//////////////////////////////////////////////////////////////////////
// difference of two matrices
//////////////////////////////////////////////////////////////////////
MATRIX operator-(const MATRIX& A, const MATRIX& B)
{
MATRIX result(A.rows(), A.cols());
for (int y = 0; y < A.cols(); y++)
for (int x = 0; x < A.rows(); x++)
result(x,y) = A(x,y) - B(x,y);
return result;
}
MATRIX *MATRIX::GetColumn(int j) {
MATRIX *column = new MATRIX(length,1);
for (int currRow=0;currRow<length;currRow++)
column->Set(currRow,0,Get(currRow,j));
return( column );
}
MATRIX *MATRIX::GetRow(int i) {
MATRIX *row = new MATRIX(1,width);
for (int currColumn=0;currColumn<width;currColumn++)
row->Set(0,currColumn,Get(i,currColumn));
return( row );
}
//////////////////////////////////////////////////////////////////////
// Vector-matrix multiply
//////////////////////////////////////////////////////////////////////
VECTOR operator*(VECTOR& x, MATRIX& A)
{
assert(A.rows() == x.size());
VECTOR y(A.cols());
for (int i = 0; i < A.cols(); i++)
for (int j = 0; j < A.rows(); j++)
y[i] += A(j, i) * x(j);
return y;
}
//////////////////////////////////////////////////////////////////////
// Matrix-vector multiply
//////////////////////////////////////////////////////////////////////
VECTOR operator*(const MATRIX& A, const VECTOR& x)
{
VECTOR y(A.rows());
for (int i = 0; i < A.rows(); i++)
for (int j = 0; j < A.cols(); j++)
y(i) += x(j) * A(i, j);
return y;
}
//////////////////////////////////////////////////////////////////////
// Scale matrix
//////////////////////////////////////////////////////////////////////
MATRIX operator*(float alpha, const MATRIX& A)
{
MATRIX y(A.rows(), A.cols());
for (int i = 0; i < A.rows(); i++)
for (int j = 0; j < A.cols(); j++)
y(i,j) = A(i, j) * alpha;
return y;
}
static MATRIX RotateZ(float a){
float cosinus=cosf(a);
float sinus=sinf(a);
MATRIX ret;
ret.Identity();
ret.m[0][0]=cosinus;
ret.m[1][1]=cosinus;
ret.m[0][1]=-sinus;
ret.m[1][0]=sinus;
return ret;
}
MATRIX *MATRIX::CountValues(int i1, int i2, int j1, int j2, int maxVal) {
MATRIX *valueCount = new MATRIX(1,maxVal,0);
for (int i=i1;i<i2;i++)
for (int j=j1;j<j2;j++)
valueCount->Add(0,int(Get(i,j)),1);
return( valueCount );
}
/*************
* DESCRIPTION: Draw a brush
* INPUT: disp display class
* stack matrix stack
* OUTPUT: none
*************/
void BRUSH_OBJECT::Draw(DISPLAY *disp,MATRIX_STACK *stack)
{
VECTOR size, trans;
MATRIX m;
switch(disp->display)
{
case DISPLAY_BBOX:
case DISPLAY_WIRE:
switch(brush->wrap)
{
case BRUSH_WRAP_FLAT:
// draw a bounding box around pos
disp->DrawBox(stack,&bboxmin,&bboxmax);
break;
case BRUSH_WRAP_X:
SetVector(&size,
(bboxmax.y - bboxmin.y) * .5f,
bboxmax.x - bboxmin.x,
(bboxmax.z - bboxmin.z) * .5f);
m.SetRotZMatrix(90.f);
stack->Push(&m);
SetVector(&trans,
0.f,
- size.y * .5f,
0.f);
m.SetTransMatrix(&trans);
stack->Push(&m);
disp->DrawCylinder(stack, &size, flags);
stack->Pop(&m);
stack->Pop(&m);
break;
case BRUSH_WRAP_Y:
SetVector(&size,
(bboxmax.x - bboxmin.x) * .5f,
bboxmax.y - bboxmin.y,
(bboxmax.z - bboxmin.z) * .5f);
SetVector(&trans,
0.f,
- size.y * .5f,
0.f);
m.SetTransMatrix(&trans);
stack->Push(&m);
disp->DrawCylinder(stack, &size, flags);
stack->Pop(&m);
break;
case BRUSH_WRAP_XY:
disp->DrawSphere(stack, (bboxmax.x-bboxmin.x)*.5f);
break;
}
break;
}
}
int main(){
freopen("in.txt","r",stdin);
int p,q;
int n;
MATRIX initial;
initial.resize(2);
for (int i=0;i<initial.size();++i){
initial[i].resize(2);
}
initial[1][0]=1;
int kase;
scanf("%d",&kase);
for (int kk=1;kase--;++kk){
scanf("%d %d %d",&p,&q,&n);
printf("Case %d: ",kk);
if ( n==0 ){
printf("2\n");
}else if ( n==1 ){
printf("%d\n",p);
}else if ( n==2 ){
printf("%llu\n",LLL(p)*p-2*q);
}
else{
initial[0][0]=p;
initial[0][1]= -q;
MATRIX result=powerMatrix( initial ,n-2 );
LLL base1=p;
LLL base2=LLL(p)*p-2*LLL(q);
LLL rr=result[0][0]*(base2/2) +result[0][1]*(base1/2) ;
rr+=result[0][0]*(base2/2) +result[0][1]*(base1/2) ;
if ( base2 & 1 ){
rr+=result[0][0];
}
if ( base1 & 1 ){
rr+=result[0][1];
}
//printMatrix(result);
printf("%llu\n",LLL(rr) );
}
}
return 0;
}
MATRIX MATRIX::operator*(MATRIX r){
MATRIX ret;
ret.Zero();
for(int i=0;i<4;i++){
for(int j=0;j<4;j++){
ret.m[i][j]+=m[0][j]*r.m[i][0];
ret.m[i][j]+=m[1][j]*r.m[i][1];
ret.m[i][j]+=m[2][j]*r.m[i][2];
ret.m[i][j]+=m[3][j]*r.m[i][3];
}
}
return ret;
}
template<class T_SIMPLICIAL_OBJECT> typename T_SIMPLICIAL_OBJECT::SCALAR
Filled_Volume_Helper(const T_SIMPLICIAL_OBJECT& object, typename ENABLE_IF<(T_SIMPLICIAL_OBJECT::MESH::dimension==(T_SIMPLICIAL_OBJECT::VECTOR_T::m-1)),UNUSABLE>::TYPE unused=UNUSABLE())
{
typedef typename T_SIMPLICIAL_OBJECT::SCALAR T;typedef typename T_SIMPLICIAL_OBJECT::VECTOR_T TV;//enum WORKAROUND{d=T_SIMPLICIAL_OBJECT::MESH::dimension};
static const int d=T_SIMPLICIAL_OBJECT::MESH::dimension;
if(d!=TV::m-1) PHYSBAM_FATAL_ERROR("only codimension 1 objects can be filled");
const TV base=object.particles.X(object.mesh.elements(1)[1]);
T scaled_volume=0; // (d+1)!*volume
for(int t=1;t<=object.mesh.elements.m;t++){const VECTOR<int,d+1>& nodes=object.mesh.elements(t);
MATRIX<T,TV::m,d+1> DX;for(int i=1;i<=nodes.m;i++) DX.Column(i)=object.particles.X(nodes[i])-base;
scaled_volume+=DX.Parallelepiped_Measure();}
return (T)1/FACTORIAL<d+1>::value*scaled_volume;
}
void test2()
{
MATRIX a = MATRIX::Random();
for (int count = 0; count < 5; ++count) {
clock_t start = clock();
for (int j = 0; j < 5000; ++j) {
a.Transposed().Translated(1, 2, 3).Transposed().Translated(3, 2, 1).Transposed().Translated(8, 9, 10)
.Transposed().Translated(10, 9, 8).Transposed().Translated(4, 5, 6).Transposed().Translated(7, 9, 8);
}
clock_t finish = clock();
std::cout << finish - start << " milliseconds" << std::endl;
}
std::cout << std::endl;
}
void MATRIX::Target(VECTOR v,VECTOR c,float a){
VECTOR u(0,1,0);
VECTOR z=v-c;z.Normalize();
VECTOR y=u-z*Dot(u,z);y.Normalize();
VECTOR x=Cross(y,z);
MATRIX swp;
swp.Identity();
swp.m[0][0]=x.x,swp.m[0][1]=y.x,swp.m[0][2]=z.x;
swp.m[1][0]=x.y,swp.m[1][1]=y.y,swp.m[1][2]=z.y;
swp.m[2][0]=x.z,swp.m[2][1]=y.z,swp.m[2][2]=z.z;
swp.m[3][0]=-Dot(c,x);
swp.m[3][1]=-Dot(c,y);
swp.m[3][2]=-Dot(c,z);
*this=RotateZ(-a)*swp;
}
MATRIX multiply(MATRIX &a, MATRIX &b) {
MATRIX res;
res.resize( a.size() );
for (int i=0;i<res.size();++i){
res[i].resize( b[0].size() );
}
for (int i = 0; i < a.size(); i++)
for (int j = 0; j < b[i].size(); j++)
for (int k = 0; k < a[i].size() ; k++) //col of A and row of B must be same which is equal to a[i].size()
res[i][j] = ( res[i][j] + ( ( (a[i][k] % mod ) * (b[k][j] % mod))) % mod ) %mod;
return res;
}
void processMatrix(MATRIX & mat, int match, FuncType &processor)
{
set<int> row;
set<int> col;
for (int i = 0; i < mat.size(); ++i)
{
for (int j = 0; j < mat[i].size(); ++j)
{
if (mat[i][j] == match)
{
row.insert(i);
col.insert(j);
}
}
}
// Process matrix
for (int i : row)
{
processor(mat, i, match, ROW);
}
for (int i : col)
{
processor(mat, i, match, COL);
}
}
bool is_symmetric(const MATRIX &n)
{
unsigned int x, y;
for (y = 0; y < n.GetHeight(); ++y)
{
for (x = 0; x < n.GetWidth(); ++x)
{
if (*n.Get(y, x) != *n.Get(x, y))
{
return false;
}
}
}
return true;
}
void cholesky_invert (MATRIX &M)
{
using namespace ublas;
typedef typename MATRIX::size_type size_type;
typedef typename MATRIX::value_type value_type;
size_type size = M.size1();
// determine the inverse of the lower traingular matrix
for (size_type i = 0; i < size; ++ i) {
M(i,i) = 1 / M(i,i);
for (size_type j = i+1; j < size; ++ j) {
value_type elem(0);
for (size_type k = i; k < j; ++ k) {
elem -= M(j,k)*M(k,i);
}
M(j,i) = elem / M(j,j);
}
}
// multiply the upper and lower inverses together
M = prod(trans(triangular_adaptor<MATRIX,lower>(M)), triangular_adaptor<MATRIX,lower>(M));
}
void MatrixApplier::concat(const MATRIX& m)
{
float matrix[16];
m.get4DMatrix(matrix);
lsglMultMatrixf(matrix);
rt->setMatrixUniform(LSGL_MODELVIEW);
}
/*
* function members
*/
explicit TSP(const MATRIX &_costs)
: MATRIX(_costs),
current_tour(_costs.size()),
best_tour(_costs.size()),
epsilon(0.000001),
n(_costs.size()),
updatecalls(0),
swap_count(0),
slide_count(0),
reverse_count(0),
improve_count(0) {
pgassert(n == MATRIX::size());
bestCost = MATRIX::tourCost(best_tour);
current_cost = MATRIX::tourCost(current_tour);
pgassert(bestCost == current_cost);
}
size_t cholesky_decompose(MATRIX& A)
{
using namespace ublas;
const MATRIX& A_c(A);
const size_t n = A.size1();
for (size_t k=0 ; k < n; k++) {
double qL_kk = A_c(k,k) - inner_prod( project( row(A_c, k), range(0, k) ),
project( row(A_c, k), range(0, k) ) );
if (qL_kk <= 0) {
return 1 + k;
} else {
double L_kk = sqrt( qL_kk );
matrix_column<MATRIX> cLk(A, k);
project( cLk, range(k+1, n) )
= ( project( column(A_c, k), range(k+1, n) )
- prod( project(A_c, range(k+1, n), range(0, k)),
project(row(A_c, k), range(0, k) ) ) ) / L_kk;
A(k,k) = L_kk;
}
}
return 0;
}
/*************
* DESCRIPTION: Push a matrix
* INPUT: m matrix
* OUTPUT: TRUE if ok else FALSE
*************/
BOOL INVMATRIX_STACK::Push(MATRIX *m)
{
STACK_ITEM *si;
MATRIX mat;
si = new STACK_ITEM;
if(!si)
return FALSE;
si->m = *m;
si->Insert((DLIST**)&root);
mat.MultMat(&matrix,m);
matrix = mat;
return TRUE;
}
// Makes and returns a deep copy of *this, including all the BLOB_CHOICEs
// on the lists, but not any LanguageModelState that may be attached to the
// BLOB_CHOICEs.
MATRIX* MATRIX::DeepCopy() const {
int dim = dimension();
int band_width = bandwidth();
MATRIX* result = new MATRIX(dim, band_width);
for (int col = 0; col < dim; ++col) {
for (int row = col; row < dim && row < col + band_width; ++row) {
BLOB_CHOICE_LIST* choices = get(col, row);
if (choices != NULL) {
BLOB_CHOICE_LIST* copy_choices = new BLOB_CHOICE_LIST;
copy_choices->deep_copy(choices, &BLOB_CHOICE::deep_copy);
result->put(col, row, copy_choices);
}
}
}
return result;
}
/*************
* DESCRIPTION: Calculate with three angles three vectors such that all are
* mutually perpendicular. The vectors are normalized
* INPUT: align alignment
* orient result vectors
* OUTPUT: none
*************/
void CalcOrient(VECTOR *align, VECTOR *orient_x, VECTOR *orient_y, VECTOR *orient_z)
{
MATRIX matrix;
matrix.SetRotMatrix(align);
// x-orientation
SetVector(orient_x, 1.f, 0.f, 0.f);
matrix.MultVectMat(orient_x);
// y-orientation
SetVector(orient_y, 0.f, 1.f, 0.f);
matrix.MultVectMat(orient_y);
// z-orientation
SetVector(orient_z, 0.f, 0.f, 1.f);
matrix.MultVectMat(orient_z);
}
/*************
* DESCRIPTION: Push a matrix at the end of the stack
* INPUT: m matrix
* OUTPUT: TRUE if ok else FALSE
*************/
BOOL MATRIX_STACK::PushEnd(MATRIX *m)
{
STACK_ITEM *si;
MATRIX tmp;
si = new STACK_ITEM;
if(!si)
return FALSE;
si->m = *m;
si->Append((DLIST**)&root);
si->matrix = *m;
tmp.MultMat(&matrix, m);
matrix = tmp;
return TRUE;
}
void printMatrix(MATRIX mat){
for (int i=0;i<mat.size();++i){
for (int j=0;j<mat[i].size();++j){
printf("%3lld",mat[i][j]);
}
printf("\n");
}
printf("\n");
}
void Wordrec::ProcessSegSearchPainPoint(
float pain_point_priority,
const MATRIX_COORD &pain_point, const char* pain_point_type,
GenericVector<SegSearchPending>* pending, WERD_RES *word_res,
LMPainPoints *pain_points, BlamerBundle *blamer_bundle) {
if (segsearch_debug_level > 0) {
tprintf("Classifying pain point %s priority=%.4f, col=%d, row=%d\n",
pain_point_type, pain_point_priority,
pain_point.col, pain_point.row);
}
ASSERT_HOST(pain_points != NULL);
MATRIX *ratings = word_res->ratings;
// Classify blob [pain_point.col pain_point.row]
if (!pain_point.Valid(*ratings)) {
ratings->IncreaseBandSize(pain_point.row + 1 - pain_point.col);
}
ASSERT_HOST(pain_point.Valid(*ratings));
BLOB_CHOICE_LIST *classified = classify_piece(word_res->seam_array,
pain_point.col, pain_point.row,
pain_point_type,
word_res->chopped_word,
blamer_bundle);
BLOB_CHOICE_LIST *lst = ratings->get(pain_point.col, pain_point.row);
if (lst == NULL) {
ratings->put(pain_point.col, pain_point.row, classified);
} else {
// We can not delete old BLOB_CHOICEs, since they might contain
// ViterbiStateEntries that are parents of other "active" entries.
// Thus if the matrix cell already contains classifications we add
// the new ones to the beginning of the list.
BLOB_CHOICE_IT it(lst);
it.add_list_before(classified);
delete classified; // safe to delete, since empty after add_list_before()
classified = NULL;
}
if (segsearch_debug_level > 0) {
print_ratings_list("Updated ratings matrix with a new entry:",
ratings->get(pain_point.col, pain_point.row),
getDict().getUnicharset());
ratings->print(getDict().getUnicharset());
}
// Insert initial "pain points" to join the newly classified blob
// with its left and right neighbors.
if (classified != NULL && !classified->empty()) {
if (pain_point.col > 0) {
pain_points->GeneratePainPoint(
pain_point.col - 1, pain_point.row, LM_PPTYPE_SHAPE, 0.0,
true, segsearch_max_char_wh_ratio, word_res);
}
if (pain_point.row + 1 < ratings->dimension()) {
pain_points->GeneratePainPoint(
pain_point.col, pain_point.row + 1, LM_PPTYPE_SHAPE, 0.0,
true, segsearch_max_char_wh_ratio, word_res);
}
}
(*pending)[pain_point.col].SetBlobClassified(pain_point.row);
}
/*************
* DESCRIPTION: Pop a matrix
* INPUT: -
* OUTPUT: -
*************/
void INVMATRIX_STACK::Pop()
{
STACK_ITEM *si;
MATRIX mat;
if(!root)
return;
root->Remove((DLIST**)&root);
matrix.IdentityMatrix();
si = root;
while(si)
{
mat.MultMat(&si->m,&matrix);
matrix = mat;
si = (STACK_ITEM*)si->GetNext();
}
}
int main(){
//freopen("in.txt","r",stdin);
int n,m;
MATRIX initial;
initial.resize(DIM);
for (int i=0;i<initial.size();++i){
initial[i].resize(DIM);
}
for (int i=0;i<DIM;++i){
for (int j=0;j<DIM;++j){
initial[i][j]=1;
}
}
initial[1][1]=0;
int kase;
LLL x,y;
scanf("%d",&kase);
for (int kk=1;kase--;++kk){
scanf("%d %d %d %d",&x,&y,&n,&m);
mod=LLL ( pow(10,m)+1e-6 );
printf("Case %d: ",kk);
if( n==0 ){
printf("%d\n",x%mod);
continue;
}else if ( n==1 ){
printf("%d\n",y%mod);
continue;
}
MATRIX result=powerMatrix( initial , n-1 );
printf("%d\n",( result[0][0]*y+result[0][1]*x ) %mod);
}
return 0;
}
void testMotionExtract (void) {
MATRIX AffineMatrix (3,2);
MATRIX_CONTENT_TYPE** AffineData = AffineMatrix.getDataPtr ();
double theta = 3.14 / 6;
cout << "theta: " << theta << endl;
// row 1
AffineData[0][0] = cos (theta);
AffineData[1][0] = sin (theta);
AffineData[2][0] = 1;
// row 2
AffineData[0][1] = - sin (theta);
AffineData[1][1] = cos (theta);
AffineData[2][1] = 2;
showMotion (AffineMatrix);
}
