void strassen_mm(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A, const int incRowA,
const Dtype *B, const int incRowB,
Dtype *C, const int incRowC){
int max_length = maxThree(m, n, k);
int new_length = getNumberLargerThanXAndIsPowerOfTwo(max_length);
Dtype* newA = pad_matrix(A, m, k, incRowA, new_length, new_length);
Dtype* newB = pad_matrix(B, k, n, incRowB, new_length, new_length);
Dtype* newC = pad_matrix(C, m, n, incRowC, new_length, new_length);
strassen_mm_worker(
new_length, new_length, new_length,
newA, new_length,
newB, new_length,
newC, new_length);
matrix_copyTo(newC, new_length, new_length, new_length,
C, m, n, incRowC);
// remove the extra workspace
remove_matrix(newA);
remove_matrix(newB);
remove_matrix(newC);
}
ImplicitSystem::~ImplicitSystem ()
{
// Clear data
this->clear();
remove_matrix("System Matrix");
}
Dtype* strassen_make_M2_submatrix(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A_2_1, const int incRowA_2_1,
const Dtype *A_2_2, const int incRowA_2_2,
const Dtype *B_1_1, const int incRowB_1_1){
/*
construct M2 by the formula
M2 = (A_2_1 + A_2_2) * B_1_1
*/
// T1 = A_2_1 + A_2_2
Dtype* T1 = make_matrix(m, k);
matrix_addition(m, k,
A_2_1, incRowA_2_1,
A_2_2, incRowA_2_2,
T1, k);
Dtype* M2 = make_matrix(m, k);
strassen_mm_worker(
m, n, k,
T1, k,
B_1_1, incRowB_1_1,
M2, k);
remove_matrix(T1);
return M2;
}
Dtype* strassen_make_M5_submatrix(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A_1_1, const int incRowA_1_1,
const Dtype *A_1_2, const int incRowA_1_2,
const Dtype *B_2_2, const int incRowB_2_2){
/*
construct M5 by the formula
M5 = (A_1_1 + A_1_2) * B_2_2
*/
// T1 = A_1_1 + A_1_2
Dtype* T1 = make_matrix(m, k);
matrix_addition(m, k,
A_1_1, incRowA_1_1,
A_1_2, incRowA_1_2,
T1, k);
Dtype* M5 = make_matrix(m, k);
strassen_mm_worker(
m, n, k,
T1, k,
B_2_2, incRowB_2_2,
M5, k);
remove_matrix(T1);
return M5;
}
Dtype* strassen_make_M4_submatrix(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A_2_2, const int incRowA_2_2,
const Dtype *B_2_1, const int incRowB_2_1,
const Dtype *B_1_1, const int incRowB_1_1){
/*
construct M4 by the formula
M4 = A_2_2 * (B_2_1 - B_1_1)
*/
Dtype* T1 = make_matrix(m, k);
// T1 = B_2_1 - B_1_1
matrix_subtraction(m, k,
B_2_1, incRowB_2_1,
B_1_1, incRowB_1_1,
T1, k);
Dtype* M4 = make_matrix(m, k);
strassen_mm_worker(
m, n, k,
A_2_2, incRowA_2_2,
T1, k,
M4, k);
remove_matrix(T1);
return M4;
}
Dtype* strassen_make_M3_submatrix(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A_1_1, const int incRowA_1_1,
const Dtype *B_1_2, const int incRowB_1_2,
const Dtype *B_2_2, const int incRowB_2_2){
/*
construct M3 by the formula
M3 = A_1_1 * (B_1_2 - B_2_2)
*/
// T1 = B_1_2 - B_2_2
Dtype* T1 = make_matrix(m, k);
matrix_subtraction(m, k,
B_1_2, incRowB_1_2,
B_2_2, incRowB_2_2,
T1, k);
Dtype* M3 = make_matrix(m, k);
strassen_mm_worker(
m, n, k,
A_1_1, incRowA_1_1,
T1, k,
M3, k);
remove_matrix(T1);
return M3;
}
void Main_win::clear_clicked()
{
math_->clear();
remove_matrix();
build_matrix(mat_dim_);
reset_display();
}
void Main_win::load_clicked()
{
try
{
QString q_form = QFileDialog::getOpenFileName(this, tr("Load Matrix"));
std::ifstream f;
f.open(q_form.toStdString(), std::ios_base::in);
if(f.is_open())
{
int row = 0;
int col = 0;
char c = 0;
bool flag = true;
while(f.get(c))
{
if(flag && (c == ' '))
col++;
if(c == '\n')
{
row++;
flag = false;
}
}
f.clear();
f.seekg(0, f.beg);
std::istream_iterator<double> ii{f};
std::istream_iterator<double> eos{};
std::vector<double> v{ii, eos};
f.close();
remove_matrix();
build_matrix(row, col);
mat_dim_.first = row;
mat_dim_.second = col;
mat_dim_tmp_.first = row;
mat_dim_tmp_.second = col;
display_matrix(row, col, v);
}
else throw std::ios_base::failure("cannot open file");
}
catch(std::exception& e)
{
e.what();
to_display(e.what());
}
}
void Main_win::set_dim_clicked()
{
Set_dim dialog_set_dim(this, mat_dim_tmp_);
dialog_set_dim.setModal(true);
dialog_set_dim.show();
dialog_set_dim.exec();
remove_matrix();
build_matrix(mat_dim_tmp_);
mat_dim_ = mat_dim_tmp_;
}
// M1 = (A_1_1 + A_2_2) * (B_1_1 + B_2_2)
Dtype* strassen_make_M1_submatrix(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A_1_1, const int incRowA_1_1,
const Dtype *A_2_2, const int incRowA_2_2,
const Dtype *B_1_1, const int incRowB_1_1,
const Dtype *B_2_2, const int incRowB_2_2){
/*
construct M1 by the formula
M1 = (A_1_1 + A_2_2) * (B_1_1 + B_2_2)
*/
// T1 = (A_1_1 + A_2_2)
Dtype* T1 = make_matrix(m, k);
matrix_addition(m, k,
A_1_1, incRowA_1_1,
A_2_2, incRowA_2_2,
T1, k);
// T2 = (B_1_1 + B_2_2)
Dtype* T2 = make_matrix(m, k);
matrix_addition(m, k,
B_1_1, incRowB_1_1,
B_2_2, incRowB_2_2,
T2, k);
// M1 = T1 * T2
Dtype* M1 = make_matrix(m, k);
strassen_mm_worker(
m, n, k,
T1, k,
T2, k,
M1, k);
remove_matrix(T1);
remove_matrix(T2);
return M1;
}
void Main_win::display_result(const Matrix& m)
{
remove_matrix();
build_matrix(m.rows(), m.cols());
mat_dim_.first = m.rows();
mat_dim_.second = m.cols();
mat_dim_tmp_.first = m.rows();
mat_dim_tmp_.second = m.cols();
display_matrix(m);
}
// M7 = (A_1_2 - A_2_2) * (B_2_1 + B_2_2)
Dtype* strassen_make_M7_submatrix(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A_1_2, const int incRowA_1_2,
const Dtype *A_2_2, const int incRowA_2_2,
const Dtype *B_2_1, const int incRowB_2_1,
const Dtype *B_2_2, const int incRowB_2_2){
/*
construct M7 by the formula
M7 = (A_1_2 - A_2_2) * (B_2_1 + B_2_2)
*/
Dtype* T1 = make_matrix(m, k);
Dtype* T2 = make_matrix(m, k);
// T1 = (A_1_2 - A_2_2)
matrix_subtraction(m, k,
A_1_2, incRowA_1_2,
A_2_2, incRowA_2_2,
T1, k);
// T2 = (B_2_1 + B_2_2)
matrix_addition(m, k,
B_2_1, incRowB_2_1,
B_2_2, incRowB_2_2,
T2, k);
// M7 = T1 * T2
Dtype* M7 = make_matrix(m, k);
strassen_mm_worker(
m, n, k,
T1, k,
T2, k,
M7, k);
remove_matrix(T1);
remove_matrix(T2);
return M7;
}
/* this script only works for square matrices
where the length is a power of 2
*/
void strassen_mm_worker(
const unsigned int m,
const unsigned int n,
const unsigned int k,
const Dtype *A, const int incRowA,
const Dtype *B, const int incRowB,
Dtype *C, const int incRowC){
// the matrices must have positive dimension
assert(m > 0);
assert(n > 0);
assert(k > 0);
// the matrix must be a square matrix
assert(m == n);
assert(m == k);
/* check if the base case has reached
the base condition is defined as when all the dimensions are smaller than 256
*/
if(m <= limit_X && n <= limit_X && k <= limit_X){
return matrix_multiplication_base_case(
m, n, k,
A, incRowA,
B, incRowB,
C, incRowC);
}
/*
We divide A, B, C into subsections as the following:
A = |A_1_1, A_1_2| B = |B_1_1, B_1_2| C = |C_1_1, C_1_2|
|A_2_1, A_2_2| |B_2_1, B_2_2| |C_2_1, C_2_2|
We first calculate 7 temporary matrices as the follow:
M1 = (A_1_1 + A_2_2) * (B_1_1 + B_2_2)
M2 = (A_2_1 + A_2_2) * B_1_1
M3 = A_1_1 * (B_1_2 - B_2_2)
M4 = A_2_2 * (B_2_1 - B_1_1)
M5 = (A_1_1 + A_1_2) * B_2_2
M6 = (A_2_1 - A_1_1) * (B_1_1 + B_1_2)
M7 = (A_1_2 - A_2_2) * (B_2_1 + B_2_2)
Then, we compute C section by section according to:
C_1_1 = M1 + M4 - M5 + M7
C_1_2 = M3 + M5
C_2_1 = M2 + M4
C_2_2 = M1 - M2 + M3 + M6
*/
const unsigned int m1 = m / 2;
const unsigned int n1 = n / 2;
const unsigned int k1 = k / 2;
const Dtype* A_1_1 = A;
const Dtype* A_1_2 = A_1_1 + k1;
const Dtype* A_2_1 = A_1_1 + incRowA*m1;
const Dtype* A_2_2 = A_2_1 + k1;
Dtype* C_1_1 = C;
Dtype* C_1_2 = C_1_1 + n1;
Dtype* C_2_1 = C_1_1 + incRowC*m1;
Dtype* C_2_2 = C_2_1 + n1;
const Dtype* B_1_1 = B;
const Dtype* B_1_2 = B_1_1 + n1;
const Dtype* B_2_1 = B_1_1 + incRowB*k1;
const Dtype* B_2_2 = B_2_1 + n1;
/*
construct M1 by the formula
M1 = (A_1_1 + A_2_2) * (B_1_1 + B_2_2)
*/
Dtype* M1 = strassen_make_M1_submatrix(
m1, n1, k1,
A_1_1, incRowA,
A_2_2, incRowA,
B_1_1, incRowB,
B_2_2, incRowB);
/*
construct M2 by the formula
M2 = (A_2_1 + A_2_2) * B_1_1
*/
Dtype* M2 = strassen_make_M2_submatrix(
m1, n1, k1,
A_2_1, incRowA,
A_2_2, incRowA,
B_1_1, incRowB);
/*
construct M3 by the formula
M3 = A_1_1 * (B_1_2 - B_2_2)
*/
Dtype* M3 = strassen_make_M3_submatrix(
m1, n1, k1,
A_1_1, incRowA,
B_1_2, incRowB,
B_2_2, incRowB);
/*
construct M4 by the formula
M4 = A_2_2 * (B_2_1 - B_1_1)
*/
Dtype* M4 = strassen_make_M4_submatrix(
m1, k1, k1,
A_2_2, incRowA,
B_2_1, incRowB,
B_1_1, incRowB);
/*
construct M5 by the formula
M5 = (A_1_1 + A_1_2) * B_2_2
*/
Dtype* M5 = strassen_make_M5_submatrix(
m1, n1, k1,
A_1_1, incRowA,
A_1_2, incRowA,
B_2_2, incRowB);
/*
construct M6 by the formula
M6 = (A_2_1 - A_1_1) * (B_1_1 + B_1_2)
*/
Dtype* M6 = strassen_make_M6_submatrix(
m1, n1, k1,
A_2_1, incRowA,
A_1_1, incRowA,
B_1_1, incRowB,
B_1_2, incRowB);
/*
construct M7 by the formula
M7 = (A_1_2 - A_2_2) * (B_2_1 + B_2_2)
*/
Dtype* M7 = strassen_make_M7_submatrix(
m1, n1, k1,
A_1_2, incRowA,
A_2_2, incRowA,
B_2_1, incRowB,
B_2_2, incRowB);
/*
compute C_1_1 by the formula
C_1_1 = M1 + M4 - M5 + M7
*/
strassen_calculate_C_1_1(
m1, n1, k1,
M1, M4, M5, M7,
C_1_1, incRowC);
/*
compute C_1_2 by the formula
C_1_2 = M3 + M5
*/
strassen_calculate_C_1_2(
m1, n1, k1,
M3, M5,
C_1_2, incRowC);
/*
compute C_2_1 by the formula
C_2_1 = M2 + M4
*/
strassen_calculate_C_2_1(
m1, n1, k1,
M2, M4,
C_2_1, incRowC);
/*
compute C_2_2 by the formula
C_2_2 = M1 - M2 + M3 + M6
*/
strassen_calculate_C_2_2(
m1, n1, k1,
M1, M2, M3, M6,
C_2_2, incRowC);
/*
remove the working space
*/
remove_matrix(M1);
remove_matrix(M2);
remove_matrix(M3);
remove_matrix(M4);
remove_matrix(M5);
remove_matrix(M6);
remove_matrix(M7);
}