Changeset 1411 in Sophya for trunk/SophyaLib

Timestamp:

Feb 20, 2001, 7:28:26 PM (25 years ago)

Author:

ansari

Message:

MAJ documentation - Reza 20/2/2001

Location:

trunk/SophyaLib/Manual

Files:

• blue_sophya_400.eps (added)
• defsophya.sty (modified) (1 diff)
• sophya.tex (modified) (5 diffs)

trunk/SophyaLib/Manual/defsophya.sty

@@ -34 +34 @@
 {
 \vspace{1cm}
-\makebox[30mm][c]{\includegraphics[width=3cm]{hfi_icon_vsmall.eps}}
-\hspace{5mm} \raisebox{12mm}{\rule{85 mm}{0.5 mm}\makebox[40 mm]{\bf Sophya }}
+\makebox[160mm][c]{\includegraphics[width=6cm]{blue_sophya_400.eps}}
+% \hspace{7mm} \raisebox{6mm}{\rule{100 mm}{0.5 mm} }
+% \makebox[40 mm]{\bf Sophya }
 \vspace{2cm}
 \begin{center}

trunk/SophyaLib/Manual/sophya.tex

@@ -432 +432 @@
 arrays {\tt (int, float, double, complex, \ldots)}. The include
 file {\tt array.h} declares all the classes and definitions 
-in module TArray.  
+in module TArray. {\bf Array} is a typdef for arrays 
+with double precision floating value elements. \\
+{\tt typedef TArray$<$r\_8$>$ Array ; }
 
 \begin{figure}[hbt]
@@ -445 +447 @@
 The example below shows basic usage of arrays, creation, initialization
 and arithmetic operations. Different kind of {\bf Sequence} objects
-can be used for initializing arrays.
+can be used for initializing arrays. 
+
 \begin{figure}[hbt]
 \dclsbb{Sequence}{RandomSequence}
@@ -460 +463 @@
 ia = es;
 cout << "Array<int> ia = " << ia;
-// 2-D array of float filled with random numbers  
 // 2-D array of floats 
 TArray<r_4> b(6,4), c(6,4);
@@ -489 +491 @@
 \end{verbatim} 
 
-\subsection{Working with sub-arrays and Ranges}
-
-
 \subsection{Matrices and vectors}
 \index{\tcls{TMatrix}}  \index{\tcls{TVector}}
@@ -500 +499 @@
 along one dimension is equal 1 for vectors. Column vectors
 have {\tt NCols() = 1} and row vectors have {\tt NRows() = 1}.
-
-Example of a simple low-pass filter on a one dimensional array (Vector) 
+Mathematical expressions involving matrices and vectors can easily 
+be translated into C++ code using {\tt TMatrix} and 
+{\tt TVector} objects. {\bf Matrix} and {\bf Vector} are 
+typedefs for double precision float matrices and vectors.
+The operator {\bf *} beteween matrices is redefined to 
+perform matrix multiplication. One can then write: \\
+\begin{verbatim}
+  // We create a row vector
+  Vector v(1000, BaseArray::RowVector);
+  // Initialize values with a random sequence
+  v = RandomSequence();
+  // Compute the vector length (norm)
+  double norm = (v*v.Transpose()).toScalar();
+  cout << "Norm(v) = " << norm << endl;
+\end{verbatim}
+
+This module contains also simple Gauss matrix inversion algorithm
+which can be used to solve linear systems, as illustrated by the 
+example below:
+\begin{verbatim}
+#include "sopemtx.h"
+// ...
+// Creation of a random 5x5 matrix
+Matrix A(5,5);
+A = RandomSequence(RandomSequence::Flat);
+Vector X0(5);
+X0 = RandomSequence(RandomSequence::Gaussian);
+// Computing B = A*X0
+Vector B = A*X0;
+// Solving the system A*X = B 
+Vector X;
+LinSolve(A, B, X);
+// Checking the result
+Vector diff = X-X0;
+cout << "X-X0= " << diff ;
+double min,max;
+diff.MinMax(min, max);
+cout << " Min(X-X0) = " << min << " Max(X-X0) = " << max << endl; 
+\end{verbatim}
+
+\subsection{Working with sub-arrays and Ranges}
+A powerful mechanism is included in array classes for working with 
+sub-arrays. The class {\bf Range} can be used to specify range of array 
+indexes in any of the array dimensions. Any regularly spaced index
+range can be specified, using the {\tt start} and {\tt end} index
+and an optional step (or stride). It is also possible to specify
+the {\tt start} index and the number of elements.
+In the following example, a simple low-pas filter, on a one 
+dimensional stream (Vector) has been written using sub-arrays:  
+
 \begin{verbatim}
 // Input Vector containing a noisy periodic signal