%
% Math 451 - DeLillo - Fall 2012 diary
%
% Here is what I did in class on Aug. 22, 2012.
% (Some of the html output may look a little strange
% but the MATLA commands should be readable.)
%
%
tanh(e)
{??? Undefined function or variable 'e'.
}
e=exp(1)
e =
2.7183
format long
e
e =
2.718281828459046
tanh(e)
ans =
0.991328915800600
tanh(1)
ans =
0.761594155955765
help log
LOG Natural logarithm.
LOG(X) is the natural logarithm of the elements of X.
Complex results are produced if X is not positive.
See also log1p, log2, log10, exp, logm, reallog.
Reference page in Help browser
doc log
log10(2)
ans =
0.301029995663981
x=log10(2)
x =
0.301029995663981
10^x
ans =
2.000000000000000
Arg(1+i)
{??? Undefined function or method 'Arg' for input arguments of type
'double'.
}
angle(1+i)
ans =
0.785398163397448
pi/4
ans =
0.785398163397448
help atan
ATAN Inverse tangent, result in radians.
ATAN(X) is the arctangent of the elements of X.
See also atan2, tan, atand.
Reference page in Help browser
doc atan
help atan2
ATAN2 Four quadrant inverse tangent.
ATAN2(Y,X) is the four quadrant arctangent of the real parts of the
elements of X and Y. -pi <= ATAN2(Y,X) <= pi.
See also atan.
Reference page in Help browser
doc atan2
atan2(1,1)
ans =
0.785398163397448
angle(1+sqrt(2)*i)
ans =
0.955316618124509
atan2(sqrt(2),1)
ans =
0.955316618124509
load usapolgon
{??? Error using ==> load
Unable to read file usapolgon: No such file or directory.
}
load usapolygon
plot(uslon,uslat)
axis equal
b=[1;2]
b =
1
2
clc
b
b =
1
2
A=[2 1;1 1]
A =
2 1
1 1
x=A\b
x =
-1.000000000000000
3.000000000000000
size(A)
ans =
2 2
size(b)
ans =
2 1
size(x)
ans =
2 1
B=rand(5,5)
B =
Columns 1 through 3
0.814723686393179 0.097540404999410 0.157613081677548
0.905791937075619 0.278498218867048 0.970592781760616
0.126986816293506 0.546881519204984 0.957166948242946
0.913375856139019 0.957506835434298 0.485375648722841
0.632359246225410 0.964888535199277 0.800280468888800
Columns 4 through 5
0.141886338627215 0.655740699156587
0.421761282626275 0.035711678574190
0.915735525189067 0.849129305868777
0.792207329559554 0.933993247757551
0.959492426392903 0.678735154857773
help rand
RAND Uniformly distributed pseudorandom numbers.
R = RAND(N) returns an N-by-N matrix containing pseudorandom values drawn
from the standard uniform distribution on the open interval(0,1). RAND(M,N)
or RAND([M,N]) returns an M-by-N matrix. RAND(M,N,P,...) or
RAND([M,N,P,...]) returns an M-by-N-by-P-by-... array. RAND returns a
scalar. RAND(SIZE(A)) returns an array the same size as A.
Note: The size inputs M, N, P, ... should be nonnegative integers.
Negative integers are treated as 0.
R = RAND(..., 'double') or R = RAND(..., 'single') returns an array of
uniform values of the specified class.
Compatibility Note: In versions of MATLAB prior to 7.7, you controlled
the internal state of the random number stream used by RAND by calling
RAND directly with the 'seed', 'state', or 'twister' keywords. That
syntax is still supported for backwards compatibility, but is deprecated.
Beginning in MATLAB 7.7, use the default stream as described in
RANDSTREAM.
The sequence of numbers produced by RAND is determined by the internal
state of the uniform pseudorandom number generator that underlies RAND,
RANDI, and RANDN. Control that default random number stream using its
properties and methods. See RANDSTREAM for details about the default
stream.
Resetting the default stream to the same fixed state allows computations
to be repeated. Setting the stream to different states leads to unique
computations, however, it does not improve any statistical properties.
Since MATLAB uses the same state each time it starts up, RAND, RANDN, and
RANDI will generate the same sequence of numbers in each session unless
the state is changed.
Examples:
Generate values from the uniform distribution on the interval [a, b].
r = a + (b-a).*rand(100,1);
Generate integer values from the uniform distribution on the set 1:n.
r = randi(100,1);
Save the current state of the default stream, generate 5 values,
restore the state, and repeat the sequence.
defaultStream = RandStream.getDefaultStream;
savedState = defaultStream.State;
u1 = rand(1,5)
defaultStream.State = savedState;
u2 = rand(1,5) % contains exactly the same values as u1
Replace the default stream with a stream whose seed is based on CLOCK, so
RAND will return different values in different MATLAB sessions. NOTE: It
is usually not desirable to do this more than once per MATLAB session.
RandStream.setDefaultStream(RandStream('mt19937ar','seed',sum(100*clock)));
rand(1,5)
See also randi, randn, RandStream, RandStream/rand, RandStream/getDefaultStream,
sprand, sprandn, randperm.
Overloaded methods:
RandStream/rand
Reference page in Help browser
doc rand
C=randn(5)
C =
Columns 1 through 3
1.034693009917860 0.888395631757642 1.438380292815098
0.726885133383238 -1.147070106969150 0.325190539456198
-0.303440924786016 -1.068870458168032 -0.754928319169703
0.293871467096658 -0.809498694424876 1.370298540095228
-0.787282803758638 -2.944284161994896 -1.711516418853698
Columns 4 through 5
-0.102242446085491 -0.030051296196269
-0.241447041607358 -0.164879019209038
0.319206739165502 0.627707287528727
0.312858596637428 1.093265669039484
-0.864879917324456 1.109273297614398
clc
b=rand(5,1)
b =
0.276025076998578
0.679702676853675
0.655098003973841
0.162611735194631
0.118997681558377
x=A\b
{??? Error using ==> mldivide
Matrix dimensions must agree.
}
x=B\b
x =
-0.984962569993773
2.439563814021091
3.312426384116443
-5.651468242811344
1.708489008830043
b-Bx
{??? Undefined function or variable 'Bx'.
}
b-B*x
ans =
1.0e-15 *
0
-0.111022302462516
0.111022302462516
0
-0.222044604925031
A
A =
2 1
1 1
clc
A
A =
2 1
1 1
A(1,1)
ans =
2
A(2,1)
ans =
1
b
b =
0.276025076998578
0.679702676853675
0.655098003973841
0.162611735194631
0.118997681558377
b(3)
ans =
0.655098003973841
clear
clc
A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
A(3,1)=6
A =
1 2 3
4 5 6
6 8 9
A(3,1)=7
A =
1 2 3
4 5 6
7 8 9
x=[1;0;1]
x =
1
0
1
A*x
ans =
4
10
16
clear
clc
A=[1 2;1 0]
A =
1 2
1 0
B=[3 1;-1 2]
B =
3 1
-1 2
A*B
ans =
1 5
3 1
C=inv(A)
C =
0 1.000000000000000
0.500000000000000 -0.500000000000000
A*C
ans =
1 0
0 1
C*A
ans =
1 0
0 1
diary off
diary off