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AMITY UNIVERSITY UTTAR PRADESH
AMITY SCHOOL OF ENGINEERING AND TECHNOLOGY,
NOIDA
Computer Science & Engineering
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Experiment 1
Date : 05/01/2016
Aim : create a one and two dimensional array then
i)
ii)
Perfom arithmetic operations : addition , subtraction , multiplaction and exponential.
Perfom matrix operations : inverse , transpose ,rank.
Software Required : MATLAB 7.0
Introduction :
Addition: C = A + B adds arrays A and B and returns the result in C.
C = plus(A,B) is an alternate way to execute A + B, but is rarely used. It enable operator overloading for
classes.
Subtraction: C = A - B subtracts array B from array A and returns the result in C.
C = minus(A,B) is an alternate way to execute A - B, but is rarely used. It enables
for classes.
operator overloading
Multiplication: C = A*B is the matrix product of A and B. If A is an m-by-p and
then C is an m-by-n matrix defined by
B is a p-by-n matrix,
This definition says that C(i,j) is the inner product of the ith row of A with the jth column of B. You can
write this definition using the MATLAB® colon operator as
C(i,j) = A(i,:)*B(:,j)
For nonscalar A and B, the number of columns of A must equal the number of rows of B. Matrix
multiplication is not universally commutative for nonscalar inputs. That is, A*B is typically not equal to
B*A. If at least one input is scalar, then A*B is equivalent to A.*B and is commutative.
C = mtimes(A,B) is an alternative way to execute A*B, but is rarely used. It enables operator overloading
for classes.
Exponentiation: Y = expm(X) computes the matrix exponential of X. Although it is not computed this
way, if X has a full set of eigenvectors V with corresponding eigenvalues D, then [V,D] = eig(X) and
expm(X) = V*diag(exp(diag(D)))/V
Use exp for the element-by-element exponential.
Inverse: Y = inv(X) returns the inverse of the square matrix X. A warning message is printed if X is
badly scaled or nearly singular.
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Transpose: B = A.' returns the nonconjugate transpose of A, that is, interchanges the row and column
index for each element. If A contains complex elements, then A.' does not affect the sign of the imaginary
parts. For example, if A(3,2) is 1+2i and B = A.', then the element B(2,3) is also 1+2i.
B = transpose(A) is an alternate way to execute A.' and enables operator overloading for classes.
Rank: The rank function provides an estimate of the number of linearly independent rows or columns of
a full matrix.
k = rank(A) returns the number of singular values of A that are larger than the default tolerance,
max(size(A))*eps(norm(A)).
k = rank(A,tol) returns the number of singular values of A that are larger than tol.Code :
a=3;
b=5;
sum=a+b
sub=a-b
mul=a*b
exp=a^b
Result :
sum =
8
sub =
-2
mul =
15
exp =
243
>>
Code:
a=[1 6 7 ];
transpose(a)
a'
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rank(a)
Code:
a=[1 6 7 ; 40 15 3];
transpose(a)
a'
rank(a)
OUTPUT
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CODE:
a=[3 4 1; 6 7 1; 1 4 2]
t=transpose(a)
r=rank(a)
i=inv(a)
OUTPUT:
a=
3
4
1
6
7
1
1
4
2
3
6
1
4
7
4
1
1
2
t=
r=
3
i=
0.0962 0.0769 -0.3269
-0.1058
0.1154
0.2596
0.1635 -0.2692
0.1442
>>
Code:
a=[1 6 7 ; 40 15 3; 50 3 2];
transpose(a)
a'
rank(a)
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Code:
a=[1 4; 1 10];
b=[15 10; 2 3];
sum=a+b
sub=b-a
mult=a*b
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Code:
a=[1 4 5; 0 10 1;3 4 1];
b=[15 10 8; 2 3 7; 2 7 4];
sum=a+b
sub=b-a
mult=a*b
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EXPERIMENT-2
Date-19/01/2016
Aim- 1.Perfoming matrix manipulations Concatenation, Indexing ,Sorting, Shifting, Reshaping,
Resizing, flipping about an axis.
2.Creating arrays and performing, a) Relational operations- <,>,=
b) Logical operations- and ,or ,nor,xnor,not
THEORY:
PASCAL
Pascal matrix SyntaxA = pascal(n)
A = pascal(n,1)
A = pascal(n,2)
DescriptionA = pascal(n) returns the Pascal matrix of order n: a symmetric positive definite matrix with
integer entries taken from Pascal's triangle. The inverse of A has integer entries. A = pascal(n,1) returns
the lower triangular Cholesky factor (up to the signs of the columns) of the Pascal matrix. It is involutary,
that is, it is its own inverse. A = pascal(n,2) returns a transposed and permuted version of pascal(n,1). A is
a cube root of the identity matrix
RAND
Uniformly distributed random numbers and arrays SyntaxY = rand(n)
Y = rand(m,n)
Y = rand([m n])
Y = rand(m,n,p,...)
Y = rand([m n p...])
Y = rand(size(A))
rand
s = rand('state')
DescriptionThe rand function generates arrays of random numbers whose elements are uniformly
distributed in the interval (0,1). Y = rand(n) returns an n-by-n matrix of random entries. An error message
appears if n is not a scalar. Y = rand(m,n) or Y = rand([m n]) returns an m-by-n matrix of random entries.
Y = rand(m,n,p,...) or Y = rand([m n p...]) generates random arrays. Y = rand(size(A)) returns an array of
random entries that is the same size as A. rand, by itself, returns a scalar whose value changes each time
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it's referenced. s = rand('state') returns a 35-element vector containing the current state of the uniform
generator.
Magic
Magic square SyntaxM = magic(n)
DescriptionM = magic(n) returns an n-by-n matrix constructed from the integers 1 through n^2
with equal row and column sums. The order n must be a scalar greater than or equal to 3.
RemarksA magic square, scaled by its magic sum, is doubly stochastic.
Reshape
Reshape array SyntaxB = reshape(A,m,n)
B = reshape(A,m,n,p,...)
B = reshape(A,[m n p ...])
B = reshape(A,...,[],...)
B = reshape(A,siz)
DescriptionB = reshape(A,m,n) returns the m-by-n matrix B whose elements are taken columnwise from A. An error results if A does not have m*n elements. B = reshape(A,m,n,p,...) or B =
reshape(A,[m n p ...]) returns an n-dimensional array with the same elements as A but reshaped
to have the size m-by-n-by-p-by-... . The product of the specified dimensions, m*n*p*..., must be
the same as prod(size(A)). B = reshape(A,...,[],...) calculates the length of the dimension
represented by the placeholder [], such that the product of the dimensions equals prod(size(A)).
The value of prod(size(A)) must be evenly divisible by the product of the specified dimensions.
You can use only one occurence of []. B = reshape(A,siz) returns an n-dimensional array with the
same elements as A, but reshaped to siz, a vector representing the dimensions of the reshaped
array. The quantity prod(siz) must be the same as prod(size(A)).
FLIPLR
Flip matrices left-right SyntaxB = fliplr(A)
DescriptionB = fliplr(A) returns A with columns flipped in the left-right direction, that is, about a vertical
axis. If A is a row vector, then fliplr(A) returns a vector of the same length with the order of its elements
reversed. If A is a column vector, then fliplr(A) simply returns A.
FLIPUD
Flip matrices up-down SyntaxB = flipud(A)
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DescriptionB = flipud(A) returns A with rows flipped in the up-down direction, that is, about a horizontal
axis. If A is a column vector, then flipud(A) returns a vector of the same length with the order of its
elements reversed. If A is a row vector, then flipud(A) simply returns A.
Concatenation: An alternative to using the [] operator for concatenation are the three functions
cat, horzcat, and vertcat. With these functions, you can construct matrices (or multidimensional arrays)
along a specified dimension. Either of the following commands accomplish the same task as the
command C = [A; B] used in the section on Concatenating Matrices:
C = cat(1, A, B);
C = vertcat(A, B);
% Concatenate along the first dimension
% Concatenate vertically
Indexing: Indexing into a matrix is a means of selecting a subset of elements from the matrix.
MATLAB® has several indexing styles that are not only powerful and flexible, but also readable and
expressive. Indexing is a key to the effectiveness of MATLAB at capturing matrix-oriented ideas in
understandable computer programs.
Sorting: B = sort(A) sorts the elements of A in ascending order along the first array dimension whose
size does not equal 1.



If A is a vector, then sort(A) sorts the vector elements.
If A is a matrix, then sort(A) treats the columns of A as vectors and sorts each column.
If A is a multidimensional array, then sort(A) operates along the first array dimension whose size
does not equal 1, treating the elements as vectors.
Shifting: Y = circshift(A,K) circularly shifts the elements in array A by K positions. Specify K as
an integer to shift the rows of A, or as a vector of integers to specify the shift amount in each
dimension.
example
Y = circshift(A,K,dim) circularly shifts the values in array A by K positions along dimension
dim. Inputs K and dim must be scalars.
Logical Operations: OR- A | B | ... performs a logical OR of all input arrays A, B, etc., and
returns an array containing elements set to either logical 1 (true) or logical 0 (false). An element
of the output array is set to 1 if any input arrays contain a nonzero element at that same array
location. Otherwise, that element is set to 0
.
AND- A & B & ... performs a logical AND of all input arrays A, B, etc., and returns an
array containing elements set to either logical 1 (true) or logical 0 (false). An element of the
output array is set to 1 if all input arrays contain a nonzero element at that same array location.
Otherwise, that element is set to 0.
NOT- ~A performs a logical NOT of input array A, and returns an array containing
elements set to either logical 1 (true) or logical 0 (false). An element of the output array is set to 1
if the input array contains a zero value element at that same array location. Otherwise, that
element is set
XOR
Exclusive or SyntaxC = xor(A,B)
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DescriptionC = xor(A,B) performs an exclusive OR operation on the corresponding elements of arrays A
and B. The resulting element C(i,j,...) is logical true (1) if A(i,j,...) or B(i,j,...), but not both, is nonzero.
CODE:
A=[2, 3. 4; 5, 1, 2]
B=[4, 7, 1 ; 9, 6, 2;4 ,5, 8]
C=[A;B]
OUTPUT:
A=
2
3
4
5
1
2
4
7
1
9
6
2
4
5
8
2
3
4
5
1
2
4
7
1
9
6
2
4
5
8
B=
C=
CODE:
A=magic(3)
sort(A,'ascend')
B=rand(4)
sort(B,'descend')
C=rand(2,3)
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sort(C,'ascend')
D=pascal(2)
sort(D,'descend')
OUTPUT
A=
8
1
6
3
5
7
4
9
2
3
1
2
4
5
6
8
9
7
ans =
B=
0.9501 0.8913 0.8214 0.9218
0.2311 0.7621 0.4447 0.7382
0.6068 0.4565 0.6154 0.1763
0.4860 0.0185 0.7919 0.4057
ans =
0.9501 0.8913 0.8214 0.9218
0.6068 0.7621 0.7919 0.7382
0.4860 0.4565 0.6154 0.4057
0.2311 0.0185 0.4447 0.1763
C=
0.4451 0.4660 0.8462
0.9318 0.4186 0.5252
ans =
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0.4451 0.4186 0.5252
0.9318 0.4660 0.8462
D=
1
1
1
2
ans =
1
2
1
1
>>
Code:
A=[2 3 5; 6 8 2; 4 3 2; 1 4 8]
r=reshape(A,3,4)
t=reshape(A,6,2)
rotatematrix=rot90(A)
fliplr(A)
flipud(A)
OUTPUT:
A=
2
3
5
6
8
2
4
3
2
1
4
8
2
1
3
2
6
3
4
2
4
8
5
8
r=
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t=
2
3
6
4
4
5
1
2
3
2
8
8
rotatematrix =
5
2
2
8
3
8
3
4
2
6
4
1
5
3
2
2
8
6
2
3
4
8
4
1
1
4
8
4
3
2
6
8
2
2
3
5
ans =
ans =
CODE:
A=[3 4 5 ; 6 7 8]
B=[7 1 2 ; 6 3 0]
C=A>B
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D=A<B
E=[A==B]
F=or(A,B)
G=and(A,B)
H=not(A)
I=not(or(A,B))
J=xor(A,B)
OUPUT:
A=
3
4
5
6
7
8
7
1
2
6
3
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
B=
C=
D=
E=
F=
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G=
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
\H =
I=
J=
A2305214162
EXPERIMENT-3
Date-2/02/2016
Aim- 1.Generate random sequence numbers and plot them.
2.To calculate sum matrix, cumulative sum matrix.
Theory: RANDOM:
Syntax :X= random('name',A1,A2,A3,m,n)
Description :y = random('name',A1,A2,A3,m,n) returns a matrix of random numbers, where 'name' is a
string containing the name of the distribution, and A1, A2, and A3 are matrices of distribution
parameters. Depending on the distribution some of the parameters may not be necessary. Vector or
matrix inputs must all have the same size.
PLOT:
Syntax: plot(Y)
Description :plot(Y) plots the columns of Y versus their index if Y is a real number. If Y is complex, plot(Y)
is equivalent to plot(real(Y),imag(Y)). In all other uses of plot, the imaginary component is ignored.).
CUMSUM :
Syntax B = cumsum(A)
B = cumsum(A,dim)
Description :B = cumsum(A) returns the cumulative sum along different dimensions of an array. If A is a
vector, cumsum(A) returns a vector containing the cumulative sum of the elements of A. If A is a matrix,
cumsum(A) returns a matrix the same size as A containing the cumulative sums for each column of A. If
A is a multidimensional array, cumsum(A) works on the first nonsingleton dimension. B =
cumsum(A,dim) returns the cumulative sum of the elements along the dimension of A specified by
scalar dim. For example, cumsum(A,1) works across the first dimension (the rows).
SUM
Syntax B = sum(A)
Description: B = sum(A) returns sums along different dimensions of an array. If A is a vector, sum(A)
returns the sum of the elements. If A is a matrix, sum(A) treats the columns of A as vectors, returning a
row vector of the sums of each column. If A is a multidimensional array, sum(A) treats the values along
the first non-singleton dimension as vectors, returning an array of row vectors.
Code:
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a=rand(4,3)
plot(a)
cumsum(a,1)
cumsum(a,2)
sum(a)
OUTPUT
a=
0.9318 0.5252 0.0196
0.4660 0.2026 0.6813
0.4186 0.6721 0.3795
0.8462 0.8381 0.8318
Plot(a):
ans =
0.9318 0.5252 0.0196
1.3978 0.7278 0.7009
1.8165 1.3999 1.0804
2.6627 2.2381 1.9122
ans =
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0.9318 1.4570 1.4766
0.4660 0.6686 1.3499
0.4186 1.0908 1.4703
0.8462 1.6843 2.5161
ans =
2.6627 2.2381 1.9122
Code:
b=[ 3 4 6; 7 8 9]
plot(b)
cumsum(b,1)
cumsum(b,2)
sum(b)
c=magic(4)
plot(c)
cumsum(c,1)
cumsum(c,2)
plot(cumsum(c,2))
sum(c)
Output
b=
3
4
6
7
8
9
Plot(b):
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ans =
3
4
6
10 12 15
ans =
3
7 13
7 15 24
ans =
10 12 15
c=
16
2
3 13
5 11 10
9
7
8
6 12
4 14 15
1
ans =
16
2
3 13
21 13 13 21
30 20 19 33
34 34 34 34
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ans =
16 18 21 34
5 16 26 34
9 16 22 34
4 18 33 34
Plot(c):
plot(cumsum(c,2))
ans =
34 34 34 34
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Experiment
Date : /0/2016
Aim :
Software Required : MATLAB 7.0
Introduction :
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Experiment-4
Date-09/02/16
Aim- (a)Evaluate a given expression and rounding it to the nearest integer value using round ,ceil,floor
and fixed functions.
(b) Tringnometric functions ex-sin,cos,tan,cosec,cot,sec.
(c) Logarthimic function
(d) Square root
TOOL USED: MATLAB 7.0
THEORY:.COS
Cosine of an argument in radians Syntax Y = cos(X)
DescriptionThe cos function operates element-wise on arrays. The function's domains and ranges include
complex values. All angles are in radians. Y = cos(X) returns the circular cosine for each element of X.
TAN:
Tangent of an argument in radians SyntaxY = tan(X)
DescriptionThe tan function operates element-wise on arrays. The function's domains and ranges include
complex values. All angles are in radians. Y = tan(X) returns the circular tangent of each element of X.
SIN:
Sine of an argument in radians SyntaxY = sin(X)
Description The sin function operates element-wise on arrays. The function's domains and ranges include
complex values. All angles are in radians. Y = sin(X) returns the circular sine of the elements of X.
POWER:
Financial time series power Syntaxnewfts = tsobj .^ array
newfts = array .^tsobj
newfts = tsobj_1 .^ tsobj_2
ArgumentstsobjFinancial time series object arrayA scalar value or array with the number of rows equal to
the number of dates in tsobj and the number of columns equal to the number of data series in
tsobj.tsobj_1, tsobj_2A pair of financial time series objects Descriptionnewfts = tsobj .^ array raises all
values in the data series of the financial time series object tsobj element by element to the power indicated
by the array value.
log :
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Natural logarithm SyntaxY = log(X)
DescriptionThe log function operates element-wise on arrays. Its domain includes complex and negative
numbers, which may lead to unexpected results if used unintentionally. Y = log(X) returns the natural
logarithm of the elements of X. For complex or negative , where , the complex logarithm is returned.
log(z) = log(abs(z)) + i*atan2(y,x)
SQRT :Square root SyntaxB = sqrt(X)
DescriptionB = sqrt(X) returns the square root of each element of the array X. For the elements of X that
are negative or complex, sqrt(X) produces complex results.
(a) given expression and rounding it to the nearest integer value using round ,ceil,floor and fixed
functions.
Code:
a=rand(1,3)
round(a)
floor(a)
ceil(a)
fix(a)
b=5678.934
round(b)
floor(b)
ceil(b)
fix(b)
OUTPUT
a=
0.4565 0.0185 0.8214
ans =
0
0
1
0
0
ans =
0
ans =
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1
1
1
0
0
ans =
0
b=
5.6789e+003
ans =
5679
ans =
5678
ans =
5679
ans =
5678
(b) Trignometric functions
Code:
a=8;
f=100;
t=0:0.1:100 ;
x=a*cos(2*pi*f*t);
plot(x,t)
y=a*sin(2*pi*f*t);
figure, plot(t,y)
z=a*tan(2*pi*f*t);
plot(t,z)
j=a*cot(2*pi*f*t);
plot(t,j)
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i=a*sec(2*pi*f*t);
plot(t,i)
OUTPUT
(a) Cos
(b) Sin
(c) tan
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(d) cot
(e) sec
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(c) Logrithmic function
Code:
a=90
loga=log(a)
b=rand(2,3)
logb=log(b)
c=magic(3)
logc=log(c)
OUTPUT
a=
90
loga =
4.4998
b=
0.3529 0.0099 0.2028
0.8132 0.1389 0.1987
logb =
-1.0417 -4.6191 -1.5957
-0.2068 -1.9741 -1.6158
c=
8
1
6
3
5
7
4
9
2
logc =
2.0794
0 1.7918
1.0986 1.6094 1.9459
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1.3863 2.1972 0.6931
(d) Sqaure root
a=679;
sqrt(a)
b=magic(3)
sqrt(b)
OUTPUT
ans =
26.0576
b=
8
1
6
3
5
7
4
9
2
ans =
2.8284 1.0000 2.4495
1.7321 2.2361 2.6458
2.0000 3.0000 1.4142
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EXPERIMENT-5
Aim- (a) To create a vector X with elements X=(-1)^(n+1)/(2n-1) and add the 100 elements.
(b) Plot x,x^3,exp(x),exp(x^3) for the interval(0-4)
THEORY:
POWER:
Syntax:newfts = tsobj .^ array
newfts = array .^tsobj
ArgumentstsobjFinancial time series object arrayA scalar value or array with the number of rows equal to
the number of dates in tsobj and the number of columns equal to the number of data series in
tsobj.tsobj_1, tsobj_2A pair of financial time series objects Descriptionnewfts = tsobj .^ array raises all
values in the data series of the financial time series object tsobj element by element to the power indicated
by the array value.
EXP : Exponential SyntaxY = exp(X)
Description:The exp function is an elementary function that operates element-wise on arrays. Its domain
includes complex numbers. Y = exp(X) returns the exponential for each element of X. For complex , it
returns the complex exponentiaL.
PLOT :Linear 2-D plot Syntaxplot(Y)
plot(X1,Y1,...)
plot(X1,Y1,LineSpec,...)
plot(...,'PropertyName',PropertyValue,...)
plot(axes_handle,...)
h = plot(...)
hlines = plot('v6',...)
Descriptionplot(Y) plots the columns of Y versus their index if Y is a real number. If Y is complex,
plot(Y) is equivalent to plot(real(Y),imag(Y)). In all other uses of plot, the imaginary component is
ignored. plot(X1,Y1,...) plots all lines defined by Xn versus Yn pairs.
(a)
Code:
n=0:100;
X=(power(-1,(n+1)))/(2*n-1);
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a=sum(X)
OUTPUT
a=
-7.4252e-005
>>
(b) Plot x,x^3,exp(x),exp(x^3) for the interval(0-4)
Code:
n=0:100;
X=(power(-1,(n+1)))/(2*n-1);
X=0:4;
plot(X)
b=exp(X);
plot(b)
a=power(X,3);
plot(a)
c=exp(power(X,2));
plot(c)
OUTPUT
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(c) plot exp(x)
(d) plot exp(x^2)
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EXPERIMENT- 6
Date-16/02/16
AIM- Generating a sinusodial signal of internal frequency 100hz and plotting with graphical
enhancements - title name, (x n y)labeling, adding text, and grid on ,adding legend,adding new text to
existing plot.
Theory
Text
Create text object in current axes Syntaxtext(x,y,'string')
text(x,y,z,'string')
text(...'PropertyName',PropertyValue...)
h = text(...)
Descriptiontext is the low-level function for creating text graphics objects. Use text to place character
strings at specified locations.
The statements plot(0:pi/20:2*pi,sin(0:pi/20:2*pi))
text(pi,0,' \leftarrow sin(\pi)','FontSize',18)
annotate the point at (pi,0) with the string sin()
Sin
Sine of an argument in radians SyntaxY = sin(X)
Description The sin function operates element-wise on arrays. The function's domains and ranges include
complex values. All angles are in radians. Y = sin(X) returns the circular sine of the elements of X.
xlabel, ylabel, zlabel
Label the x-, y-, and z-axis Syntaxxlabel('string')
xlabel(fname)
xlabel(...,'PropertyName',PropertyValue,...)
xlabel(axes_handle,...)
h = xlabel(...)
ylabel(...)
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ylabel(axes_handle,...)
h = ylabel(...)
TITLE
Add title to current axes Syntaxtitle('string')
title(fname)
title(...,'PropertyName',PropertyValue,...)
h = title(...)
LEGEND
Display a legend on graphs Syntaxlegend('string1','string2',...)
legend(h,'string1','string2',...)
legend(string_matrix)
legend(h,string_matrix)
GRID
Grid lines for two- and three-dimensional plots Syntaxgrid on
grid off
grid minor
grid
grid(axes_handle,...)
Codea=1;
f=100;
t=0:0.001:0.5;
x=a*sin(2*pi*t*f);
plot(x)
xlabel('time')
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ylabel('Sinewave')
title('Sinosoidal Wave plot')
grid on
legend('sin(t)')
text(100,0,' \leftarrow sin(\pi)','fontsize',18);
OUTPUT
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EXPERIMENT -7
Date-23/02/16
Aim-Solve for first order diffrential equations using built in functions.
TOOL USED – MATLAB 7.0
THEORYDSOLVE
Symbolic solution of ordinary differential equations :Syntaxr = dsolve('eq1,eq2,...', 'cond1,cond2,...', 'v')
Description:dsolve('eq1,eq2,...', 'cond1,cond2,...', 'v') symbolically solves the ordinary differential
equation(s) specified by eq1, eq2,... using v as the independent variable and the boundary and/or initial
condition(s) specified by cond1,cond2,.... The default independent variable is t. The letter D denotes
differentiation with respect to the independent variable; with the primary default, this is d/dx. A D
followed by a digit denotes repeated differentiation. For example, D2 is d2/dx2. Any character
immediately following a differentiation operator is a dependent variable If the number of initial
conditions specified is less than the number of dependent variables, the resulting solutions will contain
the arbitrary constants C1, C2,.... You can also input each equation and/or initial condition as a separate
symbolic equation. dsolve accepts up to 12 input arguments. Three different types of output are
possible. For one equation and one output, dsolve returns the resulting solution with multiple solutions
to a nonlinear equation in a symbolic vector. For several equations and an equal number of outputs,
dsolve sorts the results in lexicographic order and assigns them to the outputs.
Code:
dsolve('Dy = a*x')
dsolve('Df = f + sin(t)')
dsolve('(Dy)^2 + y^2 = 1','s')
dsolve('Dy = a*y', 'y(0) = b')
dsolve('D2y = -a^2*y', 'y(0) = 1', 'Dy(pi/a) = 0')
dsolve('Dx = y', 'Dy = -x')
y = dsolve('(Dy)^2 + y^2 = 1','y(0) = 0')
OUTPUT:
ans =
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a*x*t+C1
ans =
-1/2*cos(t)-1/2*sin(t)+exp(t)*C1
ans =
1
-1
sin(s-C1)
-sin(s-C1)
ans =
b*exp(a*t)
ans =
cos(a*t)
ans =
x: [1x1 sym]
y: [1x1 sym]
y=
-sin(t)
sin(t)
>>
Single Differential Equation
dsolve('Dy=1+y^2')
(To specify an initial condition, use)
y = dsolve('Dy=1+y^2','y(0)=1')
y = dsolve('D2y=cos(2*x)-y','y(0)=1','Dy(0)=0', 'x');
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simplify(y)
OUTPUT:
ans =
tan(t+C1)
y=
tan(t+1/4*pi)
ans =
4/3*cos(x)-2/3*cos(x)^2+1/3
>>
Code:
Several Differential Equations
y = dsolve('Dy+4*y = exp(-t)', 'y(0) = 1')
OUTPUT:
y=
(1/3*exp(3*t)+2/3)*exp(-4*t)
>>
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EXPERIMENT-8
Date:8/03/2016
AIM- Write a brief script with a request for an input using input command .Evaluate the function h(t)
using if-else statement where, h(t)=(t-10) for 0<t<100 and h(t)=(0.45t+900) for t>100.
Exercise:
i)
ii)
t=5,h=-5
t=110,h=949.5
THEORY:
IF
Syntax :if expression
statements
end
Description:MATLAB evaluates the expression and, if the evaluation yields a logical true or nonzero
result, executes one or more MATLAB commands denoted here as statements. When you are nesting ifs,
each if must be paired with a matching end. When using elseif and/or else within an if statement, the
general form of the statement is if expression1
statements1
elseif expression2
statements2
else
statements3
end
INPUT
Request user input Syntaxuser_entry = input('prompt')
user_entry = input('prompt','s')
DescriptionThe response to the input prompt can be any MATLAB expression, which is evaluated using
the variables in the current workspace. user_entry = input('prompt') displays prompt as a prompt on the
screen, waits for input from the keyboard, and returns the value entered in user_entry. user_entry =
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input('prompt','s') returns the entered string as a text variable rather than as a variable name or
numerical value.
CODE:
t=input('input the value of t for the function h(t)')
if(0<t && t<100)
display('value of h')
h=(t-10)
elseif(t>100)
display ('value of h')
h=(0.45*t+900)
else display('error')
end
OUTPUT:
i)input the value of t for the function h(t)5
t=
5
value of h
h=
-5
ii) input the value of t for the function h(t)110
t=
110
value of h
h=
949.500
>>
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EXPERIMENT-9
Date- 15/03/16
Aim-Generate the square wave from the sum of sine wave of certain amplititude and frequency.
TheorySIN
Sine of an argument in radians SyntaxY = sin(X)
Description The sin function operates element-wise on arrays. The function's domains and ranges
include complex values. All angles are in radians. Y = sin(X) returns the circular sine of the elements of X.
Loop Control
for, while, continue, breakWith loop control statements, you can repeatedly execute a block of code,
looping back through the block while keeping track of each iteration with an incrementing index
variable. Use the for statement to loop a specific number of times. The while statement is more suitable
for basing the loop execution on how long a condition continues to be true or false. The continue and
break statements give you more control on exiting the loop. forThe for loop executes a statement or
group of statements a predetermined number of times. Its syntax is for index = start:increment:end
statements
end
The default increment is 1. You can specify any increment, including a negative one. For positive indices,
execution terminates when the value of the index exceeds the end value; for negative increments, it
terminates when the index is less than the end value.
Code:
t=0:0.01:10;
X=sin(t);
plot(t,X)
xlabel('time')
ylabel('x')
title('sinosoidal wave')
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f=5;
w=2*pi*f;
t=0:0.0001:1;
y=0;
for n=1:2:99
//loop for making harmonic function
y=y+(1/n)*sin(n*w*t)
end
plot(t,y)
xlabel('x')
ylabel('y')
OUTPUT:
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