Conjugate transpose: Difference between revisions

=={{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>