I am using the Eigen library in C++.
I need to insert a row and column to an existing matrix at specific index.
For example, say I need to insert a 0 row and 0 column at the 2nd index...
ORIGINAL MATRIX (A)
1 2 3
1 2 3
1 2 3
NEW MATRIX (B)
1 2 0 3
1 2 0 3
0 0 0 0
1 2 0 3
Thanks for the help in advance!
The new matrix B can be constructed from the original matrix A by using the block operations .topRows() and .bottomRows():
MatrixXd B = MatrixXd::Zero(4, 3);
B.topRows(2) = A.topRows(2);
B.bottomRows(1) = A.bottomRows(1);
This will insert a row of zeros between the second and third row. Analogous operations with .rightCols() and .leftCols() can be used to insert a column of zeros.
Related
Sorry if this is a duplicate, but I did not find any answers which match mine.
Consider that I have a vector which contains 3 values. I want to construct another vector of a specified length from this vector. For example, let's say that the length n=3 and the vector contains the following values 0 1 2. The output that I expect is as follows:
0 0 0
0 0 1
0 0 2
0 1 0
0 1 1
0 1 2
0 2 0
0 2 1
0 2 2
1 0 0
1 0 1
1 0 2
1 1 0
1 1 1
1 1 2
1 2 0
1 2 1
1 2 2
2 0 0
2 0 1
2 0 2
2 1 0
2 1 1
2 1 2
2 2 0
2 2 1
2 2 2
My current implementation simply constructs for loops based on nand generates the expected output. I want to be able to construct output vectors of different lengths and with different values in the input vector.
I have looked at possible implementations using next_permutation, but unfortunately passing a length value does not seem to work.
Are there time and complexity algorithms that one can use for this case? Again, I might have compute this for up to n=17and sizeof vector around 6.
Below is my implementation for n=3. Here, encis the vector which contains the input.
vector<vector<int> > combo_3(vector<double>enc,int bw){
vector<vector<int> > possibles;
for (unsigned int inner=0;inner<enc.size();inner++){
for (unsigned int inner1=0;inner1<enc.size();inner1++){
for (unsigned int inner2=0;inner2<enc.size();inner2++){
cout<<inner<<" "<<inner1<<" "<<inner2<<endl;
unsigned int arr[]={inner,inner1,inner2};
vector<int>current(arr,arr+sizeof(arr)/sizeof(arr[0]));
possibles.push_back(current);
current.clear();
}
}
}
return possibles;
}
What you are doing is simple counting. Think of your output vector as a list of a list of digits (a vector of a vector). Each digit may have one of m different values where m is the size of your input vector.
This is not permutation generation. Generating every permutation means generating every possible ordering of an input vector, which is not what you're looking for at all.
If you think of this as a counting problem the answer may become clearer to you. For example, how would you generate all base 10 numbers with 5 digits? In that case, your input vector has size 10, and each vector in your output list has length 5.
Suppose I wanted to apply some generic operation a matrix consisting of some subset of its values that are not necessarily contiguous. How can I do this?
If the values were contiguous I would simply use the Eigen::block operation, but what if they are not?
One application might be that I have an eigen matrix of positive integers:
Eigen::Matrix<int, 4, 1> mat;
mat << 4, 1, 2, 8;
And I wanted to return the 0th, 2nd and 3rd values. If they were contiguous (0th, 1st and 2nd) I could simply use the block operation on this matrix, but what do I do in this case?
How about rearranging the elements to make them contiguous?
1 0 0 0 4 4
0 0 1 0 x 1 = 2
0 0 0 1 2 8
0 0 0 0 8 0
So I have to fill in a square matrix recursively. For size N=5, it should be:
1 1 1 1 1
1 2 2 2 1
1 2 3 2 1
1 2 2 2 1
1 1 1 1 1
but my program shows:
1 1 1 1 1
1 2 2 2 1
1 2 3 3 1
1 2 2 2 1
1 1 1 1 1
void llenar5 (int** mat, int n, int f=0, int c=0,int k=2)
{
if (f<n)
{
if (c<n)
{
if (f==0 ||c==0||f==n-1||c==n-1)
{
*(*(mat+f)+c)=1;
llenar5(mat,n,f,c+1,k); //move to the right
}
else if (f==k-1 ||c==k-1||f==n-k||c==n-k)
{
*(*(mat+f)+c)=k;
llenar5(mat,n,f,c+1,k++);
}
}
llenar5(mat,n,f+1,c,k);
}
}
I am creating a matrix in dynamic memory, and I tried calling the function llenar5(mat,n,f+1,c+1,k+1) to jump a column and row while incrementing the values.
void llenar5 (int** mat, int n, int f=0, int c=0,int k=1)
{
if (f<n)
{
if (c<n)
{
if (f==k-1 ||c==k-1||f==n-k||c==n-k)
{
*(*(mat+f)+c)=k;
llenar5(mat,n,f,c+1,k+1);
}
llenar5(mat,n,f,c+1,k);
}
llenar5(mat,n,f+1,c,k);
}
}
I think it will help if you, temporarily, consider a matrix with 0-based numbers. For example, your initial matrix would look instead something like this:
0 0 0 0 0
0 1 1 1 0
0 1 2 1 0
0 1 1 1 0
0 0 0 0 0
If you inspect this matrix, you should quickly observe a fundamental property of this matrix. The value of each cell is the minimum distance from the cell to its closest horizontal or vertical edge.
So, for cell at coordinates (x,y), with the matrix of size w (width) and h (height), the value of each cell is:
min(x, y, (w-1-x), (h-1-y))
Where the min() function is a classical minimum function, that computes the minimum value of its arguments.
Then, it should be obvious that going from a 0-based matrix to a 1-based matrix you should simply add 1 to the result.
So, in conclusion your code should be trivially simple:
Loop over all the x and y coordinates.
Set the value of the corresponding cell based on the above formula.
Your code seems to be unnecessarily complicated. All that recursion is completely unneeded. This can be done using a single pass over their entire matrix, top to bottom, left to right. You don't need to know the values of adjacent cells, to compute the value in the next cell.
I'm trying to transpose a sparse matrix in c++. I'm struggling with the traversal of the new transposed matrix. I want to enter everything from the first row of the matrix to the first column of the new matrix.
Each row has the column index the number should be in and the number itself.
Input:
colInd num colInd num colInd num
Input:
1 1 2 2 3 3
1 4 2 5 3 6
1 7 2 8 3 9
Output:
1 1 2 4 3 7
1 2 2 5 3 8
1 3 2 6 3 9
How do I make the list traverse down the first column inserting the first element as it goes then go back to the top inserting down the second column. Apologies if this is two hard to follow. But all I want help with is traversing the Transposed matrix to be in the right place at the right time inserting a nz(non zero) object in the right place.
Here is my code
list<singleRow> tran;
//Finshed reading so transpose
for (int i = 0; i < rows.size(); i++){ // Initialize transposed matrix
singleRow trow;
tran.push_back(trow);
}
list<singleRow>::const_iterator rit;
list<singleRow>::const_iterator trowit;
int rowind;
for (rit = rows.begin(), rowind = 1; rit != rows.end(); rit++, rowind++){//rit = row iterator
singleRow row = *rit;
singleRow::const_iterator nzit;
trowit = tran.begin(); //Start at the beginning of the list of rows
trow = *trowit;
for (nzit = row.begin(); nzit != row.end(); nzit++){//nzit = non zero iterator
int col = nzit->getCol();
double val = nzit->getVal();
trow.push_back(nz(rowind,val)); //How do I attach this to tran so that it goes in the right place?
trowit++;
}
}
Your representation of the matrix is inefficient: it doesn't use the fact that the matrix is sparse. I say so because it includes all the rows of the matrix, even if most of them are zero (empty), like it usually happens with sparse matrices.
Your representation is also hard to work with. So i suggest converting the representation first (to a regular 2-D array), transposing the matrix, and convert back.
(Edited:)
Alternatively, you can change the representation, for example, like this:
Input: rowInd colInd num
1 1 1
1 2 2
1 2 3
2 1 4
2 2 5
2 3 6
3 1 7
3 2 8
3 3 9
Output:
1 1 1
2 1 2
3 1 3
1 2 4
2 2 5
3 2 6
1 3 7
2 3 8
3 3 9
The code would be something like this:
struct singleElement {int row, col; double val;};
list<singleElement> matrix_input, matrix_output;
...
// Read input matrix from file or some such
list<singleElement>::const_iterator i;
for (i = matrix_input.begin(); i != matrix_input.end(); ++i)
{
singleElement e = *i;
std::swap(e.row, e.col);
matrix_output.push_back(e);
}
Your choice of list-of-list representation for a sparse matrix is poor for transposition. Sometimes, when considering algorithms and data structures, the best thing to do is to take the hit for transforming your data structure into one better suited for your algorithm than to mangle your algorithm to work with the wrong data structure.
In this case you could, for example, read your matrix into a coordinate list representation which would be very easy to transpose, then write into whatever representation you like. If space is a challenge, then you might need to do this chunk by chunk, allocating new columns in your target representation 1 by 1 and deallocating columns in your old representation as you go.
Description:
There are m * n (m <= 100, n <=100) coins on the desktop forming a m row n column coin matrix. Every coin either face upward, or face backward, represented by 0 or 1.
Rules of the game are:
(1) every time, you are allowed to inverse one row of coins.
(2) every time, you are allowed to swap two columns.
Object:
from initial matrix -> target matrix
Input:
1. k the count of test caese
2. m n the count of rows and columns
3. the numbers of the inital matrix and the target matrix
Output
the least steps from initial matrix to target matrix, if it is not possible to transfer from initial to target, output -1.
sample intput
2
4 3
1 0 1
0 0 0
1 1 0
1 0 1
1 0 1
1 1 1
0 1 1
1 0 1
4 3
1 0 1
0 0 0
1 0 0
1 1 1
1 1 0
1 1 1
0 1 1
1 0 1
sample output
2
-1
I have coded one solution: mysolution.cc, which enumerate all posibilities and which is correct but it is too slow, could you provide a correct but fast solution.
Thanks.
The rows always stay in the same place, so if row r starts with k ones, it will always have either k ones or columns - k.
for each row, check if count_of_ones(initial,row) == count_of_ones(target,row), if yes, fine, else check if count_of_ones(initial,row) = columns - count_of_ones(target,row), if so, flip row, else output -1. As #maniek pointed out, it's not so easy when exactly half of the columns contain ones. Such rows would have to be treated in step 2 to try and form the required columns.
for each column, count the number of ones int the target and the working matrix (after flipping rows as appropriate). If the sequences of counts are not permutations of each other, output -1, otherwise try to find a permutation of columns that transforms working to target (any columns identical between working and target have to be kept fixed). If not possible, output -1, otherwise find minimum number of swaps necessary to achieve that permutation.
I will give you some thoughts. You compare row by row. If the i-th row of the first matrix has the same number of 1 as in the i-th row of the second matrix - then you don't inverse. If the i-th row of the first matrix has the same number of 1 as the 0 in the i-th row of the second matrix - then you must inverse. If neither of this is true, then there is no solution. This is all about inversing.
Now all columns are equal but in a different order(the second matrix has permuted columns from the first matrix). If the columns are not permutation of each other - return -1. This problem is equal to find the minimum number of swaps to convert a one permutation to other.