I am currently trying to implement matrix multiplication methods using the Microsoft SEAL library. I have created a vector<vector<double>> as input matrix and encoded it with CKKSEncoder. However the encoder packs an entire vector into a single Plaintext so I just have a vector<Plaintext> which makes me lose the 2D structure (and then of course I'll have a vector<Ciphertext> after encryption). Having a 1D vector allows me to access only the rows entirely but not the columns.
I managed to transpose the matrices before encoding. This allowed me to multiply component-wise the rows of the first matrix and columns (rows in transposed form) of the second matrix but I am unable to sum the elements of the resulting vector together since it's packed into a single Ciphertext. I just need to figure out how to make the vector dot product work in SEAL to perform matrix multiplication. Am I missing something or is my method wrong?
It has been suggested by KyoohyungHan in the issue: https://github.com/microsoft/SEAL/issues/138 that it is possible to solve the problem with rotations by rotating the output vector and summing it up repeatedly.
For example:
// my_output_vector is the Ciphertext output
vector<Ciphertext> rotations_output(my_output_vector.size());
for(int steps = 0; steps < my_output_vector.size(); steps++)
{
evaluator.rotate_vector(my_output_vector, steps, galois_keys, rotations_output[steps]);
}
Ciphertext sum_output;
evaluator.add_many(rotations_output, sum_output);
vector of vectors is not the same as an array of arrays (2D, matrix).
While one-dimentional vector<double>.data() points to contiguous memory space (e.g., you can do memcpy on that), each of "subvectors" allocates own, separate memory buffer. Therefore vector<vector<double>>.data() makes no sense and cannot be used as a matrix.
In C++, two-dimensional array array2D[W][H] is stored in memory identically to array[W*H]. Therefore both can be processed by the same routines (when it makes sense). Consider the following example:
void fill_array(double *array, size_t size, double value) {
for (size_t i = 0; i < size; ++i) {
array[i] = value;
}
}
int main(int argc, char *argv[])
{
constexpr size_t W = 10;
constexpr size_t H = 5;
double matrix[W][H];
// using 2D array as 1D to fill all elements with 5.
fill_array(&matrix[0][0], W * H, 5);
for (const auto &row: matrix) {
for (const auto v : row) {
cout << v << '\t';
}
cout << '\n';
}
return 0;
}
In the above example, you can substitute double matrix[W][H]; with vector<double> matrix(W * H); and feed matrix.data() into fill_array(). However, you cannot declare vector(W) of vector(H).
P.S. There are plenty of C++ implementations of math vector and matrix. You can use one of those if you don't want to deal with C-style arrays.
Related
I have a collection of 512D std::vector to store face embeddings. I create my index and perform training on a subset of the data.
int d = 512;
size_t nb = this->templates.size() // 95000
size_t nt = 50000; // training data size
std::vector<float> training_set(nt * d);
faiss::IndexFlatIP coarse_quantizer(d);
int ncentroids = int(4 * sqrt(nb)));
faiss::IndexIVFPQ index(&coarse_quantizer,d,ncentroids,4,8);
std::vector<float> training_set(nt*d);
The this->templates has an index value in [0] and the 512D vectors in [1]. My question is about the training and indexing. I have this currently:
int v=0;
for (auto const& element : this->templates)
{
std::vector<double> enrollment_template = element.second;
for (int i=0;i<d;i++){
training_set[(v*d)+i] = (float)enrollment_template.at(i);
v++;
}
index.train(nt,training_set.data());
FAISS Index.Train function
virtual void train(idx_t n, const float *x)
Perform training on a representative set of vectors
Parameters:
n – nb of training vectors
x – training vecors, size n * d
Is that the proper way of adding the 512D vector data into Faiss for training? It seems to me that if I have 2 face embeddings that are 512D in size, the training_set would be like this:
training_set[0-511] - Face #1's 512D vectors
training_set[512-1024] - Face #2's 512D vectors
and since Faiss knows we are working with 512D vectors, it will intelligently parse them out of the array.
Here's a more efficient way to write it:
int v = 0;
for (auto const& element : this->templates)
{
auto& enrollment_template = element.second; // not copy
if (v + d > training_set.size()) {
break; // prevent overflow, "nt" is smaller than templates.size()
}
for (int i = 0; i < d; i++) {
training_set[v] = enrollment_template[i]; // not at()
v++;
}
}
We avoid a copy with auto& enrollment_template, avoid extra branching with enrollment_template[i] (you know you won't be out of bounds), and simplify the address computation with training_set[v] by making v a count of elements rather than rows.
Further efficiency could be gained if templates can be changed to store floats rather than doubles--then you'd just be bitwise-copying 512 floats rather than converting doubles to floats.
Also, be sure to declare d as constexpr to give the compiler the best chance of optimizing the loop.
I do not know the value of V before. It is found within a file I open in the program. It cannot be defined as such #DEFINE V __. It does not work as a global variable. The input file changes V based on the contents. Expected the parameters to pass and use the djisktra's algorithm found on Geeks for Geeks.
I have tried declaring V globally, but I am given an error saying "variable must have constant value."
void dijkstra(int graph[V][V], int src, int V)
//array function being pasted, error is the V in graph[V]
//V is defined at beginning of main as
int V;
//where V is changed
while(std::getline(file2,newstr))
{
if(newstr.find(check) != std::string::npos)
{
V++;
}
}
//where it is passed in main
for(int i = 0; i < V; i++)
{
size = V;
dijkstra(array[size][size], i, V);
}
Don't use C-style arrays. Use std::vector and friends from the Standard Library where you can ask for the size if you want to know.
Converted:
void dijkstra(const std::vector<std::vector<int>>& graph, int src) {
auto v = graph.size();
// ... Other code.
}
For inserting you can use push_back:
std::vector<std::vector<int>> graph;
while(std::getline(file2,newstr)) {
if(newstr.find(check) != std::string::npos) {
std::vector<int> row;
row.push_back(...);
graph.push_back(row);
}
}
Then pass it in like a regular variable:
dijkstra(graph, src);
If all that vector stuff looks really ugly, typedef it to something more friendly looking.
For c style arrays, you need to know the size at compile time. A variable like int N; is a runtime value. A variable like constexpr int N = 9; is usable at compile time and cannot be mutated.
If you need an array sizeable at runtime, you need some sort of dynamic array. The most common one is std::vector.
void dijkstra(std::vector<int> graph, int src, int V)
std::vector<int> graph;
graph.resize(V * V); // vector are resizable
for(int i = 0; i < V; i++)
{
size = V;
dijkstra(graph, i, V);
}
Is it possible to pass a variable length array as a parameter in C++.
No.
Variable length arrays are not supported in std C++, But read on, they have an alternative that is surprisingly better.
I do not know the value of V before it is found within a file I open
in the program.
A 1d vector is trivial to create, after your code has found V, no compile time constant required.
Early in the startup in one of my programs, the gBoard vector is built using argv[3] and argv[4]. Here is a snippet:
aTermPFN += argv[1]; // ouput tty, /dev/pts/<argv[1]>
fillPatternChoiceLetter = argv[2][0];
aMaxRow = stoi(argv[3]);
aMaxCol = stoi(argv[4]);
userDim = true;
Clearly, the program has already started ... and V size is easily computed from (aMaxRow * aMaxCol).
I find it easy to access a 1d vector (or 1d array), in row major order, as if it is a 2d matrix, with the following function:
// game-board-index: computes index into the single dimension vector
// from 2d (row, col) matrix coordinates
size_t gbIndx(int r, int c) { return static_cast<size_t>((r * maxCol) + c); }
// a 2d game board of cells
// 2d access (row major order) implemented using 1d access
Cell_t* getCell( int r, int c ) { return (gBoard [gbIndx(r,c)]); }
// 1d access is surprisingly convenient for many functions
Cell_t* getCell( uint gbIndex ) { return (gBoard [gbIndex]); }
Sample initialization usage:
// vvvvvvvvvvvvvvvvvvv_-- 2d matrix access
gBoard [ gbIndx((midRow+1), midCol) ] -> setOptionX();
// ^^^^^^--1d row-major order index
A randomized gGoard is trivial in 1d:
void GOLUtil_t::setRandom()
{
CellVec_t myVec(gBoard); // copy cell vector
random_device rd;
mt19937_64 gen(rd());
shuffle (myVec.begin(), myVec.end(), gen); // shuffle order
int count = 1;
for ( auto it : myVec ) // randomly mark half the cells
{
if(count++ & 1)
it->setAlive(); // every odd cell
}
}
Note from https://en.cppreference.com/w/cpp/container/vector:
"The elements are stored contiguously, which means that elements can be accessed not only through iterators, but also using offsets to regular pointers to elements. This means that a pointer to an element of a vector may be passed to any function that expects a pointer to an element of an array."
I was surprised how often the 1d access enabled simpler code.
for (auto it : gBoard)
it->init(); // command each cell to init
Summary:
Despite variable-length-arrays (vla) not being supported in std C++, I believe you will find std::vector a better alternative. And you will find that passing the vector within your code works.
I am trying to create an array of X pointers referencing matrices of dimensions Y by 16. Is there any way to accomplish this in C++ without the use of triple pointers?
Edit: Adding some context for the problem.
There are a number of geometries on the screen, each with a transform that has been flattened to a 1x16 array. Each snapshot represents the transforms for each of number of components. So the matrix dimensions are 16 by num_components by num_snapshots , where the latter two dimensions are known at run-time. In the end, we have many geometries with motion applied.
I'm creating a function that takes a triple pointer argument, though I cannot use triple pointers in my situation. What other ways can I pass this data (possibly via multiple arguments)? Worst case, I thought about flattening this entire 3D matrix to an array, though it seems like a sloppy thing to do. Any better suggestions?
What I have now:
function(..., double ***snapshot_transforms, ...)
What I want to accomplish:
function (..., <1+ non-triple pointer parameters>, ...)
Below isn't the function I'm creating that takes the triple pointer, but shows what the data is all about.
static double ***snapshot_transforms_function (int num_snapshots, int num_geometries)
{
double component_transform[16];
double ***snapshot_transforms = new double**[num_snapshots];
for (int i = 0; i < num_snapshots; i++)
{
snapshot_transforms[i] = new double*[num_geometries];
for (int j = 0; j < num_geometries; j++)
{
snapshot_transforms[i][j] = new double[16];
// 4x4 transform put into a 1x16 array with dummy values for each component for each snapshot
for (int k = 0; k < 16; k++)
snapshot_transforms[i][j][k] = k;
}
}
return snapshot_transforms;
}
Edit2: I cannot create new classes, nor use C++ features like std, as the exposed function prototype in the header file is getting put into a wrapper (that doesn't know how to interpret triple pointers) for translation to other languages.
Edit3: After everyone's input in the comments, I think going with a flattened array is probably the best solution. I was hoping there would be some way to split this triple pointer and organize this complex data across multiple data pieces neatly using simple data types including single pointers. Though I don't think there is a pretty way of doing this given my caveats here. I appreciate everyone's help =)
It is easier, better, and less error prone to use an std::vector. You are using C++ and not C after all. I replaced all of the C-style array pointers with vectors. The typedef doublecube makes it so that you don't have to type vector<vector<vector<double>>> over and over again. Other than that the code basically stays the same as what you had.
If you don't actually need dummy values I would remove that innermost k loop completely. reserve will reserve the memory space that you need for the real data.
#include <vector>
using std::vector; // so we can just call it "vector"
typedef vector<vector<vector<double>>> doublecube;
static doublecube snapshot_transforms_function (int num_snapshots, int num_geometries)
{
// I deleted component_transform. It was never used
doublecube snapshot_transforms;
snapshot_transforms.reserve(num_snapshots);
for (int i = 0; i < num_snapshots; i++)
{
snapshot_transforms.at(i).reserve(num_geometries);
for (int j = 0; j < num_geometries; j++)
{
snapshot_transforms.at(i).at(j).reserve(16);
// 4x4 transform put into a 1x16 array with dummy values for each component for each snapshot
for (int k = 0; k < 16; k++)
snapshot_transforms.at(i).at(j).at(k) = k;
}
}
return snapshot_transforms;
}
Adding a little bit of object-orientation usually makes the code easier to manage -- for example, here's some code that creates an array of 100 Matrix objects with varying numbers of rows per Matrix. (You could vary the number of columns in each Matrix too if you wanted to, but I left them at 16):
#include <vector>
#include <memory> // for shared_ptr (not strictly necessary, but used in main() to avoid unnecessarily copying of Matrix objects)
/** Represents a (numRows x numCols) 2D matrix of doubles */
class Matrix
{
public:
// constructor
Matrix(int numRows = 0, int numCols = 0)
: _numRows(numRows)
, _numCols(numCols)
{
_values.resize(_numRows*_numCols);
std::fill(_values.begin(), _values.end(), 0.0f);
}
// copy constructor
Matrix(const Matrix & rhs)
: _numRows(rhs._numRows)
, _numCols(rhs._numCols)
{
_values.resize(_numRows*_numCols);
std::fill(_values.begin(), _values.end(), 0.0f);
}
/** Returns the value at (row/col) */
double get(int row, int col) const {return _values[(row*_numCols)+col];}
/** Sets the value at (row/col) to the specified value */
double set(int row, int col, double val) {return _values[(row*_numCols)+col] = val;}
/** Assignment operator */
Matrix & operator = (const Matrix & rhs)
{
_numRows = rhs._numRows;
_numCols = rhs._numCols;
_values = rhs._values;
return *this;
}
private:
int _numRows;
int _numCols;
std::vector<double> _values;
};
int main(int, char **)
{
const int numCols = 16;
std::vector< std::shared_ptr<Matrix> > matrixList;
for (int i=0; i<100; i++) matrixList.push_back(std::make_shared<Matrix>(i, numCols));
return 0;
}
In Python I normally use functions like vstack, stack, etc to easily create a 3D array by stacking 2D arrays one onto another.
Is there any way to do this in C++?
In particular, I have loaded a image into a Mat variable with OpenCV like:
cv::Mat im = cv::imread("image.png", 0);
I would like to make a 3D array/Mat of N layers by stacking copies of that Mat variable.
EDIT: This new 3D matrix has to be "travellable" by adding an integer to any of its components, such that if I am in the position (x1,y1,1) and I add +1 to the last component, I arrive to (x1,y1,2). Similarly for any of the coordinates/components of the 3D matrix.
SOLVED: Both answers from #Aram and #Nejc do exactly what expected. I set #Nejc 's answer as the correct one for his shorter code.
The Numpy function vstack returns a contiguous array. Any C++ solution that produces vectors or arrays of cv::Mat objects does not reflect the behaviour of vstack in this regard, becase separate "layers" belonging to individual cv::Mat objects will not be stored in contiguous buffer (unless a careful allocation of underlying buffers is done in advance of course).
I present the solution that copies all arrays into a three-dimensional cv::Mat object with a contiguous buffer. As far as the idea goes, this answer is similar to Aram's answer. But instead of assigning pixel values one by one, I take advantage of OpenCV functions. At the beginning I allocate the matrix which has a size N X ROWS X COLS, where N is the number of 2D images I want to "stack" and ROWS x COLS are dimensions of each of these images.
Then I make N steps. On every step, I obtain the pointer to the location of the first element along the "outer" dimension. I pass that pointer to the constructor of temporary Mat object that acts as a kind of wrapper around the memory chunk of size ROWS x COLS (but no copies are made) that begins at the address that is pointed-at by pointer. I then use copyTo method to copy i-th image into that memory chunk. Code for N = 2:
cv::Mat img0 = cv::imread("image0.png", CV_IMREAD_GRAYSCALE);
cv::Mat img1 = cv::imread("image1.png", CV_IMREAD_GRAYSCALE);
cv::Mat images[2] = {img0, img1}; // you can also use vector or some other container
int dims[3] = { 2, img0.rows, img0.cols }; // dimensions of new image
cv::Mat joined(3, dims, CV_8U); // same element type (CV_8U) as input images
for(int i = 0; i < 2; ++i)
{
uint8_t* ptr = &joined.at<uint8_t>(i, 0, 0); // pointer to first element of slice i
cv::Mat destination(img0.rows, img0.cols, CV_8U, (void*)ptr); // no data copy, see documentation
images[i].copyTo(destination);
}
This answer is in response to the question above of:
In Python I normally use functions like vstack, stack, etc to easily create a 3D array by stacking 2D arrays one onto another.
This is certainly possible, you can add matrices into a vector which would be your "stack"
For instance you could use a
std::vector<cv::Mat>>
This would give you a vector of mats, which would be one slice, and then you could "layer" those by adding more slices vector
If you then want to have multiple stacks you can add that vector into another vector:
std::vector<std::vector<cv::Mat>>
To add matrix to an array you do:
myVector.push_back(matrix);
Edit for question below
In such case, could I travel from one position (x1, y1, z1) to an immediately upper position doing (x1,y1,z1+1), such that my new position in the matrix would be (x1,y1,z2)?
You'll end up with something that looks a lot like this. If you have a matrix at element 1 in your vector, it doesn't really have any relationship to the element[2] except for the fact that you have added it into that point. If you want to build relationships then you will need to code that in yourself.
You can actually create a 3D or ND mat with opencv, you need to use the constructor that takes the dimensions as input. Then copy each matrix into (this case) the 3D array
#include <opencv2/opencv.hpp>
using namespace cv;
using namespace std;
int main() {
// Dimensions for the constructor... set dims[0..2] to what you want
int dims[] = {5, 5, 5}; // 5x5x5 3d mat
Mat m = Mat::zeros(5, 5, CV_8UC1);
for (size_t i = 0; i < 5; i++) {
for (size_t k = 0; k < 5; k++) {
m.at<uchar>(i, k) = i + k;
}
}
// Mat with constructor specifying 3 dimensions with dimensions sizes in dims.
Mat 3DMat = Mat(3, dims, CV_8UC1);
// We fill our 3d mat.
for (size_t i = 0; i < m2.size[0]; i++) {
for (size_t k = 0; k < m2.size[1]; k++) {
for (size_t j = 0; j < m2.size[2]; j++) {
3DMat.at<uchar>(i, k, j) = m.at<uchar>(k, j);
}
}
}
// We print it to show the 5x5x5 array.
for (size_t i = 0; i < m2.size[0]; i++) {
for (size_t k = 0; k < m2.size[1]; k++) {
for (size_t j = 0; j < m2.size[2]; j++) {
std::cout << (int) 3DMat.at<uchar>(i, k, j) << " ";
}
std::cout << endl;
}
std::cout << endl;
}
return 0;
}
Based on the question and comments, I think you are looking for something like this:
std::vector<cv::Mat> vec_im;
//In side for loop:
vec_im.push_back(im);
Then, you can access it by:
Scalar intensity_1 = vec_im[z1].at<uchar>(y, x);
Scalar intensity_2 = vec_im[z2].at<uchar>(y, x);
This assumes that the image is single channel.
Eigen is a well known matrix Library in c++. I am having trouble finding an in built function to simply push an item on to the end of a matrix. Currently I know that it can be done like this:
Eigen::MatrixXd matrix(10, 3);
long int count = 0;
long int topCount = 10;
for (int i = 0; i < listLength; ++i) {
matrix(count, 0) = list.x;
matrix(count, 1) = list.y;
matrix(count, 2) = list.z;
count++;
if (count == topCount) {
topCount *= 2;
matrix.conservativeResize(topCount, 3);
}
}
matrix.conservativeResize(count, 3);
And this will work (some of the syntax may be out). But its pretty convoluted for a simple thing to do. Is there already an in built function?
There is no such function for Eigen matrices. The reason for this is such a function would either be very slow or use excessive memory.
For a push_back function to not be prohibitively expensive it must increase the matrix's capacity by some factor when it runs out of space as you have done. However when dealing with matrices, memory usage is often a concern so having a matrix's capacity be larger than necessary could be problematic.
If it instead increased the size by rows() or cols() each time the operation would be O(n*m). Doing this to fill an entire matrix would be O(n*n*m*m) which for even moderately sized matrices would be quite slow.
Additionally, in linear algebra matrix and vector sizes are nearly always constant and known beforehand. Often when resizeing a matrix you don't care about the previous values in the matrix. This is why Eigen's resize function does not retain old values, unlike std::vector's resize.
The only case I can think of where you wouldn't know the matrix's size beforehand is when reading from a file. In this case I would either load the data first into a standard container such as std::vector using push_back and then copy it into an already sized matrix, or if memory is tight run through the file once to get the size and then a second time to copy the values.
There is no such function, however, you can build something like this yourself:
using Eigen::MatrixXd;
using Eigen::Vector3d;
template <typename DynamicEigenMatrix>
void push_back(DynamicEigenMatrix& m, Vector3d&& values, std::size_t row)
{
if(row >= m.rows()) {
m.conservativeResize(row + 1, Eigen::NoChange);
}
m.row(row) = values;
}
int main()
{
MatrixXd matrix(10, 3);
for (std::size_t i = 0; i < 10; ++i) {
push_back(matrix, Vector3d(1,2,3), i);
}
std::cout << matrix << "\n";
return 0;
}
If this needs to perform too many resizes though, it's going to be horrendously slow.