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898c3ad
Jacobi Theta functions
evanmiller Jul 7, 2020
c78dcd7
[CI SKIP] Jacobi theta: Add special-value tests and more
evanmiller Jul 7, 2020
10fc561
Jacobi theta: Test two more of Watson's identities [CI SKIP]
evanmiller Jul 7, 2020
4b6701d
Improve precision of Jacobi theta functions [CI SKIP]
evanmiller Jul 8, 2020
9c68c11
Jacobi theta: Make changes suggested in #394 [CI SKIP]
evanmiller Jul 8, 2020
aa382f5
Add quadrature tests to Jacobi theta functions [CI SKIP]
evanmiller Jul 8, 2020
45e8ab9
Test Jacobi thetas against elliptic functions and elliptic integrals …
evanmiller Jul 9, 2020
0d3bc43
Test Jacobi Thetas against their Laplace transforms [CI SKIP]
evanmiller Jul 9, 2020
c293d48
Add a note on using log1p with Jacobi theta functions [CI SKIP]
evanmiller Jul 9, 2020
6b8dd5a
Merge branch 'develop' into jacobi-theta [CI SKIP]
evanmiller Jul 9, 2020
08391cd
Add random data tests to Jacobi Theta functions [CI SKIP]
evanmiller Jul 9, 2020
d73472e
Add small-tau tests and simplify Jacobi Theta code [CI SKIP]
evanmiller Jul 10, 2020
78fc9e2
Merge branch 'develop' into jacobi-theta [CI SKIP]
evanmiller Jul 13, 2020
98bc16c
Merge branch 'develop' into jacobi-theta [CI SKIP]
evanmiller Jul 17, 2020
2ecdf32
Merge branch 'develop' into jacobi-theta [CI SKIP]
evanmiller Jul 23, 2020
32a4d73
Merge branch 'develop' into jacobi-theta [CI SKIP]
evanmiller Jul 27, 2020
a2499bb
Add user documentation for Jacobi Theta functions [CI SKIP]
evanmiller Jul 29, 2020
041ca09
Add function graphs to Jacobi Theta docs [CI SKIP]
evanmiller Jul 30, 2020
3a0e3f3
Define Jacobi Theta test tolerances [CI SKIP]
evanmiller Jul 31, 2020
4630855
Merge branch 'develop' into jacobi-theta [CI SKIP]
evanmiller Jul 31, 2020
cf7ff40
Add implementation note on Jacobi theta functions [CI SKIP]
evanmiller Jul 31, 2020
b116c75
Consolidate Jacobi Theta ULPs plotting programs [CI SKIP]
evanmiller Aug 1, 2020
9fab61b
Fix q domain checking of jacobi_theta4 [CI SKIP]
evanmiller Aug 1, 2020
fb8d3f3
Add ULPs plots to Jacobi Theta docs [CI SKIP]
evanmiller Aug 1, 2020
dd2fcd1
Add missing Jacobi Theta ULPs plots [CI SKIP]
evanmiller Aug 1, 2020
d629f80
Add LaTeX source for Jacobi Theta equations [CI SKIP]
evanmiller Aug 1, 2020
ef39393
Remove unused Jacobi Theta PNG equations [CI SKIP]
evanmiller Aug 1, 2020
7ecda0f
Add Jacobi Theta performance script [CI SKIP]
evanmiller Aug 2, 2020
8cea3e9
Remove vestigial eps*eps check from jacobi_theta3 [CI SKIP]
evanmiller Aug 2, 2020
2902061
Update Jacobi Theta docs per code review comments [CI SKIP]
evanmiller Aug 2, 2020
5bea1e5
Enable arg promotion for Jacobi Theta functions [CI SKIP]
evanmiller Aug 3, 2020
46c59f8
Fix Jacobi Theta plotting script [CI SKIP]
evanmiller Aug 3, 2020
c9ac3a6
Change Jacobi Theta convergence criterion [CI SKIP]
evanmiller Aug 4, 2020
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Update Jacobi Theta docs per code review comments [CI SKIP]
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evanmiller committed Aug 2, 2020
commit 29020614dca2f7eb4e5dda2f97c21e1ec020ffc6
2 changes: 1 addition & 1 deletion doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html
Original file line number Diff line number Diff line change
Expand Up @@ -105,7 +105,7 @@ <h5>
</p>
</blockquote></div>
<p>
The envelope represents the function's <a class="link" href="../cond.html" title="Condition Numbers">condition
The envelope represents the function's <a class="ulink" href="https://en.wikipedia.org/wiki/Condition_number#One_variable" target="_top">condition
number</a>. Note that relative accuracy degenerates periodically near
θ<sub>1</sub>=0.
</p>
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2 changes: 1 addition & 1 deletion doc/html/math_toolkit/jacobi_theta/jacobi_theta2.html
Original file line number Diff line number Diff line change
Expand Up @@ -105,7 +105,7 @@ <h5>
</p>
</blockquote></div>
<p>
The envelope represents the function's <a class="link" href="../cond.html" title="Condition Numbers">condition
The envelope represents the function's <a class="ulink" href="https://en.wikipedia.org/wiki/Condition_number#One_variable" target="_top">condition
number</a>. Note that relative accuracy degenerates periodically near
θ<sub>2</sub>=0.
</p>
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2 changes: 1 addition & 1 deletion doc/html/math_toolkit/jacobi_theta/jacobi_theta3.html
Original file line number Diff line number Diff line change
Expand Up @@ -122,7 +122,7 @@ <h5>
</p>
</blockquote></div>
<p>
The envelope represents the function's <a class="link" href="../cond.html" title="Condition Numbers">condition
The envelope represents the function's <a class="ulink" href="https://en.wikipedia.org/wiki/Condition_number#One_variable" target="_top">condition
number</a>. Note that relative accuracy degenerates periodically near
θ<sub>3</sub>=1.
</p>
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2 changes: 1 addition & 1 deletion doc/html/math_toolkit/jacobi_theta/jacobi_theta4.html
Original file line number Diff line number Diff line change
Expand Up @@ -122,7 +122,7 @@ <h5>
</p>
</blockquote></div>
<p>
The envelope represents the function's <a class="link" href="../cond.html" title="Condition Numbers">condition
The envelope represents the function's <a class="ulink" href="https://en.wikipedia.org/wiki/Condition_number#One_variable" target="_top">condition
number</a>. Note that relative accuracy degenerates periodically near
θ<sub>4</sub>=1.
</p>
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26 changes: 17 additions & 9 deletions doc/html/math_toolkit/jacobi_theta/jacobi_theta_overview.html
Original file line number Diff line number Diff line change
Expand Up @@ -35,7 +35,7 @@
<a href="#ftn.math_toolkit.jacobi_theta.jacobi_theta_overview.f0" class="footnote" name="math_toolkit.jacobi_theta.jacobi_theta_overview.f0"><sup class="footnote">[5]</sup></a> <a href="#ftn.math_toolkit.jacobi_theta.jacobi_theta_overview.f1" class="footnote" name="math_toolkit.jacobi_theta.jacobi_theta_overview.f1"><sup class="footnote">[6]</sup></a> <a href="#ftn.math_toolkit.jacobi_theta.jacobi_theta_overview.f2" class="footnote" name="math_toolkit.jacobi_theta.jacobi_theta_overview.f2"><sup class="footnote">[7]</sup></a>.
</p>
<p>
Mathematically, the functions are described by:
They are
</p>
<div class="blockquote"><blockquote class="blockquote">
<p>
Expand All @@ -61,15 +61,15 @@

</p>
</blockquote></div>
<p>
Graphically, setting <span class="emphasis"><em>q</em></span>=0.15:
</p>
<div class="blockquote"><blockquote class="blockquote">
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_theta.svg" align="middle"></span>

</p>
</blockquote></div>
<p>
Plots of the four theta functions for <span class="emphasis"><em>q</em></span>=0.15.
</p>
<p>
Appropriately multiplied and divided, these four theta functions can be used
to implement the <a class="link" href="../jacobi/jac_over.html" title="Overview of the Jacobi Elliptic Functions">Jacobi elliptic
Expand All @@ -82,8 +82,12 @@
<code class="computeroutput"><a class="link" href="jacobi_theta2.html" title="Jacobi Theta Function θ2">jacobi_theta2</a></code>,
<code class="computeroutput"><a class="link" href="jacobi_theta3.html" title="Jacobi Theta Function θ3">jacobi_theta3</a></code>,
and <code class="computeroutput"><a class="link" href="jacobi_theta4.html" title="Jacobi Theta Function θ4">jacobi_theta4</a></code>,
where <span class="emphasis"><em>q</em></span> is restricted to the domain (0, 1). However,
a second τ parameterization is provided for all four functions, where
where <span class="emphasis"><em>q</em></span> is restricted to the domain (0, 1). These four
functions are equivalent to Mathematica's <a class="ulink" href="https://reference.wolfram.com/language/ref/EllipticTheta.html" target="_top">EllipticTheta</a>
function (whose first argument is the function number).
</p>
<p>
A second τ parameterization is also provided for all four functions, where
</p>
<div class="blockquote"><blockquote class="blockquote">
<p>
Expand All @@ -92,9 +96,13 @@
</p>
</blockquote></div>
<p>
Note that Boost assumes that τ is a purely imaginary number. This assumption
is not required by the mathematics, but it does cover the most common application
domains.
Note that there is a slight difference between τ in the equation above and
the <code class="computeroutput"><span class="identifier">tau</span></code> in the Boost function
signatures. The mathematical τ is assumed to be a purely imaginary number,
but the Boost argument is real-valued. Boost treats its real-valued argument
as an imaginary number; that is, it implicitly multiplies the argument by
<span class="emphasis"><em>i</em></span>. This assumption of τ's imaginarity is not required
by the mathematics, but it does cover the most common application domains.
</p>
<h5>
<a name="math_toolkit.jacobi_theta.jacobi_theta_overview.h0"></a>
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