[lisplab-cvs] r59 - doc/manual

[Jørn Inge Vestgården]

Author: jivestgarden
Date: Mon Jul 20 03:54:44 2009
New Revision: 59

Log:
manual

Added:
   doc/manual/Makefile
Modified:
   doc/manual/lisplab.texi

Added: doc/manual/Makefile
==============================================================================
--- (empty file)
+++ doc/manual/Makefile	Mon Jul 20 03:54:44 2009
@@ -0,0 +1,9 @@
+source=lisplab.texi
+
+all:	html
+
+html:	$(source)
+	makeinfo --html $(source)
+
+pdf:	$(source)
+	texi2pdf $(source)
\ No newline at end of file

Modified: doc/manual/lisplab.texi
==============================================================================
--- doc/manual/lisplab.texi	(original)
+++ doc/manual/lisplab.texi	Mon Jul 20 03:54:44 2009
@@ -338,9 +338,111 @@
 @end example
 which is also settable. Note that the matrices are column major order. 
 
- at section Matrix manipulation
+ at section The dotted algebra
+The element-vise functions by conventions have names starting 
+with a dot (period). The dotted algebra works on the single elements and 
+is structure agnostic. The functions of the dotted algebra 
+introduce a programming style 
+much the same as for Matlab, and combined with the linear algebra
+functions, you can write compact programs, without the slower 
+single element references. 
+ at example
+LL> (.sin (drow 0 1))
+#<MATRIX-DGE  1x2
+0.0 0.8414709848078965 
+ @{BB1FE21@}>
+ at end example 
+And so also for the algebraic operations 
+ at example
+LL> (let ((a (drow 0 1))
+	  (b (dcol 0.1 0.2)))
+      (.+ a (.* b 2)))
+#<MATRIX-DGE  1x2
+0.2 1.4 
+ @{BC5AC51@}>
+ at end example
+Note here that the @code{.+}, @code{.*}, etc. ignore the structure 
+so that it is completely valid to add a row and a column matrix. Note
+also that the scalar is multiplied element-vise.  
+
+The dotted algebra is to some extent also implemented for 
+general element matrices
+ at example
+LL> (.+ (row 'matrix-ge 1/2 3/2) 1)
+#<MATRIX-GE  1x2
+3/2 5/2 
+ @{B5AE9B9@}>
+ at end example 
+
 
 @section Linear algebra
+The linear algebra functions (unlike the dotted algebra) 
+The linear algebra functions often start with @i{m}, although this 
+conventions is not strictly enforced. Currently there is no a wide 
+spectrum of linear algebra function, but you find matrix multiplication, 
+matrix inversion, transpose, conjugate transpose and eigenvalues. 
+
+Matrix multiplications
+ at example
+LL>(let ((a (dmat (1 0) (0 -1)))
+	 (b (dcol 0.1 0.2)))
+      (m* a b))
+#<MATRIX-DGE  2x1
+0.1 
+-0.2 
+ @{BD45221@}>
+ at end example
+Matrix inversion
+ at example
+LL> (minv (dmat (1 2) (-2 1)))
+#<MATRIX-DGE  2x2
+0.2 -0.4 
+0.4 0.2 
+ @{BD85161@}>
+ at end example
+Transpose
+ at example
+LL> (mtp (dmat (1 2) (-2 1)))
+#<MATRIX-DGE  2x2
+1.0 -2.0 
+2.0 1.0 
+ @{BD99B11@}>
+ at end example
+Conjugate transpose
+ at example
+LL> (mct (zmat (1 (* 2 %i)) (-2 1)))
+#<MATRIX-ZGE  2x2
+#C(1.0 -0.0) #C(-2.0 -0.0) 
+#C(0.0 -2.0) #C(1.0 -0.0) 
+ @{BDC1DC9@}>
+ at end example
+Eigenvalues
+ at example
+LL> (eigenvalues (dmat (1 2) (0 0.5)))
+#<MATRIX-DGE  2x1
+1.0 
+0.5 
+ @{B2C5B19@}>
+ at end example
+Eigenvectors
+ at example
+LL> (eigenvectors (dmat (1 2) (0 0.5)))
+(#<MATRIX-DGE  2x1
+1.0 
+0.5 
+ @{B3368C1@}>
+ #<MATRIX-DGE  2x2
+1.0 -0.9701425001453319 
+0.0 0.24253562503633297 
+ @{B3361A9@}>)
+ at end example
+
+Some of the linear algebra functions also work for 
+general element matrices 
+ at example
+
+ at end example 
+
 
 @section Matrix IO