Transcript Embedded Communications in Wireless Sensor Network

Chapter 5:
MuPAD Objects I
Numbers, Identifiers, Expressions
MATLAB
for Scientist and Engineers
Using Symbolic Toolbox
You are going to
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
See that MuPAD handles objects
Get to know MuPAD numbers, identifiers and
expression types
Use these objects for various purposes
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Domain Types
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Every MuPAD object belongs to some data
type, called the domain type.
Domain Types
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MuPAD Kernel: DOM_INT, DOM_RAT, etc.
MuPAD Language: Dom::Matrix(R), etc
User Defined Types
Identifying Domain Types
3
Fundamental Domain Types
4
Fundamental Domain Types (cont.)
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Operands: op and nops
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A MuPAD object can be
decomposed into operands.
Functions for accessing operands.
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Accessing sub-operands
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6
Operands: Example
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Accessing specific operands
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Operands: Nested Lists
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Object:
Operands and sub-operands
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Exercise
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The following call of solve returns a set:
Extract the value of the solution for y and
assign it to the identifier y.
Solution:
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Numbers
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Number Data Types
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Accessing Components
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Numbers (cont.)
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Integral Quotient and Remainder
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Number? Not a Number!
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Functions & Operators for Numbers
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Exercise
 


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Compute the decimal expansions of
and

163
3
with a precision of 10 and 100 digits,
e
respectively.
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What is the 234th digit after the decimal point
of  ?
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Exercise
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After you execute x:= 10^50/3.0, only the
first DIGITS decimal digits of x are
guaranteed to be correct.
a.
Truncating the fractional part via trunc is
therefore questionable. What does MuPAD do?
b.
What is returned for x after increasing DIGITS?
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Identifiers
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Identifiers are names such as x or f that may
represent variables and unknowns.
DOM_IDENT
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_assign and assign
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The operator := is
a short form of
the system function
_assign.
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assign: sets or lists
of equations are
transformed into
assignments:
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Identifier Concatenation
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Concatenation operator “.”
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Exercise
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Read the help page for solve. Solve the
system of equations
x1 + x2 = 1, x2 + x3 = 1, . . . , x19 + x20 = 1, x20 = π
in the unknowns x1, x2, . . . , x20.
Read the help page for assign and assign the
values of the solution to the unknowns.
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Symbolic Expressions
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An object containing symbolic terms
Number of Operands
Top Level Operator
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Expression Tree
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Graphical Representation of Expression
op(f,0)
=
+
op(f,[1,0])
0
op(f,2)
op(f,[1,1,0])
sin
*
x
g
x
0.3
op(f,[1,3])
?
1/5
y
op(f,[1,2,1,2])
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21
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System Functions vs. Operators
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They are equivalent
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Variable number of arguments
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Operators are converted into system
functions internally.
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Sequence and Range
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$ and ..
Sequence Operator
Range Operator
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Used with other operators
 1  2  3  ...  100
 1 2  3  ... 10
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Mapping a Function
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Applies a function to all operands of a
MuPAD object.
Function
Concatenation Operator
Use Back-ticks for
Operator Symbols
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Operator Priorities
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Higher priority operators apply first
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Example
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Key Takeaways
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Now, you are able to
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use op() and nops() to access operands of
MuPAD objects,
draw an expression tree for an expression,
tell how to use the following system functions and
operators.
dom_type
_mult
.
$
delete
..
op
map
assign
_sum
nops
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Notes
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