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→Initial Profile
[[File:neuralnet_chart.jpg]]
After the initial profile it is obvious that the dot product function consumes 97.94% of our run time. Additionally, the transpose function also consumes 1.45% which seems messily, however during back propagation transpose is also called, as well as two rectifiers(activation functions), reluPrime and relu.
vector<float> dyhat = (yhat - b_y);
// dW3 = a2.T * dyhat
// dW1 = X.T * dz1
vector<float> dW1 = dot(transpose( &b_X[0], BATCH_SIZE, 784 ), dz1, 784, BATCH_SIZE, 128);
vector <float> dot (const vector <float>& m1, const vector <float>& m2, const int m1_rows, const int m1_columns, const int m2_columns) {
/* Returns the product of two matrices: m1 x m2.
Inputs:
m1: vector, left matrix of size m1_rows x m1_columns
m2: vector, right matrix of size m1_columns x m2_columns (the number of rows in the right matrix
must be equal to the number of the columns in the left one)
m1_rows: int, number of rows in the left matrix m1
m1_columns: int, number of columns in the left matrix m1
m2_columns: int, number of columns in the right matrix m2
Output: vector, m1 * m2, product of two vectors m1 and m2, a matrix of size m1_rows x m2_columns
*/
vector <float> output (m1_rows*m2_columns);
for( int row = 0; row != m1_rows; ++row ) {
for( int col = 0; col != m2_columns; ++col ) {
output[ row * m2_columns + col ] = 0.f;
for( int k = 0; k != m1_columns; ++k ) {
output[ row * m2_columns + col ] += m1[ row * m1_columns + k ] * m2[ k * m2_columns + col ];
}
}
}
return output;
}
=====Ray Tracing=====