void transpose(mat_ZZ& X, const mat_ZZ& A)
{
long n = A.NumRows();
long m = A.NumCols();
long i, j;
if (&X == & A) {
if (n == m)
for (i = 1; i <= n; i++)
for (j = i+1; j <= n; j++)
swap(X(i, j), X(j, i));
else {
mat_ZZ tmp;
tmp.SetDims(m, n);
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
tmp(j, i) = A(i, j);
X.kill();
X = tmp;
}
}
else {
X.SetDims(m, n);
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
X(j, i) = A(i, j);
}
}
static
long image(ZZ& det, mat_ZZ& B, mat_ZZ* U, long verbose)
{
long m = B.NumRows();
long n = B.NumCols();
long force_reduce = 1;
vec_long P;
P.SetLength(m);
vec_ZZ D;
D.SetLength(m+1);
D[0] = 1;
vec_vec_ZZ lam;
lam.SetLength(m);
long j;
for (j = 1; j <= m; j++)
lam(j).SetLength(m);
if (U) ident(*U, m);
long s = 0;
long k = 1;
long max_k = 0;
while (k <= m) {
if (k > max_k) {
IncrementalGS(B, P, D, lam, s, k);
max_k = k;
}
if (k == 1) {
force_reduce = 1;
k++;
continue;
}
if (force_reduce)
for (j = k-1; j >= 1; j--)
reduce(k, j, B, P, D, lam, U);
if (P(k-1) != 0 && P(k) == 0) {
force_reduce = swap(k, B, P, D, lam, U, max_k, verbose);
k--;
}
else {
force_reduce = 1;
k++;
}
}
det = D[s];
return s;
}
void mul_aux(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B)
{
long n = A.NumRows();
long l = A.NumCols();
long m = B.NumCols();
if (l != B.NumRows())
Error("matrix mul: dimension mismatch");
X.SetDims(n, m);
long i, j, k;
ZZ acc, tmp;
for (i = 1; i <= n; i++) {
for (j = 1; j <= m; j++) {
clear(acc);
for(k = 1; k <= l; k++) {
mul(tmp, A(i,k), B(k,j));
add(acc, acc, tmp);
}
X(i,j) = acc;
}
}
}
vec_ZZ GS_reduce(mat_ZZ mat, vec_ZZ vec, ZZ weight)
{
vec_ZZ target;
ZZ_mat<mpz_t> mat_fp;
mat_ZZ mat_exp;
int row, col;
row = mat.NumRows();
col = mat.NumCols();
mat_exp.SetDims(row+1, col+1);
for(int i=0;i<row;i++)
{
for(int j=0;j<col;j++)
{
mat_exp[i][j] = mat[i][j];
}
}
for(int i=0;i<col;i++)
{
mat_exp[row][i] = vec[i];
}
mat_exp[row][col] = weight;
mat_fp = convert<ZZ_mat<mpz_t> ,mat_ZZ >(mat_exp);
lllReduction(mat_fp, 0.99,0.51, LM_WRAPPER,FT_DEFAULT, 0, LLL_DEFAULT);
mat_exp = convert<mat_ZZ ,ZZ_mat<mpz_t> >(mat_fp);
target.SetLength(col);
for (int i=0;i<col;i++)
target[i] = mat_exp[row][i];
// cout<<target<<endl;
return target;
}
void power(mat_ZZ& X, const mat_ZZ& A, const ZZ& e)
{
if (A.NumRows() != A.NumCols()) Error("power: non-square matrix");
if (e == 0) {
ident(X, A.NumRows());
return;
}
mat_ZZ T1, T2;
long i, k;
k = NumBits(e);
T1 = A;
for (i = k-2; i >= 0; i--) {
sqr(T2, T1);
if (bit(e, i))
mul(T1, T2, A);
else
T1 = T2;
}
if (e < 0)
inv(X, T1);
else
X = T1;
}
void conv(mat_ZZ_p& x, const mat_ZZ& a)
{
long n = a.NumRows();
long m = a.NumCols();
long i;
x.SetDims(n, m);
for (i = 0; i < n; i++)
conv(x[i], a[i]);
}
static
long MaxBits(const mat_ZZ& A)
{
long m = 0;
long i, j;
for (i = 0; i < A.NumRows(); i++)
for (j = 0; j < A.NumCols(); j++)
m = max(m, NumBits(A[i][j]));
return m;
}
RR ReductionQualityChecker::computeOrthogonalityDefect(mat_ZZ &mat) {
RR multResult = sqrt(normsq(mat(1)));
for (int i = 2; i <= mat.NumRows(); i++) {
multResult *= sqrt(normsq(mat(i)));
}
mat_ZZ B = mat * transpose(mat);
RR denominator = sqrt(determinant(B));
return pow(multResult/denominator, 1./mat.NumRows());
}
void mul(mat_ZZ& X, const mat_ZZ& A, long b)
{
long n = A.NumRows();
long m = A.NumCols();
X.SetDims(n, m);
long i, j;
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
mul(X[i][j], A[i][j], b);
}
static
void ExactDiv(mat_ZZ& x, const ZZ& d)
{
long n = x.NumRows();
long m = x.NumCols();
long i, j;
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
if (!divide(x[i][j], x[i][j], d))
Error("inexact division");
}
void negate(mat_ZZ& X, const mat_ZZ& A)
{
long n = A.NumRows();
long m = A.NumCols();
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
negate(X(i,j), A(i,j));
}
void sub(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B)
{
long n = A.NumRows();
long m = A.NumCols();
if (B.NumRows() != n || B.NumCols() != m)
Error("matrix sub: dimension mismatch");
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
sub(X(i,j), A(i,j), B(i,j));
}
void clear(mat_ZZ& x)
{
long n = x.NumRows();
long i;
for (i = 0; i < n; i++)
clear(x[i]);
}
NTL_START_IMPL
static
long CharPolyBound(const mat_ZZ& a)
// This bound is computed via interpolation
// through complex roots of unity.
{
long n = a.NumRows();
long i;
ZZ res, t1, t2;
set(res);
for (i = 0; i < n; i++) {
InnerProduct(t1, a[i], a[i]);
abs(t2, a[i][i]);
mul(t2, t2, 2);
add(t2, t2, 1);
add(t1, t1, t2);
if (t1 > 1) {
SqrRoot(t1, t1);
add(t1, t1, 1);
}
mul(res, res, t1);
}
return NumBits(res);
}
static
void IncrementalGS(mat_ZZ& B, vec_long& P, vec_ZZ& D, vec_vec_ZZ& lam,
long& s, long k)
{
long n = B.NumCols();
long m = B.NumRows();
static ZZ u, t1, t2;
long i, j;
for (j = 1; j <= k-1; j++) {
long posj = P(j);
if (posj == 0) continue;
InnerProduct(u, B(k), B(j));
for (i = 1; i <= posj-1; i++) {
mul(t1, D[i], u);
mul(t2, lam(k)(i), lam(j)(i));
sub(t1, t1, t2);
div(t1, t1, D[i-1]);
u = t1;
}
lam(k)(posj) = u;
}
InnerProduct(u, B(k), B(k));
for (i = 1; i <= s; i++) {
mul(t1, D[i], u);
mul(t2, lam(k)(i), lam(k)(i));
sub(t1, t1, t2);
div(t1, t1, D[i-1]);
u = t1;
}
if (u == 0) {
P(k) = 0;
}
else {
s++;
P(k) = s;
D[s] = u;
}
}
long IsIdent(const mat_ZZ& A, long n)
{
if (A.NumRows() != n || A.NumCols() != n)
return 0;
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i != j) {
if (!IsZero(A(i, j))) return 0;
}
else {
if (!IsOne(A(i, j))) return 0;
}
return 1;
}
NTL_START_IMPL
void add(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B)
{
long n = A.NumRows();
long m = A.NumCols();
if (B.NumRows() != n || B.NumCols() != m)
LogicError("matrix add: dimension mismatch");
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
add(X(i,j), A(i,j), B(i,j));
}
long IsDiag(const mat_ZZ& A, long n, const ZZ& d)
{
if (A.NumRows() != n || A.NumCols() != n)
return 0;
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i != j) {
if (!IsZero(A(i, j))) return 0;
}
else {
if (A(i, j) != d) return 0;
}
return 1;
}
void mul(vec_ZZ& x, const mat_ZZ& A, const vec_ZZ& b)
{
if (&b == &x || A.alias(x)) {
vec_ZZ tmp;
mul_aux(tmp, A, b);
x = tmp;
}
else
mul_aux(x, A, b);
}
void mul(vec_ZZ& x, const mat_ZZ& A, const vec_ZZ& b)
{
if (&b == &x || A.position1(x) != -1) {
vec_ZZ tmp;
mul_aux(tmp, A, b);
x = tmp;
}
else
mul_aux(x, A, b);
}
mat_ZZ mat_expand(mat_ZZ M, vec_ZZ v)
{
int len, col, row;
mat_ZZ mat_exp;
len = v.length();
col = M.NumCols();
row = M.NumRows();
if (len!=col)
cout<<"Incompatible rows"<<endl;
mat_exp = M;
mat_exp.SetDims(row+1, col);
mat_exp[row] = v;
return mat_exp;
}
void gen_svpchallenge(mat_ZZ& B,int n,ZZ seed,int bit=10) {
vec_ZZ v;
generate_random_HNF(v,n,bit,seed);
B.SetDims(n,n); clear(B);
B(1,1) = v(1);
for (int i=2; i<=n; i++)
{
B(i,1)=v(i);
B(i,i)=1;
}
}
long IsZero(const mat_ZZ& a)
{
long n = a.NumRows();
long i;
for (i = 0; i < n; i++)
if (!IsZero(a[i]))
return 0;
return 1;
}
void ident(mat_ZZ& X, long n)
{
X.SetDims(n, n);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i == j)
set(X(i, j));
else
clear(X(i, j));
}
void gen_randlat(mat_ZZ& basis, ZZ determinant, int dim) {
basis.SetDims(dim, dim);
ZZ s;
s= time(NULL);
SetSeed(s);
for(int i= 0; i < dim; i++) {
basis[i][0]= RandomBnd(determinant);
basis[i][i]= 1;
}
basis[0][0]= determinant;
}
void diag(mat_ZZ& X, long n, const ZZ& d_in)
{
ZZ d = d_in;
X.SetDims(n, n);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i == j)
X(i, j) = d;
else
clear(X(i, j));
}
static
void ComputeGS(mat_ZZ& B, xdouble **B1, xdouble **mu, xdouble *b,
xdouble *c, long k, xdouble bound, long st, xdouble *buf)
{
long n = B.NumCols();
long i, j;
xdouble s, t1, y, t;
ZZ T1;
xdouble *mu_k = mu[k];
if (st < k) {
for (i = 1; i < st; i++)
buf[i] = mu_k[i]*c[i];
}
for (j = st; j <= k-1; j++) {
if (b[k]*b[j] < NTL_FDOUBLE_PRECISION*NTL_FDOUBLE_PRECISION) {
double z = 0;
xdouble *B1_k = B1[k];
xdouble *B1_j = B1[j];
for (i = 1; i <= n; i++)
z += B1_k[i].x * B1_j[i].x;
s = z;
}
else {
s = InnerProduct(B1[k], B1[j], n);
if (s*s <= b[k]*b[j]/bound) {
InnerProduct(T1, B(k), B(j));
conv(s, T1);
}
}
xdouble *mu_j = mu[j];
t1 = 0;
for (i = 1; i <= j-1; i++)
MulAdd(t1, t1, mu_j[i], buf[i]);
mu_k[j] = (buf[j] = (s - t1))/c[j];
}
s = 0;
for (j = 1; j <= k-1; j++)
MulAdd(s, s, mu_k[j], buf[j]);
c[k] = b[k] - s;
}
static
void MixedMul(vec_ZZ& x, const vec_zz_p& a, const mat_ZZ& B)
{
long n = B.NumRows();
long l = B.NumCols();
if (n != a.length())
Error("matrix mul: dimension mismatch");
x.SetLength(l);
long i, k;
ZZ acc, tmp;
for (i = 1; i <= l; i++) {
clear(acc);
for (k = 1; k <= n; k++) {
mul(tmp, B(k, i), rep(a(k)));
add(acc, acc, tmp);
}
x(i) = acc;
}
}
RR findShortestNormVector (mat_ZZ &mat) {
ZZ shortestVectNormSq = -1;
for (int i = 1; i <= mat.NumRows(); i++){
ZZ normSq = normsq(mat(i));
if((shortestVectNormSq == -1) || shortestVectNormSq > normSq){
shortestVectNormSq = normSq;
}
}
return sqrt(shortestVectNormSq);
}
static
void mul_aux(vec_ZZ& x, const mat_ZZ& A, const vec_ZZ& b)
{
long n = A.NumRows();
long l = A.NumCols();
if (l != b.length())
Error("matrix mul: dimension mismatch");
x.SetLength(n);
long i, k;
ZZ acc, tmp;
for (i = 1; i <= n; i++) {
clear(acc);
for (k = 1; k <= l; k++) {
mul(tmp, A(i,k), b(k));
add(acc, acc, tmp);
}
x(i) = acc;
}
}