/*
* Invert a toeplitz matrix. Input is the first column of the matrix and also
* is the output.
* IMP - size must be a power of two.
*/
void serial_matrix_inversion(size_t size, const fftw_complex *input, fftw_complex *result) {
if(size < 1) return;
//base case
result[0] = 1 / input[0];
if(size < 2) return;
result[1] = - result[0] * input[1] * result[0];
unsigned int current_size = 2;
while(current_size < size) {
fftw_complex *reversed_input = alloc_reverse_from_vec(current_size * 2 - 1, input);
fftw_complex *temporary = alloc_complex(current_size);
//first convolution
toeplitz_mult(current_size, reversed_input, result, temporary);
fftw_complex *reversed_inverted_pad = alloc_complex(current_size * 2 - 1);
zero_memory(current_size * 2 - 1, reversed_inverted_pad);
memcpy(reversed_inverted_pad + (current_size-1), result,
current_size * sizeof(fftw_complex));
reverse_vec(current_size * 2 - 1, reversed_inverted_pad);
//second convolution
reverse_vec(current_size, temporary);
toeplitz_mult(current_size, reversed_inverted_pad, temporary, reversed_input);
//complement sign
for(int i=0; i < current_size; i++)
reversed_input[i] = - reversed_input[i];
reverse_vec(current_size, reversed_input);
//finally copy in result vec
memcpy(result + current_size, reversed_input, current_size * sizeof(fftw_complex));
fftw_free(temporary);
fftw_free(reversed_input);
fftw_free(reversed_inverted_pad);
current_size *= 2;
}
}
static void nufft_apply_normal(const void* _data, complex float* dst, const complex float* src)
{
const struct nufft_data* data = _data;
if (data->conf.toeplitz) {
toeplitz_mult(data, dst, src);
} else {
complex float* tmp_ksp = md_alloc(data->N + 3, data->ksp_dims, CFL_SIZE);
nufft_apply((const void*)data, tmp_ksp, src);
nufft_apply_adjoint((const void*)data, dst, tmp_ksp);
md_free(tmp_ksp);
}
}
