Conjugate transpose: Difference between revisions
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Normal?: TRUE
Unitary?: TRUE</pre>
=={{header|C}}==
<lang c>
/*28th August, 2012
Abhishek Ghosh
Uses C99 specified complex.h, complex datatype has to be defined and operation provided if used on non-C99 compilers */
#include<stdlib.h>
#include<stdio.h>
#include<complex.h>
typedef struct
{
int rows, cols;
complex **z;
} matrix;
matrix
transpose (matrix a)
{
int i, j;
matrix b;
b.rows = a.cols;
b.cols = a.rows;
b.z = (complex **) malloc (b.rows * sizeof (complex *));
for (i = 0; i < b.rows; i++)
{
b.z[i] = (complex *) malloc (b.cols * sizeof (complex));
for (j = 0; j < b.cols; j++)
{
b.z[i][j] = conj (a.z[j][i]);
}
}
return b;
}
int
isHermitian (matrix a)
{
int i, j;
matrix b = transpose (a);
if (b.rows == a.rows && b.cols == a.cols)
{
for (i = 0; i < b.rows; i++)
{
for (j = 0; j < b.cols; j++)
{
if (b.z[i][j] != a.z[i][j])
return 0;
}
}
}
else
return 0;
return 1;
}
matrix
multiply (matrix a, matrix b)
{
matrix c;
int i, j;
if (a.cols == b.rows)
{
c.rows = a.rows;
c.cols = b.cols;
c.z = (complex **) malloc (c.rows * (sizeof (complex *)));
for (i = 0; i < c.rows; i++)
{
c.z[i] = (complex *) malloc (c.cols * sizeof (complex));
c.z[i][j] = 0 + 0 * I;
for (j = 0; j < b.cols; j++)
{
c.z[i][j] += a.z[i][j] * b.z[j][i];
}
}
}
return c;
}
int
isNormal (matrix a)
{
int i, j;
matrix a_ah, ah_a;
if (a.rows != a.cols)
return 0;
a_ah = multiply (a, transpose (a));
ah_a = multiply (transpose (a), a);
for (i = 0; i < a.rows; i++)
{
for (j = 0; j < a.cols; j++)
{
if (a_ah.z[i][j] != ah_a.z[i][j])
return 0;
}
}
return 1;
}
int
isUnitary (matrix a)
{
matrix b;
int i, j;
if (isNormal (a) == 1)
{
b = multiply (a, a);
for (i = 0; i < b.rows; i++)
{
for (j = 0; j < b.cols; j++)
{
if ((i == j && b.z[i][j] != 1) || (i != j && b.z[i][j] != 0))
return 0;
}
}
return 1;
}
return 0;
}
int
main ()
{
complex z = 3 + 4 * I;
matrix a, aT;
int i, j;
printf ("Enter rows and columns :");
scanf ("%d%d", &a.rows, &a.cols);
a.z = (complex **) malloc (a.rows * sizeof (complex *));
printf ("Randomly Generated Complex Matrix A is : ");
for (i = 0; i < a.rows; i++)
{
printf ("\n");
a.z[i] = (complex *) malloc (a.cols * sizeof (complex));
for (j = 0; j < a.cols; j++)
{
a.z[i][j] = rand () % 10 + rand () % 10 * I;
printf ("\t%f + %fi", creal (a.z[i][j]), cimag (a.z[i][j]));
}
}
aT = transpose (a);
printf ("\n\nTranspose of Complex Matrix A is : ");
for (i = 0; i < aT.rows; i++)
{
printf ("\n");
aT.z[i] = (complex *) malloc (aT.cols * sizeof (complex));
for (j = 0; j < aT.cols; j++)
{
aT.z[i][j] = rand () % 10 + rand () % 10 * I;
printf ("\t%f + %fi", creal (aT.z[i][j]), cimag (aT.z[i][j]));
}
}
printf ("\n\nComplex Matrix A %s hermitian",
isHermitian (a) == 1 ? "is" : "is not");
printf ("\n\nComplex Matrix A %s unitary",
isUnitary (a) == 1 ? "is" : "is not");
printf ("\n\nComplex Matrix A %s normal",
isNormal (a) == 1 ? "is" : "is not");
return 0;
}
</lang>
{{out}}
<pre>
Enter rows and columns :3 3
Randomly Generated Complex Matrix A is :
3.000000 + 6.000000i 7.000000 + 5.000000i 3.000000 + 5.000000i
6.000000 + 2.000000i 9.000000 + 1.000000i 2.000000 + 7.000000i
0.000000 + 9.000000i 3.000000 + 6.000000i 0.000000 + 6.000000i
Transpose of Complex Matrix A is :
2.000000 + 6.000000i 1.000000 + 8.000000i 7.000000 + 9.000000i
2.000000 + 0.000000i 2.000000 + 3.000000i 7.000000 + 5.000000i
9.000000 + 2.000000i 2.000000 + 8.000000i 9.000000 + 7.000000i
Complex Matrix A is not hermitian
Complex Matrix A is not unitary
Complex Matrix A is not normal</pre>
=={{header|Factor}}==
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