MATLAB Eigen with libigl Notes 
[Y,IX] = sort(X,dim,mode)
 
igl::sort(X,dim,mode,Y,IX)
 MATLAB version allows Y to be a multidimensional matrix, but the Eigen version is only for 1D or 2D matrices. 
B(i:(i+w),j:(j+h)) = A(x:(x+w),y:(y+h))
 
B.block(i,j,w,h) = A.block(i,j,w,h)
 MATLAB version would allow w and h to be non-positive since the colon operator evaluates to a list of indices, but the Eigen version needs non-negative width and height values. 
max(A(:))
 
A.maxCoeff()
 Find the maximum coefficient over all entries of the matrix. 
min(A(:))
 
A.minCoeff()
 Find the minimum coefficient over all entries of the matrix. 
eye(w,h)
 
MatrixXd::Identity(w,h), MatrixXf::Identity(w,h), etc.
 
A(i:(i+w),j:(j+h)) = eye(w,h)
 
A.block(i,j,w,h).setIdentity()
 
[I,J,V] = find(X)
 
igl::find(X,I,J,V)
 Matlab supports finding subscripts (I and J) as well as indices (just I), but so far igl::find only supports subscripts. Also, igl::find requires X to be sparse. 
X(:,j) = X(:,j) + x
 
X.col(j).array() += x
 
Acol_sum = sum(A,1)
Arow_sum = sum(A,2)
Adim_sum = sum(Asparse,dim)
 
Acol_sum = A.colwise().sum()
Arow_sum = A.rowwise().sum()
igl::sum(Asparse,dim,Adim_sum)
 Currently the igl version only supports sparse matrix input (and dim must be 1 or 2).
For sparse matrices, one could use A*Matrix<Atype,Dynamic,1>::Ones(A.cols(),1); but this will not work as expected for SparseMatrix<bool>. 
D = diag(M)
 
igl::diag(M,D)
 Extract the main diagonal of a matrix. Currently igl version supports sparse only. 
M = diag(D)
 
igl::diag(D,M)
 Construct new square matrix M with entries of vector D along the diagonal. Currently igl version supports sparse only. Might also consider simply: M = D.asDiagonal(); 
[Y,I] = max(X,[],dim)
 
igl::mat_max(X,dim,Y,I)
 Matlab has a bizarre convention of passing [] as the second argument to mean take the max/min along dimension dim. 
Y = max(X,[],1)
Y = max(X,[],2)
Y = min(X,[],1)
Y = min(X,[],2)
 
Y = X.colwise().maxCoeff()
Y = X.rowwise().maxCoeff()
Y = X.colwise().minCoeff()
Y = X.rowwise().minCoeff()
 Matlab allows you to obtain the indices of extrema see mat_max 
C = A.*B
 
C = (A.array() * B.array()).matrix()
 
C = A.^b
 
C = A.array().pow(b).matrix()
 
A(B == 0) = C(B==0)
 
A = (B.array() == 0).select(C,A)
 
C = A + B'
 
SparseMatrixType BT = B.transpose()
SparseMatrixType C = A+BT;
 Do not attempt to combine .transpose() in expression like this: 
C = A + B.transpose()
 
[L,p] = chol(A)
 
SparseLLT<SparseMatrixType> A_LLT(A.template triangularView<Lower>())
SparseMatrixType L = A_LLT.matrixL();bool p = (L*0).eval().nonZeros()==0;
 Do not attempt to use A in constructor of A_LLT like this: 
SparseLLT<SparseMatrixType> A_LLT(A)

Do not attempt to use A_LLT.succeeded() to determine if Cholesky factorization succeeded, like this: 
bool p = A_LLT.succeeded()
 
X = U\(L\b)
 
X = b;
L.template triangularView<Lower>().solveInPlace(X);
U.template triangularView<Upper>().solveInPlace(X);
 Expects that L and U are lower and upper triangular matrices respectively 
B = repmat(A,i,j)
 
igl::repmat(A,i,j,B);
B = A.replicate(i,j);
 igl::repmat is also implemented for Sparse Matrices. 
I = low:step:hi
 
igl::colon(low,step,hi,I);
// or
const int size = ((hi-low)/step)+1;
I = VectorXi::LinSpaced(size,low,low+step*(size-1));
 IGL version should be templated enough to handle same situations as matlab's colon. The matlab keyword end does not correspond in the C++ version. You'll have to use M.size(),M.rows() or whatever. 
O = ones(m,n)
 
Matrix* O = Matrix*::Ones(m,n)
 
O = zeros(m,n)
 
Matrix* O = Matrix*::Zero(m,n)
 
B = A(I,J)
B = A(I,:)
 
igl::slice(A,I,J,B)
igl::slice(A,I,1,B)
 This is only for the case when I and J are lists of indices and not vectors of logicals. 
B(I,J) = A
B(I,:) = A
 
igl::slice_into(A,I,J,B)
igl::slice_into(A,I,1,B)
 This is only for the case when I and J are lists of indices and not vectors of logicals. 
M = mode(X,dim)
 
igl::mode(X,dim,M)
 
B = arrayfun(FUN, A)
 
B = A.unaryExpr(ptr_fun(FUN))
 If FUN is templated, the templates must be fully resolved. 
B = fliplr(A)
B = flipud(A)
 
B = A.rowwise().reverse().eval()
B =
	A.colwise().reverse().eval()
 The .eval() is not necessary if A != B 
B = IM(A)

A = IM(A);
  
B = A.unaryExpr(bind1st(mem_fun(
  static_cast<VectorXi::Scalar&(VectorXi::*)(VectorXi::Index)>
  (&VectorXi::operator())), &IM)).eval();
// or
for_each(A.data(),A.data()+A.size(),[&IM](int & a){a=IM(a);});
Where IM is an "index map" column vector and A is an arbitrary matrix. The .eval() is not necessary if A != B, but then the second option should be used. 
A = sparse(I,J,V)
 
// build std::vector<Eigen::Triplet> IJV
A.setFromTriplets(IJV);
IJV and A should not be empty! (this might be fixed) 
A = min(A,c);
 
C.array() = A.array().min(c);
Coefficient-wise minimum of matrix and scalar (or matching size matrix) 
I=1:10;
...
IP = I(P==0);
 
I = VectorXi::LinSpaced(10,0,9);
...
VectorXi IP = I;
IP.conservativeResize(stable_partition(
  IP.data(),
  IP.data()+IP.size(),
  [&P](int i){return P(i)==0;})-IP.data());
Where I is a vector of increasing indices from 0 to n, and P is a vector. Requires C++11 and #include <algorithm> 
B = A(R<2,C>1);
B = igl::slice_mask(A,R.array()<2,C.array()>1);
 
a = any(A(:))
 
bool a = any_of(A.data(),A.data()+A.size(),[](bool a){ return a;});
bool a = A.array().any();
Casts Matrix::Scalar to bool. 
B = mod(A,2)
 
igl::mod(A,2,B)
 
[IA,LOCB] = ismember(A,B)
 
igl::ismember(A,B,IA,LOCB)
 
A = A - diag(diag(A));
 
A.prune([](const int r, const int c, const Scalar)->bool{return r!=c;});
 Remove the diagonal from a sparse matrix. 
A = A - diag(diag(A));
 
A.prune([](const int r, const int c, const Scalar)->bool{return r!=c;});
 Remove the diagonal from a sparse matrix.
Eigen's "ASCII Quick Reference" with MATLAB translations
IGL Lib Tutorial