02-Jul-2023 17:49:18

exm_test():
  MATLAB/Octave version 5.2.0
  exm() is the "Experiments with MATLAB" library.

calendar_test():

  Current time using "bank" format:  2023      7      2     17     49    18.662

  Is 2023 a leap year?  Answer is false
dnum =  739069.74
dnow =  739069.00
xmas =  739245.00
days_till_xmas =  176.00
wday = Sun
c =

   687   685   685   687   684   688   684

bday =  708434
  Graphics saved as "biorhythm.png"

checkerboard_test():
  checkerboard(n) returns an nxn checkerboard matrix.
  1  0  1
  0  1  0
  1  0  1
f =

   0   0   0   0   0   0   0   0

t =

   1   2   3   4   5   6   7   8

s =

    1    2    3    5    8   13   21   34

f =

    1    2    3    5    8   13   21   34

Elapsed time is 1.51414 seconds.
f =

   1   2   3   5   8

fpf =

    2    4    6   10   16

ftf =

    1    4    9   25   64

ff =

    1    4    9   25   64

ffdf =

   1   2   3   5   8

cosfpi =

  -1   1  -1  -1   1

even =

  0  1  0  0  1

r =

          2        3/2        5/3        8/5

'hello_world' is a function from the file /home/john/public_html/m_src/exm/hello_world.m

*****************************************************************************80

 hello_world() prints a traditional greeting.

  Discussion:

    Programming languages are traditionally introduced by the
    phrase 'hello world'.  Here is a demo of some MATLAB capabilities.

  Usage:

    publish hello_world

  Licensing:

    Copyright 2014 The MathWorks, Inc.

  Author:

    Cleve Moler

  Reference:

    Cleve Moler,
    Experiments with MATLAB
    https://www.mathworks.com/moler


Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at https://www.octave.org and via the help@octave.org
mailing list.
h = hello world
ans =

h
e
l
l
o
 
w
o
r
l
d

ans = dlrow olleh
ans =

d
l
r
o
w
 
o
l
l
e
h

ans =

h          
 e         
  l        
   l       
    o      
           
      w    
       o   
        r  
         l 
          d

ans =  dehllloorw
x =

 Columns 1 through 7:

        104        101        108        108        111         32        119

 Columns 8 through 11:

        111        114        108        100

ans = hello world
ans = w
ans = khoor#zruog
H = HELLO WORLD

inregion_test():
  inregion() reports whether a point is inside or on
  the boundary of a polygonal region.

  Blue points inside, red points on boundary.
  Graphics saved as "inregion_test.png"

iteration_test()
ans =  1.2346
ans =  1.234567901234568
x =  42
phi =  1.6180
Avogadros_constant =    6.0221e+23
camelCaseComplexNumber = -3 + 4i
ans =  42
ans =  42
ans =  42
ans =  42
ans =  42
ans =  42
x =  6.5574
x =  2.7491
x =  1.9363
x =  1.7136
x =  42
 6.5574
 2.7491
 1.9363
 1.7136
 1.6473
 1.6270
 1.6208
 1.6189
 1.6183
 1.6181
 1.6181
 1.6180
k =  12
k =
    1    2    3    4    5    6    7    8    9   10   11   12

x =
   0.00000
   0.10000
   0.20000
   0.30000
   0.40000
   0.50000
   0.60000
   0.70000
   0.80000
   0.90000
   1.00000

   31    47    1.516
A =
    3.00   12.00    1.00
   12.00    0.00    2.00
    0.00    2.00    3.00

b =
   2.36
   5.26
   2.77

x =
   0.29
   0.05
   0.89

x =
   0.29   0.05   0.89

A =
    3.00   12.00    1.00
   12.00    0.00    2.00
    6.00    0.00    1.00

warning: matrix singular to machine precision
warning: called from
    linear_test at line 28 column 6
    exm_test at line 40 column 3
ans =
   0.43
   0.08
   0.08

b =
   2.36
   5.26
   2.63

x =
   0.44
   0.09
   0.00

ans =
   2.36
   5.26
   2.63

z =
  -0.16
  -0.04
   0.99

ans =
   0.00
   0.00
   0.00

t = 0.15
y =
   0.41
   0.08
   0.15

ans =
   2.36
   5.26
   2.63

A =
   8   1   6
   3   5   7
   4   9   2

ans =
   15   15   15

ans =
   15
   15
   15

ans =  15
ans =  15
ans =  15
ans =
   8   1   6
   3   5   7
   4   9   2

ans =
   8   3   4
   1   5   9
   6   7   2

ans =
   6   7   2
   1   5   9
   8   3   4

ans =
   4   9   2
   3   5   7
   8   1   6

ans =
   2   9   4
   7   5   3
   6   1   8

ans =
   2   7   6
   9   5   1
   4   3   8

ans =
   4   3   8
   9   5   1
   2   7   6

ans =
   6   1   8
   7   5   3
   2   9   4

Variables in the current scope:

   Attr Name         Size                     Bytes  Class
   ==== ====         ====                     =====  ===== 
        X          648x509                  2638656  double
        caption      2x28                        56  char
        map        128x3                       3072  double

Total is 330272 elements using 2641784 bytes

A =
   16    2    3   13
    5   11   10    8
    9    7    6   12
    4   14   15    1

A =
   16    3    2   13
    5   10   11    8
    9    6    7   12
    4   15   14    1

ans =
    15
    34
    65
   111
   175
   260
   369
   505

n =  5
M =
   17   24    1    8   15
   23    5    7   14   16
    4    6   13   20   22
   10   12   19   21    3
   11   18   25    2    9

n =  4
M =
   16    2    3   13
    5   11   10    8
    9    7    6   12
    4   14   15    1

'ismagical' is a function from the file /home/john/public_html/m_src/exm/ismagical.m

*****************************************************************************80

 ismagical() checks various magic aspects of square matrices.

  Discussion:

    m = ismagical(A) is a logical vector with four elements indicating:
    m(1) = Semimagic: all column sums and all row sums are equal.
    m(2) = Magic:  semimagic and both principal diagonals have the same sum.
    m(3) = Panmagic: magic and all the broken diagonals have the same sum.
    m(4) = Associative: all pairs of elements on oppositve sides of the
           center have the same sum, which must be twice the center value.

  Licensing:

    Copyright 2014 The MathWorks, Inc.

  Author:

    Cleve Moler

  Reference:

    Cleve Moler,
    Experiments with MATLAB
    https://www.mathworks.com/moler


Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at https://www.octave.org and via the help@octave.org
mailing list.
ans =
  1  1  0  1

ans =
  1  1  0  1

ans =
  1  1  0  1

ans =
  1  1  0  0

ans =
  1  1  0  1

ans =
  1  1  0  1

ans =
  1  1  0  1

ans =
  1  1  0  0

c =
 Columns 1 through 16:
   32   32   32   32   32   32   11    7    6    5    4    3    3    3    2    2
   32   32   32   32   32   32   32    9    6    5    4    3    3    3    2    2
   32   32   32   32   32   32   32   32    7    5    4    3    3    3    2    2
   32   32   32   32   32   32   32   32   27    5    4    3    3    3    2    2
   32   32   32   32   32   32   32   32   30    6    4    3    3    3    2    2
   32   32   32   32   32   32   32   32   13    7    4    3    3    3    2    2
   32   32   32   32   32   32   32   32   14    7    5    3    3    2    2    2
   32   32   32   32   32   32   32   32   32   17    4    3    3    2    2    2
   32   32   32   32   32   32   32   16    8   18    4    3    3    2    2    2
   32   32   32   32   32   32   32   11    6    5    4    3    3    2    2    2
   32   32   32   32   32   32   32   19    6    5    4    3    2    2    2    2
   32   32   32   32   32   32   32   23    8    4    4    3    2    2    2    2
   32   32   32   19   11   13   14   15   14    4    3    2    2    2    2    2
   22   32   12   32    7    7    7   14    6    4    3    2    2    2    2    2
   12    9    8    7    5    5    5   17    4    3    3    2    2    2    2    2
   32    7    6    5    5    4    4    4    3    3    2    2    2    2    2    1
   17    7    5    4    4    4    4    3    3    2    2    2    2    2    2    1
 Column 17:
    2
    2
    2
    2
    2
    2
    2
    2
    2
    2
    2
    2
    2
    2
    1
    1
    1

x =
   2
   4

A =
   4  -3
  -2   1

ans =
  -4
   0

ans =
   20  -14
  -14   10

ans =
   25  -11
  -11    5

R =
  -0.999774  -0.079373
  -0.155816  -0.064500

X =
  -6  -6  -7   0   7   6   6  -3  -3   0   0
  -7   2   1   8   1   2  -7  -7  -2  -2  -7

theta =  0.52360
G =
   0.86603  -0.50000
   0.50000   0.86603

theta =  30
G =
   0.86603  -0.50000
   0.50000   0.86603

v =
   0.00000   0.25000   0.50000   0.75000   1.00000

A =
   8   1   6
   3   5   7
   4   9   2

A =
   8   1   6
   3   5   7
   4   9   2

Z =
   0   0   0   0
   0   0   0   0
   0   0   0   0

E =
   1   1   1
   1   1   1
   1   1   1
   1   1   1

I =
Diagonal Matrix
   1   0   0   0
   0   1   0   0
   0   0   1   0
   0   0   0   1

M =
   8   1   6
   3   5   7
   4   9   2

R =
   0.7913706   0.0917800   0.6441463   0.0891172
   0.4827989   0.0191654   0.1504942   0.0052457

K =
   1   1   1   1
   2   2   2   2
   3   3   3   3
   4   4   4   4

J =
   1   2   3   4
   1   2   3   4
   1   2   3   4
   1   2   3   4

v =
    0.00000    0.25000    0.50000    0.75000    1.00000

n =  10
y =
    1    2    3    4    5    6    7    8    9   10

KJ =
    4    8   12   16
    8   16   24   32
   12   24   36   48
   16   32   48   64

JK =
   30   30   30   30
   30   30   30   30
   30   30   30   30
   30   30   30   30

ans =
    1    2    3    4
    2    4    6    8
    3    6    9   12
    4    8   12   16

ans =
   0.00000   0.06250   0.25000   0.56250   1.00000

v =
   0.00000
   0.25000
   0.50000
   0.75000
   1.00000

inner_prod =  1.8750
outer_prod =
   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.06250   0.12500   0.18750   0.25000
   0.00000   0.12500   0.25000   0.37500   0.50000
   0.00000   0.18750   0.37500   0.56250   0.75000
   0.00000   0.25000   0.50000   0.75000   1.00000

Z =
   1 - 0i   3 - 4i
   2 - 0i   5 - 0i

Z =
   1 + 0i   3 + 4i
   2 + 0i   5 + 0i

C =
{
  [1,1] = A
  [1,2] = rolling
  [1,3] = stone
  [1,4] = gathers
  [1,5] = momemtum
  [1,6] = .
}

ans = stone
ans =
{
  [1,1] = stone
}

ans =
{
  [1,1] = A
  [1,2] = rolling
  [1,3] = stone
}

ans = A
ans = rolling
ans = stone
ans =
{
  [1,1] = A
  [1,2] = rolling
  [1,3] = stone
}

M =
{
  [1,1] = 
  [1,2] =
  {
    [1,1] = E
    [1,2] =
    {
      [1,1] = I
      [1,2] =
      {
        [1,1] = S
        [1,2] =
        {
          [1,1] = H
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = V
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
      [1,3] =
      {
        [1,1] = U
        [1,2] =
        {
          [1,1] = F
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] = {}(0x0)
      }
    }
    [1,3] =
    {
      [1,1] = A
      [1,2] =
      {
        [1,1] = R
        [1,2] =
        {
          [1,1] = L
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] = {}(0x0)
      }
      [1,3] =
      {
        [1,1] = W
        [1,2] =
        {
          [1,1] = P
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = J
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
    }
  }
  [1,3] =
  {
    [1,1] = T
    [1,2] =
    {
      [1,1] = N
      [1,2] =
      {
        [1,1] = D
        [1,2] =
        {
          [1,1] = B
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = X
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
      [1,3] =
      {
        [1,1] = K
        [1,2] =
        {
          [1,1] = C
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = Y
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
    }
    [1,3] =
    {
      [1,1] = M
      [1,2] =
      {
        [1,1] = G
        [1,2] =
        {
          [1,1] = Z
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = Q
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
      [1,3] =
      {
        [1,1] = O
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
    }
  }
}

M =
{
  [1,1] = 
  [1,2] =
  {
    [1,1] = E
    [1,2] =
    {
      [1,1] = I
      [1,2] =
      {
        [1,1] = S
        [1,2] =
        {
          [1,1] = H
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = V
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
      [1,3] =
      {
        [1,1] = U
        [1,2] =
        {
          [1,1] = F
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] = {}(0x0)
      }
    }
    [1,3] =
    {
      [1,1] = A
      [1,2] =
      {
        [1,1] = R
        [1,2] =
        {
          [1,1] = L
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] = {}(0x0)
      }
      [1,3] =
      {
        [1,1] = W
        [1,2] =
        {
          [1,1] = P
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = J
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
    }
  }
  [1,3] =
  {
    [1,1] = T
    [1,2] =
    {
      [1,1] = N
      [1,2] =
      {
        [1,1] = D
        [1,2] =
        {
          [1,1] = B
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = X
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
      [1,3] =
      {
        [1,1] = K
        [1,2] =
        {
          [1,1] = C
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = Y
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
    }
    [1,3] =
    {
      [1,1] = M
      [1,2] =
      {
        [1,1] = G
        [1,2] =
        {
          [1,1] = Z
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
        [1,3] =
        {
          [1,1] = Q
          [1,2] = {}(0x0)
          [1,3] = {}(0x0)
        }
      }
      [1,3] =
      {
        [1,1] = O
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
    }
  }
}

M =
{
  [1,1] = T
  [1,2] =
  {
    [1,1] = N
    [1,2] =
    {
      [1,1] = D
      [1,2] =
      {
        [1,1] = B
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
      [1,3] =
      {
        [1,1] = X
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
    }
    [1,3] =
    {
      [1,1] = K
      [1,2] =
      {
        [1,1] = C
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
      [1,3] =
      {
        [1,1] = Y
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
    }
  }
  [1,3] =
  {
    [1,1] = M
    [1,2] =
    {
      [1,1] = G
      [1,2] =
      {
        [1,1] = Z
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
      [1,3] =
      {
        [1,1] = Q
        [1,2] = {}(0x0)
        [1,3] = {}(0x0)
      }
    }
    [1,3] =
    {
      [1,1] = O
      [1,2] = {}(0x0)
      [1,3] = {}(0x0)
    }
  }
}

M =
{
  [1,1] = N
  [1,2] =
  {
    [1,1] = D
    [1,2] =
    {
      [1,1] = B
      [1,2] = {}(0x0)
      [1,3] = {}(0x0)
    }
    [1,3] =
    {
      [1,1] = X
      [1,2] = {}(0x0)
      [1,3] = {}(0x0)
    }
  }
  [1,3] =
  {
    [1,1] = K
    [1,2] =
    {
      [1,1] = C
      [1,2] = {}(0x0)
      [1,3] = {}(0x0)
    }
    [1,3] =
    {
      [1,1] = Y
      [1,2] = {}(0x0)
      [1,3] = {}(0x0)
    }
  }
}

M =
{
  [1,1] = D
  [1,2] =
  {
    [1,1] = B
    [1,2] = {}(0x0)
    [1,3] = {}(0x0)
  }
  [1,3] =
  {
    [1,1] = X
    [1,2] = {}(0x0)
    [1,3] = {}(0x0)
  }
}

M =
{
  [1,1] = X
  [1,2] = {}(0x0)
  [1,3] = {}(0x0)
}

  E I S H V U F A R L W P J T N D B X K C Y M G Z Q O
  E T I A N M S U R W D K G O H V F L P J B X C Y Z Q
C =
 !"#$%&'()*+,-./0123456789:;<=>?
@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_
`abcdefghijklmnopqrstuvwxyz{|}~
 ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿
ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞß
àáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ

warning: text_renderer: skipping missing glyph for character '7f'
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    text at line 170 column 10
    morse_test at line 94 column 8
    exm_test at line 44 column 3
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warning: text_renderer: skipping missing glyph for character '7f'
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t =
   0.00000
   0.01778
   0.04446
   0.08447
   0.14449
   0.23451
   0.36955
   0.54489
   0.75386
   0.99697
   1.24446
   1.46841
   1.61987
   1.74913
   1.89244
   2.06379
   2.26545
   2.49945
   2.75092
   2.98271
   3.14243
   3.28844
   3.42900
   3.59453
   3.78965
   4.01634
   4.27094
   4.50875
   4.71590
   4.88162
   5.03193
   5.20502
   5.40716
   5.64133
   5.89280
   6.12454
   6.28319

y =
   0.00000   1.00000
   0.01778   0.99984
   0.04444   0.99901
   0.08437   0.99643
   0.14398   0.98958
   0.23237   0.97262
   0.36119   0.93247
   0.51830   0.85513
   0.68438   0.72894
   0.83963   0.54266
   0.94684   0.32036
   0.99424   0.10206
   0.99824  -0.04912
   0.98356  -0.17739
   0.94813  -0.31604
   0.88032  -0.47307
   0.76767  -0.63977
   0.59831  -0.80025
   0.38028  -0.92382
   0.15785  -0.98636
  -0.00103  -0.99888
  -0.14636  -0.98808
  -0.28334  -0.95782
  -0.43728  -0.89801
  -0.60306  -0.79613
  -0.76650  -0.64014
  -0.90287  -0.42635
  -0.97778  -0.20161
  -0.99826   0.00382
  -0.98393   0.16844
  -0.94759   0.31387
  -0.87934   0.47237
  -0.76654   0.63926
  -0.59719   0.79959
  -0.37936   0.92290
  -0.15721   0.98525
   0.00042   0.99768

ode1 is the user-defined function defined from: /home/john/public_html/m_src/exm/ode1.m

function [ t, y ] = ode1 ( F, tspan, y0 )

%*****************************************************************************80
%
%% ode1() is the world's simplest ODE solver.
%
%  Discussion:
%
%    ODE1(F,[t0,tfinal],y0) uses Euler's method to solve
%      dy/dt = F(t,y)
%    with y(t0) = y0 on the interval t0 <= t <= tfinal.
%
%  Licensing:
%
%    Copyright 2014 The MathWorks, Inc.
%
%  Author:
%
%    Cleve Moler
%
%  Reference:
%
%    Cleve Moler,
%    Experiments with MATLAB
%    https://www.mathworks.com/moler
%
  t0 = tspan(1);
  tfinal = tspan(end);
  h = ( tfinal - t0 ) / 200;
  y = y0;
  for t = t0:h:tfinal
    ydot = F(t,y);
    y = y + h * ydot;
  end

  return
end


t =  6.2832
y =
   0.032393
   1.103746

err =
   0.032393
   0.103746

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n =  6
i =
   2   6   3   4   4   5   6   1   1

j =
   1   1   2   2   3   3   3   4   6

G =
Compressed Column Sparse (rows = 6, cols = 6, nnz = 9 [25%])

  (2, 1) ->  1
  (6, 1) ->  1
  (3, 2) ->  1
  (4, 2) ->  1
  (4, 3) ->  1
  (5, 3) ->  1
  (6, 3) ->  1
  (1, 4) ->  1
  (1, 6) ->  1

j =
   1   1   2   2   3   3   3   4   6

x =
   0.321017
   0.170543
   0.106592
   0.136793
   0.064312
   0.200744

x =
   0.317744
   0.170191
   0.106711
   0.138335
   0.065204
   0.201815

x =
   0.317744
   0.170191
   0.106711
   0.138335
   0.065204
   0.201815

warning: matrix singular to machine precision, rcond = 1.14293e-17
warning: called from
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    exm_test at line 53 column 3
x =
   0.321017
   0.170543
   0.106592
   0.136793
   0.064312
   0.200744

k =  1
eta =  1
mu =  20
k =  1
eta =  1
mu =  20
ydot =
@(t, y) k * (1 - y / mu) * y

mu =
   300
   200

eta =
   400
   100

signs =
   1
  -1

pred_prey_ode =
@(t, y) signs .* (1 - flipud (y ./ mu)) .* y

period =  6.5357
warning: set: allowing normal to match units value normalized
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error: handles to nested functions are not yet supported
error: called from
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warning: gh_manager::do_close_all_figures: some graphics elements failed to close.