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#include "vektor.h"
IntegerVectorList transposeIntegerVectorList(IntegerVectorList const &l)
{
int n=l.size();
assert(n);
int m=l.begin()->size();
IntegerVectorList r;
for(int i=0;i<m;i++)
{
IntegerVector column(n);
int j=0;
for(IntegerVectorList::const_iterator J=l.begin();J!=l.end();J++)
{
column[j]=(*J)[i];
j++;
}
r.push_back(column);
}
return r;
}
IntegerVectorList multiplyIntegerVectorList(IntegerVectorList const &A, IntegerVectorList const &B)
{
int s1=A.size();
assert(s1);
int r=A.begin()->size();
int t=B.size();
assert(t);
int s2=B.begin()->size();
assert(s1==s2);
IntegerVectorList C;
for(IntegerVectorList::const_iterator I=B.begin();I!=B.end();I++)
{
IntegerVector column(r);
int j=0;
for(IntegerVectorList::const_iterator J=A.begin();J!=A.end();J++)
{
column+=(*I)[j]*(*J);
j++;
}
C.push_back(column);
}
return C;
}
/* Computes the greatest common divisor of two integers.
The result is always positive.
Asserts if both integers are zero.
*/
int gcd(int r, int s)
{
if(r<0)r=-r;
if(s<0)s=-s;
if(s<r)
{
int t;
t=r;
r=s;
s=t;
}
while(r!=0)
{
int t=s%r;
s=r;
r=t;
}
assert(s!=0);
return s;
}
/* Returns positive gcd of elements in the vector.
The result is always positive.
Asserts if the vector is the zero-vector.
*/
int gcdOfVector(IntegerVector const &v)
{
int ret=0;
for(int i=0;i<v.size();i++)if(ret=v[i])break;
if(ret<0)ret=-ret;
assert(ret!=0);
for(int i=0;i<v.size();i++)ret=gcd(ret,v[i]);
return ret;
}
/* Uses gcd to put (the direction given by) the vector in a unique form by scaling.
Only positive scaling is applied.
If the input is the zero-vector so is the output.
Otherwise, the common divisor of the output is 1.
*/
IntegerVector normalized(IntegerVector v)
{
if(v.isZero())return v;
int a=gcdOfVector(v);
for(int i=0;i<v.size();i++)v[i]/=a;
return v;
}
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