    @@ -1126,7 +1126,7 @@

    An example with a linear kernel -../_images/4ad898a2b1fbacb9a6f447f639a3a1799a56ffdd5d56e7b122e996dc7c179c64.png +../_images/67002f3f14ad30668d7118db29aad5fce45df4958bf1752831ef9fd93d3be1e6.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 - @@ -1204,7 +1204,7 @@

    Combining kernels -../_images/9451033f12106bf9544e28e31ebd872f5048b24ddc2dabe62035f568790fa329.png +../_images/d8f2ccf42bf0443c4ff2c1096b4870540cc1b34fec57e117abbb6671ed6b7ada.png

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

    @@ -1229,19 +1229,19 @@

    Combining kernels
      message: Optimization terminated successfully.
       success: True
        status: 0
    -      fun: 35.88700819020977
    -        x: [ 9.583e-01  5.792e-06  1.025e+00  1.116e+00  1.010e+00
    -             9.022e-03]
    -      nit: 21
    -      jac: [ 2.384e-06  3.338e-06 -4.768e-07  2.384e-06 -4.768e-07
    -             0.000e+00]
    - hess_inv: [[ 1.838e-02  1.101e-02 ... -1.100e-01 -6.600e-01]
    -            [ 1.101e-02  1.548e+00 ... -1.783e+00 -1.068e+01]
    +      fun: 31.224725016852602
    +        x: [-7.077e-06  4.036e-01 -1.749e+00  9.371e-01  1.001e+00
    +            -7.184e-04]
    +      nit: 45
    +      jac: [-3.338e-06  4.530e-06 -6.199e-06  4.768e-06 -1.192e-06
    +            -1.907e-06]
    + hess_inv: [[ 3.925e-01 -3.212e-02 ... -1.896e-02 -8.049e-02]
    +            [-3.212e-02  1.007e-02 ... -6.391e-03 -2.719e-02]
                 ...
    -            [-1.100e-01 -1.783e+00 ...  7.778e+00  4.663e+01]
    -            [-6.600e-01 -1.068e+01 ...  4.663e+01  2.795e+02]]
    -     nfev: 182
    -     njev: 26
    +            [-1.896e-02 -6.391e-03 ...  1.412e-01  5.995e-01]
    +            [-8.049e-02 -2.719e-02 ...  5.995e-01  2.546e+00]]
    +     nfev: 406
    +     njev: 58
     

    @@ -1268,7 +1268,7 @@

    Combining kernels -../_images/3ca5ed7d495a283a2851fad06fa287db5f2d41d2f8d69e139b58c8549b8ee2d2.png +../_images/31f2fb275604f65e95eea270cb5e204ee968db9bec3c7719b526073a10c33126.png

    Note that we get oscillatory + linear extrapolation behavior!

    diff --git a/docs/about.html b/docs/about.html index ec842f4..cc9df57 100644 --- a/docs/about.html +++ b/docs/about.html @@ -582,11 +582,11 @@

    About pycse -
    uname_result(system='Linux', node='fv-az1109-780', release='6.5.0-1023-azure', version='#24~22.04.1-Ubuntu SMP Wed Jun 12 19:55:26 UTC 2024', machine='x86_64')
    +
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     Linux
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    +fv-az714-90
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    diff --git a/docs/beginner.html b/docs/beginner.html
    index e23463f..1366c0b 100644
    --- a/docs/beginner.html
    +++ b/docs/beginner.html
    @@ -870,7 +870,7 @@ 

    A better fsolve -
    /tmp/ipykernel_2772/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
    +
    /tmp/ipykernel_2778/1685161423.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 e61d84c..8db216e 100644 --- a/docs/execution-statistics.html +++ b/docs/execution-statistics.html @@ -513,225 +513,225 @@

    Build statistics

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    diff --git a/docs/pycse.html b/docs/pycse.html index fa32e73..8024ce4 100644 --- a/docs/pycse.html +++ b/docs/pycse.html @@ -761,7 +761,7 @@

    Documentation
    [b, bint, se]
    b is a vector of the fitted parameters
    -
    bint is an array of confidence intervals bint[0] is the lower, bint[1] is the upper level.
    +
    bint is an array of confidence intervals. The ith row is for the ith parameter.
    se is an array of standard error for each parameter.
    diff --git a/objects.inv b/objects.inv index c697dbda19ba19ac62dd2dc14c744f9c09dffb0f..1362c4e6bc326d9cbe289c846d2d83569a148bdf 100644 GIT binary patch delta 30 lcmdnVd7N{Crf^YyR%&vILSABSszP3Vi9&H|$ws|y767Yh3i1E| delta 16 XcmX@kxs!8(CTnF$Mt2": [[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"]], "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": 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[[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 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"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 hyperparameters in GPR": [[34, "finding-the-hyperparameters-in-gpr"]], "Finding the maximum power of a photovoltaic device.": [[8, "finding-the-maximum-power-of-a-photovoltaic-device"]], "Finding the nth root of a periodic function": [[7, "finding-the-nth-root-of-a-periodic-function"]], "Finding the partial derivatives": [[8, "finding-the-partial-derivatives"]], "First guess": [[2, "first-guess"]], "First-order differential equations": [[17, "first-order-differential-equations"]], "Fit a line to numerical data": [[1, "fit-a-line-to-numerical-data"]], "Fitting a numerical ODE solution to data": [[1, "fitting-a-numerical-ode-solution-to-data"]], "Flexible nonlinear models for regression": [[32, "flexible-nonlinear-models-for-regression"]], "Float comparisons": [[42, "float-comparisons"]], "Fourth-order Runge-Kutta method": [[17, "fourth-order-runge-kutta-method"]], "Function extrema": [[23, "function-extrema"]], "Function integration by the Romberg method": [[6, "function-integration-by-the-romberg-method"]], "Functions": [[15, "functions"]], "Functions on arrays of values": [[0, "functions-on-arrays-of-values"]], "Functions that return multiple values": [[15, "functions-that-return-multiple-values"]], "Functions with multiple arguments": [[15, "functions-with-multiple-arguments"]], "GPR Kernels": [[34, "gpr-kernels"]], "GPR by example": [[34, "gpr-by-example"]], "GPR libraries": [[34, "gpr-libraries"]], "Gaussian (radial basis function)": [[33, "gaussian-radial-basis-function"]], "Gaussian Process Regression": [[34, "gaussian-process-regression"]], "Gaussian process regression (GPR)": [[34, "gaussian-process-regression-gpr"]], "Getting a dictionary of counts": [[10, "getting-a-dictionary-of-counts"]], "Getting derivatives from implicit functions with autograd": [[31, "getting-derivatives-from-implicit-functions-with-autograd"]], "Gibbs energy minimization and the NIST webbook": [[13, "gibbs-energy-minimization-and-the-nist-webbook"]], "Graphical methods to help get initial guesses for multivariate nonlinear regression": [[1, "graphical-methods-to-help-get-initial-guesses-for-multivariate-nonlinear-regression"]], "H2O": [[13, "h2o"]], "Handling units with dimensionless equations": [[12, "handling-units-with-dimensionless-equations"]], "Handling units with the quantities module": [[12, "handling-units-with-the-quantities-module"]], "Headings and subheadings": [[15, "headings-and-subheadings"]], "Homogeneous, first-order linear differential equations": [[17, "homogeneous-first-order-linear-differential-equations"]], "Improved interpolation?": [[3, "improved-interpolation"]], "Indexing vectors and arrays in Python": [[0, "indexing-vectors-and-arrays-in-python"]], "Inequality constraints": [[26, "inequality-constraints"]], "Integrating a batch reactor design equation": [[13, "integrating-a-batch-reactor-design-equation"]], "Integrating equations in Python": [[6, "integrating-equations-in-python"]], "Integrating functions in python": [[6, "integrating-functions-in-python"]], "Integrating the batch reactor mole balance": [[13, "integrating-the-batch-reactor-mole-balance"]], "Integration in Python": [[16, "integration-in-python"]], "Interpolate on f(t) then invert the interpolated number": [[3, "interpolate-on-f-t-then-invert-the-interpolated-number"]], "Interpolating between data points": [[29, "interpolating-between-data-points"]], "Interpolation": [[3, "interpolation"], [29, 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1/f": [[3, "invert-f-t-then-interpolate-on-1-f"]], "Is your ice cream float bigger than mine": [[6, "is-your-ice-cream-float-bigger-than-mine"]], "Isentropic compression of liquid to point 2": [[13, "isentropic-compression-of-liquid-to-point-2"]], "Isentropic expansion through turbine to point 4": [[13, "isentropic-expansion-through-turbine-to-point-4"]], "Isobaric heating to T3 in boiler where we make steam": [[13, "isobaric-heating-to-t3-in-boiler-where-we-make-steam"]], "Jupyter notebook introduction": [[14, "jupyter-notebook-introduction"]], "Keyboard shortcuts": [[15, "keyboard-shortcuts"]], "Know your tolerance": [[7, "know-your-tolerance"]], "LASSO regression": [[30, "lasso-regression"]], "Lambda Lambda Lambda": [[0, "lambda-lambda-lambda"]], "Last example": [[5, "last-example"]], "Lather, rinse and repeat": [[10, "lather-rinse-and-repeat"]], "Least Median regression": [[25, "least-median-regression"]], "Let fsolve do the work": [[2, "let-fsolve-do-the-work"]], "Leveraging linear algebra for iteration": [[28, "leveraging-linear-algebra-for-iteration"]], "Limitations of solutions by integration": [[17, "limitations-of-solutions-by-integration"]], "Linear algebra": [[5, "linear-algebra"]], "Linear algebra approaches to solving systems of constant coefficient ODEs": [[2, "linear-algebra-approaches-to-solving-systems-of-constant-coefficient-odes"]], "Linear algebra functions of arrays": [[27, "linear-algebra-functions-of-arrays"]], "Linear equality constraints for atomic mass conservation": [[13, "linear-equality-constraints-for-atomic-mass-conservation"]], "Linear least squares fitting with linear algebra": [[1, "linear-least-squares-fitting-with-linear-algebra"]], "Linear programming example with inequality constraints": [[8, "linear-programming-example-with-inequality-constraints"]], "Linear regression": [[30, "linear-regression"]], "Linear regression with confidence intervals (updated)": [[1, "linear-regression-with-confidence-intervals-updated"]], 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