Extreme Optimization > Sample Applications > M#: The .NET Language for technical Computing

Extreme Optimization Sample Applications

M#: The .NET Language for Technical Computing

Introduction
Reference

The Extreme Optimization Mathematics Library.for .NET contains extensive support for numerical linear algebra. To illustrate the range and versatility of the linear algebra classes, we created M#: the the .NET language for numerical computing. M# comes with a complete environment for linear algebra computations. The language (pronounced "M sharp") implements a subset of the Matlab language. Data types supported are boolean values, scalars, vectors, matrices and strings. It supports control flow constructs such as if, for, and while, as well as a large number of built-in functions.

The following tables list the operators and functions supported by the M# language:

Operator	Description
+	Addition, unary plus.
-	Subtraction, unary minus.
*	Multiplication, matrix multiplication.
/	Division, solution of linear system.
\	Backwards division, solution of linear system.
^	Raise a matrix or number to a power.
.*	Componentwise multiplication.
./	Componentwise division.
.\	Componentwise backward division.
.^	Componentwise power operator.
'	Matrix transpose.
== ~= < > <= >=	Relational operators.
:	Colon ('range') operator.

Table 1. Supported operators. 

Function	Description
size	Size of a matrix.
numel	Number of elements.
cat	Concatenate matrices.
horzcat	Concatenate matrices horizontally.
vertcat	Concatenate matrices vertically.
repmat	Tile a matrix horizontally and vertically.
flipud	Flip a matrix horizontally.
fliplr	Flip a matrix vertically.
find	Find non-zero elements of a matrix.
tril	Extract lower triangular matrix.
triu	Extract upper triangular matrix.

Table 2. Supported array operations. 

Function	Description
sum	Sum of elements in matrix columns.
cumsum	Cumulative sum of elements in matrix columns.
prod	Product of elements in matrix columns.
cumprod	Cumulative product of elements in matrix columns.
min	Return largest component(s).
max	Return smallest component(s).

Table 3. Supported matrix operations. 

Function	Description
zeros	Creates a matrix of all zeros.
ones	Creates a matrix of all ones.
eye	Creates an identity matrix.
rand	Creates a matrix with random components.
magic	Creates a magic square.
hilb	Creates a Hilbert matrix.
pascal	Creates a part of the Pascal triangle..
linspace	Creates a vector of equally spaced components.
logspace	Creates a vector of logarithmically spaced components.

Table 4. Supported special matrices. 

Function	Description
det	Determinant of a matrix.
trace	Trace of a matrix.
inv	Inverse matrix.
rcond	Estimate for the reciprocal of the condition number.
lu	LU decomposition of a matrix.
qr	QR decomposition of a matrix..

Table 5. Supported linear algebra operations. 

Function	Description
blanks	Returns a string of spaces.
deblank	Removes trailing spaces from a string.
findstr	Finds all occurrances of a string in another string.
lower	Converts a string to lower case.
strcat	Concatenates two or more strings.
strcmp	Compares two strings for equality.
strcmpi	Compares two strings for equality independent of case.
strjust	Aligns a string.
upper	Converts a string to upper case.

Table 6. Supported string functions. 

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