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/*
* sl2c_matrices.c
*
* This file provides the following functions for working with SL2CMatrices:
*
* void sl2c_copy(SL2CMatrix dest, CONST SL2CMatrix source);
* void sl2c_invert(CONST SL2CMatrix a, SL2CMatrix inverse);
* void sl2c_complex_conjugate(CONST SL2CMatrix a, SL2CMatrix conjugate);
* void sl2c_product(CONST SL2CMatrix a, CONST SL2CMatrix b, SL2CMatrix product);
* void sl2c_adjoint(CONST SL2CMatrix a, SL2CMatrix adjoint);
* Complex sl2c_determinant(CONST SL2CMatrix a);
* void sl2c_normalize(SL2CMatrix a);
* Boolean sl2c_matrix_is_real(CONST SL2CMatrix a);
*/
#include "kernel.h"
void sl2c_copy(
SL2CMatrix dest,
CONST SL2CMatrix source)
{
int i,
j;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
dest[i][j] = source[i][j];
}
void sl2c_invert(
CONST SL2CMatrix a,
SL2CMatrix inverse)
{
Complex temp;
temp = a[0][0];
inverse[0][0] = a[1][1];
inverse[1][1] = temp;
inverse[0][1] = complex_negate(a[0][1]);
inverse[1][0] = complex_negate(a[1][0]);
}
void sl2c_complex_conjugate(
CONST SL2CMatrix a,
SL2CMatrix conjugate)
{
int i,
j;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
conjugate[i][j] = complex_conjugate(a[i][j]);
}
void sl2c_product(
CONST SL2CMatrix a,
CONST SL2CMatrix b,
SL2CMatrix product)
{
int i,
j;
SL2CMatrix temp;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
temp[i][j] = complex_plus
(
complex_mult(a[i][0], b[0][j]),
complex_mult(a[i][1], b[1][j])
);
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
product[i][j] = temp[i][j];
}
void sl2c_adjoint(
CONST SL2CMatrix a,
SL2CMatrix adjoint)
{
int i,
j;
SL2CMatrix temp;
/*
* We initially write the result into a temporary matrix,
* so that if the matrices a and adjoint are the same the
* [1][0] entry won't overwrite the [0][1] entry.
*/
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
temp[i][j] = complex_conjugate(a[j][i]);
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
adjoint[i][j] = temp[i][j];
}
Complex sl2c_determinant(
CONST SL2CMatrix a)
{
return(
complex_minus (
complex_mult(a[0][0], a[1][1]),
complex_mult(a[0][1], a[1][0])
)
);
}
void sl2c_normalize(
SL2CMatrix a)
{
/*
* If the matrix a is nonsingular, normalize it to have determinant one.
* Otherwise, generate an error message and quit.
*/
int i,
j;
Complex det,
factor;
det = sl2c_determinant(a);
if (complex_nonzero(det) == FALSE)
uFatalError("sl2c_normalize", "sl2c_matrices");
factor = complex_sqrt(det);
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
a[i][j] = complex_div(a[i][j], factor);
}
Boolean sl2c_matrix_is_real(
CONST SL2CMatrix a)
{
int i,
j;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
if (a[i][j].imag != 0.0)
return FALSE;
return TRUE;
}
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