[genius] Mon Feb 16 14:26:02 2015 Jiri (George) Lebl <jirka 5z com>

[George Lebl <jirka src gnome org>]

commit ac98dfbb744e619c9228cafb315acf2411573f50
Author: Jiri (George) Lebl <jiri lebl gmail com>
Date:   Mon Feb 16 14:26:09 2015 -0600

    Mon Feb 16 14:26:02 2015  Jiri (George) Lebl <jirka 5z com>
    
        * examples/fourier-series-plotting.gel: Replace the hand coded
          graph with more general code that can be used to show fourier
          series for more functions

 ChangeLog                                 |    6 +++
 examples/Makefile.am                      |    2 +-
 examples/fourier-series-half-sawtooth.gel |   52 -----------------------------
 examples/fourier-series-plotting.gel      |   41 ++++++++++++++++++++++
 4 files changed, 48 insertions(+), 53 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index 524e6a4..13510aa 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@
+Mon Feb 16 14:26:02 2015  Jiri (George) Lebl <jirka 5z com>
+
+       * examples/fourier-series-plotting.gel: Replace the hand coded
+         graph with more general code that can be used to show fourier
+         series for more functions
+
 Fri Feb 13 11:46:57 2015  Jiri (George) Lebl <jirka 5z com>
 
        * gtkextra/*.c: remove the inline from roundint.  Probably not
diff --git a/examples/Makefile.am b/examples/Makefile.am
index 21cdcc4..b93e9e0 100644
--- a/examples/Makefile.am
+++ b/examples/Makefile.am
@@ -17,7 +17,7 @@ example_DATA = \
        taylor-exp.gel \
        taylor-sin.gel \
        fourier-series-animation.gel \
-       fourier-series-half-sawtooth.gel \
+       fourier-series-plotting.gel \
        rsa.gel \
        easy-matrix-examples.gel \
        peano.gel
diff --git a/examples/fourier-series-plotting.gel b/examples/fourier-series-plotting.gel
new file mode 100644
index 0000000..5b40698
--- /dev/null
+++ b/examples/fourier-series-plotting.gel
@@ -0,0 +1,41 @@
+# Category: Differential Equations
+# Name: Fourier series plotting
+
+# Define the function.  We will only use it on [-1,1] and extend
+# periodically.  There are a number of functions to try.  The more
+# regularity the function has (after extending periodically) the
+# faster the convergence.
+function f(x) = (
+  if x < 0 then 0 else x   # half sawtooth
+  #0.5*(x+1)               # sawtooth
+  #if x < 0 then 0 else 1  # step function
+  #|x|                     # function with corners
+  #-(x-1)*(x+1)            # function with sharp corner
+  #((x-1)*(x+1))^2         # function with first derivative
+);  
+
+LinePlotWindow=[-2,2,-0.5,1.5];
+LinePlotDrawLegends=false;
+
+LinePlotClear();
+PlotWindowPresent(); # Make sure the window is raised
+
+N = 20; #number of harmonics to do
+
+LinePlot(PeriodicExtension(f,-1,1));
+
+print("Computing...");
+#Compute the first N harmonics.  c will be a vector of
+#two vectors c@(1) are the cosine coefficients, c@(2) are
+#the sine coefficients 
+c = NumericalFourierSeriesCoefficients (f, 1, N);
+a = c@(1);
+b = c@(2);
+
+for n=1 to N do (
+  #wait(1); if you want to slow the anumation
+  fs = FourierSeriesFunction (a@(1:n), b@(1:n), 1);
+  print("Plotting up to the " + n + "th harmonic...");
+  LinePlot(PeriodicExtension(f,-1,1), fs);
+);
+