//******************************************
VOID nu_to_n1_vec(
USHORT num_of_bits, //in
VECTOR<DOUBLE> & in_vec) //io
{
//As in Latex, let _beta mean a subscript of beta.
//For bit beta, define
//n(beta) = diag(0,1)_beta,
//u(beta) = nbar(beta) = 1 - n(beta) = diag(1,0)_beta
//1_beta = diag(1,1)_beta
//This method replaces in_vec (a vector from the n,u basis) by
//its equivalent in the n,1 basis
//example:
//2 bits
//A00 u(1)u(0) = A00 [ ( 1)*1 + (-1)*n(0) + (-1)*n(1) + ( 1)*n(1)n(0) ]
//A01 u(1)n(0) = A01 [ ( 0)*1 + ( 1)*n(0) + ( 0)*n(1) + (-1)*n(1)n(0) ]
//A10 n(1)u(0) = A10 [ ( 0)*1 + ( 0)*n(0) + ( 1)*n(1) + (-1)*n(1)n(0) ]
//A11 n(1)n(0) = A11 [ ( 0)*1 + ( 0)*n(0) + ( 0)*n(1) + ( 1)*n(1)n(0) ]
//vector in n,u basis: [A00, A01, A10, A11]
//vector in n,1 basis: [B00, B01, B10, B11]
//where
//B00 = A00*( 1)
//B01 = A00*(-1) + A01*( 1)
//B10 = A00*(-1) + A01*( 0) + A10*( 1)
//B11 = A00*( 1) + A01*(-1) + A10*(-1) + A11*( 1)
if(num_of_bits==0)return;//do nothing since only one component
USHORT num_of_comps = (1 << num_of_bits);
ThrowIf_(in_vec.get_len()!=num_of_comps);
VECTOR<DOUBLE> n1_vec(0, num_of_comps);
BIT_VECTOR bvec(num_of_bits, 0);
for(USHORT i_n1=0; i_n1<num_of_comps; i_n1++){
for(USHORT i_nu=0; i_nu<=i_n1; i_nu++){
if( (i_nu & i_n1)==i_nu ){
//remember that i^j is bitwise mod2 addition of i and j
bvec.set_dec_rep(i_nu ^ i_n1);
if(bvec.get_num_of_ON_bits()%2){//bvec.num_of_ON_bits is odd
n1_vec[i_n1] -= in_vec[i_nu];
}else{//bvec.num_of_ON_bits is even
n1_vec[i_n1] += in_vec[i_nu];
}
}
}
}
in_vec = n1_vec;
}
//******************************************
VOID had_transform(
USHORT num_of_bits, //in
VECTOR<DOUBLE> & in_vec) //io
{
//This method replaces in_vec by its Hadamard transform.
if(num_of_bits==0)return;//do nothing since only one component
USHORT num_of_comps = (1 << num_of_bits);
ThrowIf_(in_vec.get_len()!=num_of_comps);
VECTOR<DOUBLE> prev_vec;
LONG half_num_of_comps = (1 << (num_of_bits - 1));
for(USHORT beta=0; beta < num_of_bits; beta++){
USHORT j = 0;
prev_vec = in_vec;
for(USHORT i=0; i < half_num_of_comps; i++){
DOUBLE x = prev_vec[j];
DOUBLE y = prev_vec[j + 1];
in_vec[i]= x + y;
in_vec[half_num_of_comps + i] = x - y;
j +=2;
}
}
}
