02feb partial checkin

author: bnewbold <bnewbold@eta.mit.edu> 2009-02-03 03:48:29 -0500
committer: bnewbold <bnewbold@eta.mit.edu> 2009-02-03 03:48:29 -0500
commit: 5a44d113571ca634c8582655130a2bb324a27e42 (patch)
tree: d9a39aa88a67f5c7ecadfe58062f84401bc0ecb6
parent: a3feb7494f34d60af11ac3f598dc6ac33d3bcb14 (diff)
download: 8thesis-5a44d113571ca634c8582655130a2bb324a27e42.tar.gz
8thesis-5a44d113571ca634c8582655130a2bb324a27e42.zip
5 files changed, 317 insertions, 1 deletions
diff --git a/journal/02feb2009-evolve-circle-01.png b/journal/02feb2009-evolve-circle-01.png
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diff --git a/journal/02feb2009.html b/journal/02feb2009.html
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+++ b/journal/02feb2009.html
@@ -0,0 +1,103 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
+"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head><title>bnewbold thesis</title></head>
+<body style="margin: 25px; font-family: helvetica;">
+<h1 style="border-bottom: 2px solid;">
+Journal: Jan 27, 2009</h1>
+<i>Bryan Newbold, <a href="mailto:bnewbold@mit.edu">bnewbold@mit.edu</a></i><br />
+<i><a href="http://web.mit.edu/bnewbold/thesis/">
+http://web.mit.edu/bnewbold/thesis/</a></i>
+<br /><p />
+<!-- ================================================================ -->
+<!-- ================================================================ -->
+
+Playing with crude evolution of basic differential equations:
+
+<pre style="margin:20px; border-left: solid grey 3px; background-color:lightgrey
+;padding:5px;width:750px;">
+(define J (- (* x d/dy) (* y d/dx)))
+
+(define ((((evolution order)
+	   delta-t vector-field)
+	  manifold-function)
+	 manifold-point)
+  (series:sum
+   (((exp (* delta-t vector-field))
+     manifold-function)
+    manifold-point)
+   order))
+
+(pe ((((evolution 6) 'a J) R2-chi)
+     ((R2 '-&gt;point) (up 1 0))))
+
+(pe ((((evolution 6) 2. J) R2-chi)
+     ((R2 '-&gt;point) (up 1 0))))
+
+(define mywindow (frame -4 4 -4 4))
+
+(define (plot-evolution win order initial a step)
+  (letrec 
+      ((dostep 
+	(lambda (val)
+	  (cond
+	   ((&lt; val a) (let ((this-point ((((evolution order) val J) R2-chi)
+					 ((R2 '-&gt;point) initial))))
+			(plot-point win
+				    (time this-point)
+				    (coordinate this-point))
+			(dostep (+ val step))))))))
+    (dostep 0.)))
+
+(plot-evolution mywindow 6 (up 1. 0.) 6. .01)
+</pre>
+<br />
+<img src="02feb2009-evolve-circle-01.png" />
+<br />
+Haha, not really what you'd expect at the end there... numerical error? 
+<br />
+And then interactively:
+<pre style="margin:20px; border-left: solid grey 3px; background-color:lightgrey
+;padding:5px;width:750px;">
+(define (explore-evolution window order length)
+  (define (iterate-mything i x y)
+    (if (&lt; i length)
+	(let ((this-point ((((evolution order) i J) R2-chi)
+			   ((R2 '-&gt;point) (up x y)))))
+	  (plot-point window (time this-point) (coordinate this-point))
+	  (iterate-mything (+ .01 i) x y))
+	(button-loop x y)))
+  (define (button-loop ox oy)
+    (pointer-coordinates
+     window
+     (lambda (x y button)
+       (let ((temp button))
+         (cond ((eq? temp 0) (write-line (cons x (cons y (quote ()))))
+                             (display " started.")
+                             (iterate-mything 0 x y))
+               ((eq? temp 1) (write-line (cons ox (cons oy (quote ()))))
+                             (display " continued.")
+                             (iterate-mything 0 ox oy))
+               ((eq? temp 2) (write-line (cons x (cons y (quote ()))))
+                             (display " hit.")
+                             (button-loop ox oy)))))))
+  (newline)
+  (display "Left button starts a trajectory.")
+  (newline)
+  (display "Middle button continues a trajectory.")
+  (newline)
+  (display "Right button interrogates coordinates.")
+  (button-loop 0. 0.))
+
+(explore-evolution mywindow 5 .4)
+</pre>
+<img src="02feb2009-evolve-circle-02.png" />
+<br />
+That looks a lot better!
+<br /><br />
+<a href="27jan2009.html"><i>(previous entry)</i></a>
+
+<!-- ================================================================ -->
+<!-- ================================================================ -->
+</body>
+</html>
diff --git a/journal/27jan2009.html b/journal/27jan2009.html
index 1677b17..7604d11 100644
--- a/journal/27jan2009.html
+++ b/journal/27jan2009.html
@@ -26,7 +26,8 @@ autocomplete variables in scheme buffers... which is very hard so I just
 bound Super-TAB instead. Ugh.
 
 <br /><br />
-<a href="26jan2009.html"><i>(previous entry)</i></a>
+<a href="26jan2009.html"><i>(previous entry)</i></a> - 
+<a href="02feb2009.html"><i>(next entry)</i></a>
 
 <!-- ================================================================ -->
 <!-- ================================================================ -->
diff --git a/work/funcdiff_play.scm b/work/funcdiff_play.scm
new file mode 100644
index 0000000..429933c
--- /dev/null
+++ b/work/funcdiff_play.scm
@@ -0,0 +1,212 @@
+
+;;; Jan 29th
+
+(load "~/thesis/scmutils/src/calculus/load.scm")
+
+;(define R2 (make-manifold R^n-type 2)) ; doesn't work, so...
+(define R2 (rectangular 2))
+;(define U (patch 'origin R2)) ; also undefined so going to AIM-2005-003.pdf
+
+(define R2 (rectangular 2))
+(define P2 (polar/cylindrical 2))
+
+
+(define R2-chi-inverse (R2 '->point))
+(define R2-chi (R2 '->coords))
+(define P2-chi (P2 '->coords))
+(define P2-chi-inverse (P2 '->point))
+
+;;; Feb 1st
+
+(print-expression
+ ((compose R2-chi-inverse P2-chi)
+  (up 'x0 'y0)))
+;= (up (sqrt (+ (expt x0 2) (expt y0 2))) (atan y0 x0))
+
+(print-expression
+ ((compose R2-chi P2-chi-inverse)
+  (up 'r0 'theta0)))
+
+; (up (* r0 (cos theta0)) (* r0 (sin theta0)))
+
+(define R2->R (-> (UP Real Real) Real))
+
+(define f
+  (compose (literal-function 'f-rect R2->R)
+	   R2-chi))
+; there is a simpler syntax...
+
+(define R2-point (R2-chi-inverse (up 'x0 'y0)))
+(define P2-point (P2-chi-inverse (up 'r0 'theta0)))
+
+(print-expression (f R2-point))
+; (f-rect (up x0 y0))
+(print-expression (f P2-point))
+; (f-rect (up (* r0 (cos theta0)) (* r0 (sin theta0))))
+
+(define g (literal-manifold-function 'g-polar P2))
+
+(print-expression (g R2-point))
+; (g-polar (up (sqrt (+ (expt x0 2) (expt y0 2))) (atan y0 x0)))
+
+(instantiate-coordinates R2 '(x y))
+(instantiate-coordinates P2 '(r theta))
+
+(print-expression (x R2-point))
+;x0
+
+(print-expression (theta R2-point))
+;(atan y0 x0)
+
+(define h (+ (* x (square r)) (cube y)))
+
+(print-expression (h P2-point))
+; (+ (* (expt r0 3) (expt (sin theta0) 3)) (* (expt r0 3) (cos theta0)))
+
+(print-expression (h R2-point))
+; (+ (expt x0 3) (* x0 (expt y0 2)) (expt y0 3))
+
+(print-expression
+ (D h))
+; a-euclidean-derivative
+
+; pe is print-expression
+
+(pe ((D h) R2-point))
+; (down (+ (* 3 (expt x0 2)) (expt y0 2)) (+ (* 2 x0 y0) (* 3 (expt y0 2))))
+
+;(pe (D (h R2-point)))
+; ERROR
+
+(pe ((D (compose h R2-chi-inverse)) R2-point))
+; (down (+ (* 3 (expt x0 2)) (expt y0 2)) (+ (* 2 x0 y0) (* 3 (expt y0 2))))
+
+; TODO: formal definition of operator vs. function?
+
+;;; Feb 2
+
+(define (vector-field-procedure components coordinate-system)
+  (define (the-procedure f)
+    (compose (* (D (compose f (coordinate-system '->point)))
+		components)
+	     (coordinate-system '->coords)))
+  the-procedure)
+
+(define (components->vecotr-field components coordinate-system)
+  (procedure->vector-field
+   (vector-field-procedure components coordinate-system)))
+
+(define v
+  (components->vector-field
+   (up (literal-function 'vx (-> (UP Real Real) Real))
+       (literal-function 'vy (-> (UP Real Real) Real)))
+   R2))
+
+; shorthand:
+; (define w (literal-vector-field 'v R2))
+
+;(pe ((v (literal-manifold-function 'f R2)) R2-point))
+
+(define (coordinatize vector-field coordsys)
+  (define ((v f) x)
+    (let ((b (compose (vector-field (coordsys '->coords))
+		      (coordsys '->point))))
+      (* ((D f) x) (b x))))
+  (make-operator v))
+
+#|
+(pe (((coordinatize v R2)
+      (literal-function 'f (-> (UP Real Real) Real)))
+     (up 'x0 'y0)))
+|#
+
+; Note: nice summary of vector field properties on p12
+
+;(pe ((d/dx (square r)) R2-point))
+;(pe ((d/dx (square r)) P2-point))
+
+(define J (- (* x d/dy) (* y d/dx)))
+
+(series:for-each pe 
+		 (((exp (* 'a J)) R2-chi)
+		  ((R2 '->point) (up 1 0)))
+		 6)
+;(up 1 0)
+;(up 0 a)
+;(up (* -1/2 (expt a 2)) 0)
+;(up 0 (* -1/6 (expt a 3)))
+;(up (* 1/24 (expt a 4)) 0)
+;(up 0 (* 1/120 (expt a 5)))
+
+; now do evolution on coordinates
+
+(define ((((evolution order)
+	   delta-t vector-field)
+	  manifold-function)
+	 manifold-point)
+  (series:sum
+   (((exp (* delta-t vector-field))
+     manifold-function)
+    manifold-point)
+   order))
+
+(pe ((((evolution 6) 'a J) R2-chi)
+     ((R2 '->point) (up 1 0))))
+
+(pe ((((evolution 6) 2. J) R2-chi)
+     ((R2 '->point) (up 1 0))))
+
+#|
+
+(define mywindow (frame -4 4 -4 4))
+
+(define (plot-evolution win order initial a step)
+  (letrec 
+      ((dostep 
+	(lambda (val)
+	  (cond
+	   ((< val a) (let ((this-point ((((evolution order) val J) R2-chi)
+					 ((R2 '->point) initial))))
+			(plot-point win
+				    (time this-point)
+				    (coordinate this-point))
+			(dostep (+ val step))))))))
+    (dostep 0.)))
+
+(plot-evolution mywindow 6 (up 1. 0.) 6. .01)
+
+
+
+(define (explore-evolution window order length)
+  (define (iterate-mything i x y)
+    (if (< i length)
+	(let ((this-point ((((evolution order) i J) R2-chi)
+			   ((R2 '->point) (up x y)))))
+	  (plot-point window (time this-point) (coordinate this-point))
+	  (iterate-mything (+ .01 i) x y))
+	(button-loop x y)))
+  (define (button-loop ox oy)
+    (pointer-coordinates
+     window
+     (lambda (x y button)
+       (let ((temp button))
+         (cond ((eq? temp 0) (write-line (cons x (cons y (quote ()))))
+                             (display " started.")
+                             (iterate-mything 0 x y))
+               ((eq? temp 1) (write-line (cons ox (cons oy (quote ()))))
+                             (display " continued.")
+                             (iterate-mything 0 ox oy))
+               ((eq? temp 2) (write-line (cons x (cons y (quote ()))))
+                             (display " hit.")
+                             (button-loop ox oy)))))))
+  (newline)
+  (display "Left button starts a trajectory.")
+  (newline)
+  (display "Middle button continues a trajectory.")
+  (newline)
+  (display "Right button interrogates coordinates.")
+  (button-loop 0. 0.))
+
+(explore-evolution mywindow 5 .4)
+
+|#
author	bnewbold <bnewbold@eta.mit.edu>	2009-02-03 03:48:29 -0500
committer	bnewbold <bnewbold@eta.mit.edu>	2009-02-03 03:48:29 -0500
commit	5a44d113571ca634c8582655130a2bb324a27e42 (patch)
tree	d9a39aa88a67f5c7ecadfe58062f84401bc0ecb6
parent	a3feb7494f34d60af11ac3f598dc6ac33d3bcb14 (diff)
download	8thesis-5a44d113571ca634c8582655130a2bb324a27e42.tar.gz 8thesis-5a44d113571ca634c8582655130a2bb324a27e42.zip