Basic functions in the Eigen

basic functions in the Eigen

Definition of matrices in Eigen

#include <Eigen/Dense>                  //Basic functions only need to contain this header file
matrix<double, 3, 3> A;                 A matrix that has a fixed number of rows and columns is consistent with Matrix3D.
Matrix<double, 3, dynamic> B;           Fixed number of rows.
Matrix<double, Dynamic, dynamic> C;     Consistent with Matrixxd.
Matrix<double, 3, 3, rowmajor> E;       Store by Row; Default by Column storage.
matrix3f P, Q, R;                       3x3 float matrix.
vector3f x, y, Z;                       3x1 float column vector.
Rowvector3f A, B, C;                    1x3 float line vector.
Vectorxd v;                             Dynamic length type double column vector
//Eigen          //Matlab             //Comments
x.size ()          //Length (x)          //Vector length
C.rows ()          //Size (c,1)          //Matrix rows
c.cols ()          //Size (c,2)          //Number of matrix columns
x (i)              //X (i+1)             Subscript 0 Start
C (i,j)            //C (i+1,j+1)         //

Basic use method of matrix in Eigen

A.resize (4, 4);   Triggers a run-time error if out of bounds.
B.resize (4, 9);   Triggers a run-time error if out of bounds.
A.resize (3, 3);   Ok; No cross-border.
B.resize (3, 9);   Ok; No cross-border.

A << 1, 2, 3,     //Initialize A. The elements can also be
     4, 5, 6,     //matrices, which is stacked along cols
     7, 8, 9;     And then the rows is stacked.
B << A, A, A;     B is three horizontally stacked A ' s.   Three lines A
A.fill (ten);       Fill A with all ten ' s.                  All 10

Eigen Special Matrix Generation

Eigen                            //Matlab
matrixxd::identity (rows,cols)       //Eye (rows,cols) unit matrix
c.setidentity (rows,cols)            //C = Eye (rows,cols) unit matrix
Matrixxd::zero (Rows,cols)           //Zeros (rows,cols) 0 matrix
C.setzero (rows,cols)                //C = ones (rows,cols) 0 matrix
Matrixxd::ones (Rows,cols)           //Ones (Rows,cols) all one matrix
c.setones (rows,cols)                //C = Ones (rows,cols) all one matrix
matrixxd::random (Rows,cols)         //rand (Rows,cols) *2-1        //element randomly in -1->1
c.setrandom (rows,cols)              //C = rand (rows,cols) *2-1 Ibid
. vectorxd::linspaced (Size,low,high)  //Linspace (low,high,size) ' linear distribution of arrays
v.setlinspaced (Size,low,high)       //V = linspace (low,high,size) ' linear distribution of arrays

Eigen Matrix chunking

Eigen//Matlab X.head (n)//x (1:N) for array extraction before n [vector] X.head<n > ()//X (1:N) similarly x.tail (n)//x (End-n + 1:end) Same as x.tail<n> ( )//X (End-n + 1:end) The same x.segment (i, N)//x (I+1:i+n) Same as x.segment<n> ( i)//x (i+1:i+n) P.block (i, J, rows, cols)//P (I+1:i+rows, J+1:j+cols) i,j start, Rows row cols                           Column p.block<rows, cols> (i, J)//P (I+1:i+rows, J+1:j+cols) i,j start, Rows cols column p.row (i) P (i+1,:) i row P.col (j)//P (:, j+1) J Column p.leftcols<cols> ()//P (:, 1:C OLS) left cols column p.leftcols (cols)//P (:, 1:cols) left cols column p.middlecols<cols> (j)//P (:, j+1                : J+cols) Middle from J Number cols column P.middlecols (j, cols)//P (:, J+1:j+cols) Middle from J Number cols column p.rightcols<cols> () P (:, End-cols+1:end) Right cols column p.rightcols (cols)//P (:, end-cols+1:end) Right cols column p.toprows<rows> ()//P ( 1:rows,:) same column p.toprows (rows)//P (1:rows,:) same column p.middlerows<rows> (i)//P (i+1:i+rows ,:) same column p.middlerows (i, rows)//P (i+1:i+rows,:) same column p.bottomrows<rows> ()//P (end-rows+1:e nd,:) same column p.bottomrows (rows)//P (end-rows+1:end,:) same column p.topleftcorner (rows, cols)//P (1:rows, 1:co LS) upper left corner rows row, cols column p.toprightcorner (rows, cols)//P (1:rows, end-cols+1:end) on the right corner rows row, cols column p.bottomleftcorner (rows, c OLS)//P (end-rows+1:end, 1:cols) lower left corner rows row, cols column p.bottomrightcorner (rows, cols)//P (End-rows+1:end, End-cols+1:end ) Lower right corner rows, cols column p.topleftcorner<rows,cols> ()//P (1:rows, 1:cols) ibid. p.toprightcorner<rows,cols> ()/
/P (1:rows, End-cols+1:end) ibid. p.bottomleftcorner<rows,cols> ()//P (end-rows+1:end, 1:cols) Ibid. P.bottomrightcorner<rows,cols> ()//P (End-rows+1:end, end-cols+1:end) Ibid. 

Eigen Matrix Element Exchange

Eigen                           //Matlab
r.row (i) = P.col (j);               R (i,:) = P (:, i) interchange is listed as row
r.col (J1). Swap (Mat1.col (J2));      R (:, [J1 J2]) = R (:, [J2, J1]) interchange column

Eigen Matrix Transpose

views, transpose, etc; All read-write except for. Adjoint ().
Eigen                           //Matlab
r.adjoint ()                        //R ' adjoint matrix
r.transpose ()                      //R ' or Conj (R ') transpose
r.diagonal ()                       //Diag (R) diagonal
x.asdiagonal ()                     //diag (x) diagonal Array (without overloading <<)
r.transpose (). Colwise (). reverse (); /Rot90 (R) All elements turn counterclockwise 90 degrees
r.conjugate ()                      //Conj (R) Conjugate matrix

Eigen Matrix Product

Consistent with MATLAB, but Matlab does not support *= and other forms of operation.
Matrix-vector.  Matrix-matrix.   Matrix-scalar.
Y  = m*x;          R  = p*q;        R  = p*s;
a  = b*m;          R  = p-q;      R  = s*p;
A *= M;            R  = P + Q;      R  = p/s;
                   R *= Q;          R  = s*p;
                   R + = Q;          R *= S;
                   R-= Q;          R/= S;

Eigen Matrix single element operation

vectorized operations on each element independently//Eigen//Matlab R = p.cwiseproduct (Q);   R = P. * Q corresponds to points multiplied by R = P.array () * S.array ();//R = P. * s corresponds to point multiplied by R = p.cwisequotient (q);  r = P./q The corresponding point division R = P.array ()/Q.array ();//R = P./q corresponds to the Division R = P.array () + S.array ();//R = p + s corresponding points add r = P.array ()           -S.array ();//R = p-s corresponding point subtraction r.array () + = s;           R = R + S full plus s r.array ()-= s;    R = R-s Total minus s R.array () < Q.array ();   R < Q The following is the operation of a single element of the Matrix R.array () <= Q.array ();         R <= Q Matrix element comparison, will be placed in the corresponding position 0 or 1 r.cwiseinverse ();      1./P R.array (). Inverse (); 1./P R.array (). Sin ()//Sin (P) r.array (). cos ()//cos (P) r.array (). POW (s)//p. ^ S R.A           Rray (). Square ()//p. ^ 2 R.array (). Cube ()//p. ^ 3 r.cwisesqrt ()//sqrt (P) r.array (). sqrt () sqrt (P) r.array (). exp ()//exp (P) r.array (). log ()//log (P) R.cwisemax (p)// Max (R, PThe corresponding fetch large R.array (). Max (P.array ())//MAX (R, p) corresponds to taking the large r.cwisemin (p)//min (r, p) corresponding to the small R.array (). Min (P.array ())/             /min (R, p) corresponds to take small r.cwiseabs ()//ABS (P) absolute Value R.array (). ABS ()//ABS (P) absolute Value R.CWISEABS2 ()  ABS (p.^2) absolute value Square r.array (). ABS2 ()//ABS (P.^2) absolute value squared (R.array () < s). Select (P,q); (R < s?) P:Q) This is also the operation of a single element

Eigen Matrix Simplification

Reductions.
int r, C;
Eigen                  //Matlab
R.mincoeff ()              //min (R (:)) min
R.maxcoeff ()              /MAX (R (:)) Max
s = R.mincoeff ( &r, &c)    //[s, i] = min (R (:)); [R, C] = ind2sub (Size (R), i);
s = R.maxcoeff (&r, &c)    //[s, i] = max (R (:)); [R, C] = ind2sub (Size (R), i);
R.sum ()                   //SUM (R (:)) sum
r.colwise (). SUM ()         //SUM (r) column sum 1xN
r.rowwise (). SUM ()         //SUM (r, 2) or SUM (R ') ' line sum Nx1
r.prod ()                  //prod (R (:)) all product
r.colwise (). PROD ()        //prod (r) column product
r.rowwise (). Prod ()        //prod (r, 2) or prod (r ') ' line product
r.trace ()                 //Trace (R) trace
R.all ()                   //All (R (:)) and Operation
R.colwise (). All ()         /-All (R) and Operation
R.rowwise (). All () (         R, 2) and Operation
R.any ()                   /any (R (:)) or operation C33/>r.colwise (). any ()         or any (r) or Operation
R.rowwise (). any ()         //Any (R, 2) or operation

Eigen Matrix Point Multiplication

Dot products, norms, etc.
Eigen                  //Matlab
x.norm ()                  //Norm (x).    Die
X.squarednorm ()           //Dot (x, x)   squared and
X.dot (y)                  //dot (x, y)
x.cross (y)                /Cross (x, y) Requires #include <Eigen/Geometry>

Eigen Matrix Type Conversions

Type conversion
//Eigen                           //Matlab
a.cast<double> ();                  Double (A)
a.cast<float> ();                   Single (A)
a.cast<int> ();                     Int32 (A) downward rounding
a.real ();                          Real (A)
a.imag ();                          Imag (A)
//If the original type equals destination type, no work was done

Eigen solving linear equations Group Ax = b

Solve Ax = b. Result stored in x. matlab:x = A \ b.
x = A.LDLT (). Solve (b));  #include <eigen/cholesky>ldlt decomposition method is actually an improvement of the Cholesky decomposition method
x = A.llt (). Solve (b));  A sym. p.d.      #include <Eigen/Cholesky>
x = a.lu ()  . Solve (b));  Stable and fast. #include <Eigen/LU>
x = A.QR ()  . Solve (b));  No pivoting.     #include <Eigen/QR>
x = A.SVD (). Solve (b));  Stable, slowest. #include <Eigen/SVD>
/. LDLT (), MATRIXL () and. MATRIXD ()
//. LLT ()  . MATRIXL ()
/. Lu (),   MATRIXL () and. Matrixu ()/
. QR (), MATRIXQ () and   . MATRIXR ()
//. SVD ()  - >. Matrixu (),. Singularvalues (), and. MATRIXV ()

Eigen Matrix characteristic values

//Eigen//Matlab a.eigenvalues ();     Eig (a); characteristic value eigensolver<matrix3d> Eig (a);                [Vec val] = Eig (A) eig.eigenvalues ();               Diag (Val) is the same result as the front eig.eigenvectors (); eigenvector corresponding to VEC eigenvalues