Fix some formatting in quick ref. Add references to headers.

1 files changed, 138 insertions, 135 deletions

diff --git a/doc/AsciiQuickReference.txt b/doc/AsciiQuickReference.txt
index bcf402186..b868741f3 100644
--- a/doc/AsciiQuickReference.txt
+++ b/doc/AsciiQuickReference.txt
@@ -1,11 +1,17 @@
- Matrix<double, 3, 3> A;              // Fixed rows and cols. Same as Matrix3d.
- Matrix<double, 3, Dynamic> B;        // Fixed rows, dynamic cols.
- Matrix<double, Dynamic, Dynamic> C;  // Full dynamic. Same as MatrixXd.
- Matrix<double, 3, 3, RowMajor> E;    // Row major; default is column-major.
- Matrix3f P, Q, R;                    // 3x3 float matrix.
- Vector3f x, y, z;                    // 3x1 float matrix.
- RowVector3f a, b, c;                 // 1x3 float matrix.
- double s;
+// A simple quickref for Eigen. Add anything that's missing.
+// Main author: Keir Mierle
+
+#include <Eigen/Core>
+#include <Eigen/Array>
+
+Matrix<double, 3, 3> A;               // Fixed rows and cols. Same as Matrix3d.
+Matrix<double, 3, Dynamic> B;         // Fixed rows, dynamic cols.
+Matrix<double, Dynamic, Dynamic> C;   // Full dynamic. Same as MatrixXd.
+Matrix<double, 3, 3, RowMajor> E;     // Row major; default is column-major.
+Matrix3f P, Q, R;                     // 3x3 float matrix.
+Vector3f x, y, z;                     // 3x1 float matrix.
+RowVector3f a, b, c;                  // 1x3 float matrix.
+double s;                            
 
 // Basic usage
 // Eigen          // Matlab           // comments
@@ -15,145 +21,142 @@ C.cols()          // size(C)(2)       // number of columns
 x(i)              // x(i+1)           // Matlab is 1-based
 C(i,j)            // C(i+1,j+1)       //
 
- A.resize(4, 4);  // Runtime error if assertions are on.
- B.resize(4, 9);  // Runtime error if assertions are on.
- A.resize(3, 3);  // Ok; size didn't change.
- B.resize(3, 9);  // Ok; only dynamic cols changed.
-
- A << 1, 2, 3,    // Initialize A. The elements can also be
-      4, 5, 6,    // matrices, which are stacked along cols
-      7, 8, 9;    // and then the rows are stacked.
- B << A, A, A;    // B is three horizontally stacked A's.
- A.fill(10);      // Fill A with all 10's.
- A.setRandom();   // Fill A with uniform random numbers in (-1, 1).
+A.resize(4, 4);   // Runtime error if assertions are on.
+B.resize(4, 9);   // Runtime error if assertions are on.
+A.resize(3, 3);   // Ok; size didn't change.
+B.resize(3, 9);   // Ok; only dynamic cols changed.
+                  
+A << 1, 2, 3,     // Initialize A. The elements can also be
+     4, 5, 6,     // matrices, which are stacked along cols
+     7, 8, 9;     // and then the rows are stacked.
+B << A, A, A;     // B is three horizontally stacked A's.
+A.fill(10);       // Fill A with all 10's.
+A.setRandom();    // Fill A with uniform random numbers in (-1, 1).
                   // Requires #include <Eigen/Array>.
- A.setIdentity(); // Fill A with the identity.
+A.setIdentity();  // Fill A with the identity.
 
- // Matrix slicing and blocks. All expressions listed here are read/write.
- // Templated size versions are faster. Note that Matlab is 1-based (a size N
- // vector is x(1)...x(N)).
- // Eigen                          // Matlab
- x.start(n)                        // x(1:n)
- x.start<n>()                      // x(1:n)
- x.end(n)                          // N = rows(x); x(N - n: N)
- x.end<n>()                        // N = rows(x); x(N - n: N)
- x.segment(i, n)                   // x(i+1 : i+n)
- x.segment<n>(i)                   // x(i+1 : i+n)
- P.block(i, j, rows, cols)         // P(i+1 : i+rows, j+1 : j+cols)
- P.block<rows, cols>(i, j)         // P(i+1 : i+rows, j+1 : j+cols)
- P.corner(TopLeft, rows, cols)     // P(1:rows, 1:cols)
- P.corner(TopRight, rows, cols)    // [m n]=size(P); P(1:rows, n-cols+1:n)
- P.corner(BottomLeft, rows, cols)  // [m n]=size(P); P(m-rows+1:m, 1:cols)
- P.corner(BottomRight, rows, cols) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n)
- P.corner<rows,cols>(TopLeft)      // P(1:rows, 1:cols)
- P.corner<rows,cols>(TopRight)     // [m n]=size(P); P(1:rows, n-cols+1:n)
- P.corner<rows,cols>(BottomLeft)   // [m n]=size(P); P(m-rows+1:m, 1:cols)
- P.corner<rows,cols>(BottomRight)  // [m n]=size(P); P(m-rows+1:m, n-cols+1:n)
- P.minor(i, j)                     // Something nasty.
+// Matrix slicing and blocks. All expressions listed here are read/write.
+// Templated size versions are faster. Note that Matlab is 1-based (a size N
+// vector is x(1)...x(N)).
+// Eigen                           // Matlab
+x.start(n)                         // x(1:n)
+x.start<n>()                       // x(1:n)
+x.end(n)                           // N = rows(x); x(N - n: N)
+x.end<n>()                         // N = rows(x); x(N - n: N)
+x.segment(i, n)                    // x(i+1 : i+n)
+x.segment<n>(i)                    // x(i+1 : i+n)
+P.block(i, j, rows, cols)          // P(i+1 : i+rows, j+1 : j+cols)
+P.block<rows, cols>(i, j)          // P(i+1 : i+rows, j+1 : j+cols)
+P.corner(TopLeft, rows, cols)      // P(1:rows, 1:cols)
+P.corner(TopRight, rows, cols)     // [m n]=size(P); P(1:rows, n-cols+1:n)
+P.corner(BottomLeft, rows, cols)   // [m n]=size(P); P(m-rows+1:m, 1:cols)
+P.corner(BottomRight, rows, cols)  // [m n]=size(P); P(m-rows+1:m, n-cols+1:n)
+P.corner<rows,cols>(TopLeft)       // P(1:rows, 1:cols)
+P.corner<rows,cols>(TopRight)      // [m n]=size(P); P(1:rows, n-cols+1:n)
+P.corner<rows,cols>(BottomLeft)    // [m n]=size(P); P(m-rows+1:m, 1:cols)
+P.corner<rows,cols>(BottomRight)   // [m n]=size(P); P(m-rows+1:m, n-cols+1:n)
+P.minor(i, j)                      // Something nasty.
 
- // Of particular note is Eigen's swap function which is highly optimized.
- // Eigen                          // Matlab
- R.row(i) = P.col(j);              // R(i, :) = P(:, i)
- R.col(j1).swap(mat1.col(j2));     // R(:, [j1 j2]) = R(:, [j2, j1])
+// Of particular note is Eigen's swap function which is highly optimized.
+// Eigen                           // Matlab
+R.row(i) = P.col(j);               // R(i, :) = P(:, i)
+R.col(j1).swap(mat1.col(j2));      // R(:, [j1 j2]) = R(:, [j2, j1])
 
- // Views, transpose, etc; all read-write except for .adjoint().
- // Eigen                          // Matlab
- R.adjoint()                       // R'
- R.transpose()                     // R.' or conj(R')
- R.diagonal()                      // diag(R)
- x.asDiagonal()                    // diag(x)
+// Views, transpose, etc; all read-write except for .adjoint().
+// Eigen                           // Matlab
+R.adjoint()                        // R'
+R.transpose()                      // R.' or conj(R')
+R.diagonal()                       // diag(R)
+x.asDiagonal()                     // diag(x)
 
- // All the same as Matlab, but matlab doesn't have *= style operators.
- // 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;
+// All the same as Matlab, but matlab doesn't have *= style operators.
+// 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;
 
  // Vectorized operations on each element independently
  // (most require #include <Eigen/Array>)
- // Eigen                 // Matlab
- R = P.cwise() * Q;       // R = P .* Q
- R = P.cwise() / Q;       // R = P ./ Q
- R = P.cwise() + s;       // R = P + s
- R = P.cwise() - s;       // R = P - s
- R.cwise() += s;          // R = R + s
- R.cwise() -= s;          // R = R - s
- R.cwise() *= s;          // R = R * s
- R.cwise() /= s;          // R = R / s
- R.cwise() < Q;           // R < Q
- R.cwise() <= Q;          // R <= Q
- R.cwise().inverse();     // 1 ./ P
- R.cwise().sin()          // sin(P)
- R.cwise().cos()          // cos(P)
- R.cwise().pow(s)         // P .^ s
- R.cwise().square()       // P .^ 2
- R.cwise().cube()         // P .^ 3
- R.cwise().sqrt()         // sqrt(P)
- R.cwise().exp()          // exp(P)
- R.cwise().log()          // log(P)
- R.cwise().max(P)         // max(R, P)
- R.cwise().min(P)         // min(R, P)
- R.cwise().abs()          // abs(P)
- R.cwise().abs2()         // abs(P.^2)
- (R.cwise() < s).select(P,Q);  // (R < s ? P : Q)
+// Eigen                  // Matlab
+R = P.cwise() * Q;        // R = P .* Q
+R = P.cwise() / Q;        // R = P ./ Q
+R = P.cwise() + s;        // R = P + s
+R = P.cwise() - s;        // R = P - s
+R.cwise() += s;           // R = R + s
+R.cwise() -= s;           // R = R - s
+R.cwise() *= s;           // R = R * s
+R.cwise() /= s;           // R = R / s
+R.cwise() < Q;            // R < Q
+R.cwise() <= Q;           // R <= Q
+R.cwise().inverse();      // 1 ./ P
+R.cwise().sin()           // sin(P)
+R.cwise().cos()           // cos(P)
+R.cwise().pow(s)          // P .^ s
+R.cwise().square()        // P .^ 2
+R.cwise().cube()          // P .^ 3
+R.cwise().sqrt()          // sqrt(P)
+R.cwise().exp()           // exp(P)
+R.cwise().log()           // log(P)
+R.cwise().max(P)          // max(R, P)
+R.cwise().min(P)          // min(R, P)
+R.cwise().abs()           // abs(P)
+R.cwise().abs2()          // abs(P.^2)
+(R.cwise() < s).select(P,Q);  // (R < s ? P : Q)
 
- // Reductions.
- int r, c;
- // Eigen                 // Matlab
- R.minCoeff()             // min(R(:))
- R.maxCoeff()             // max(R(:))
- s = R.minCoeff(&r, &c)   // [aa, bb] = min(R); [cc, dd] = min(aa);
+// Reductions.
+int r, c;
+// Eigen                  // Matlab
+R.minCoeff()              // min(R(:))
+R.maxCoeff()              // max(R(:))
+s = R.minCoeff(&r, &c)    // [aa, bb] = min(R); [cc, dd] = min(aa);
                           // r = bb(dd); c = dd; s = cc
- s = R.maxCoeff(&r, &c)   // [aa, bb] = max(R); [cc, dd] = max(aa);
+s = R.maxCoeff(&r, &c)    // [aa, bb] = max(R); [cc, dd] = max(aa);
                           // row = bb(dd); col = dd; s = cc
- R.sum()                  // sum(R(:))
- R.colwise.sum()          // sum(R)
- R.rowwise.sum()          // sum(R, 2) or sum(R')'
- R.trace()                // trace(R)
- R.all()                  // all(R(:))
- R.colwise().all()        // all(R)
- R.rowwise().all()        // all(R, 2)
- R.any()                  // any(R(:))
- R.colwise().any()        // any(R)
- R.rowwise().any()        // any(R, 2)
-
- // Dot products, norms, etc.
- // Eigen                 // Matlab
- x.norm()                 // norm(x).    Note that norm(R) doesn't work in Eigen.
- x.squaredNorm()          // dot(x, x)   Note the equivalence is not true for complex
- x.dot(y)                 // dot(x, y)
- x.cross(y)               // cross(x, y) Requires #include <Eigen/Geometry>
+R.sum()                   // sum(R(:))
+R.colwise.sum()           // sum(R)
+R.rowwise.sum()           // sum(R, 2) or sum(R')'
+R.trace()                 // trace(R)
+R.all()                   // all(R(:))
+R.colwise().all()         // all(R)
+R.rowwise().all()         // all(R, 2)
+R.any()                   // any(R(:))
+R.colwise().any()         // any(R)
+R.rowwise().any()         // any(R, 2)
 
- // Eigen can map existing memory into Eigen matrices.
- float array[3];
- Map<Vector3f>(array, 3).fill(10);
- int data[4] = 1, 2, 3, 4;
- Matrix2i mat2x2(data);
- MatrixXi mat2x2 = Map<Matrix2i>(data);
- MatrixXi mat2x2 = Map<MatrixXi>(data, 2, 2);
+// Dot products, norms, etc.
+// Eigen                  // Matlab
+x.norm()                  // norm(x).    Note that norm(R) doesn't work in Eigen.
+x.squaredNorm()           // dot(x, x)   Note the equivalence is not true for complex
+x.dot(y)                  // dot(x, y)
+x.cross(y)                // cross(x, y) Requires #include <Eigen/Geometry>
 
- // Solve Ax = b. Result stored in x. Matlab: x = A \ b.
- bool solved;
- solved = A.ldlt().solve(b, &x));  // A symmetric p.s.d.
- solved = A.llt() .solve(b, &x));  // A symmetric p.d.
- solved = A.lu()  .solve(b, &x));  // Stable and fast.
- solved = A.qr()  .solve(b, &x));  // No pivoting.
- solved = A.svd() .solve(b, &x));  // Most stable, slowest.
- // .ldlt() -> .matrixL() and .matrixD()
- // .llt()  -> .matrixL()
- // .lu()   -> .matrixL() and .matrixU()
- // .qr()   -> .matrixQ() and .matrixR()
- // .svd()  -> .matrixU(), .singularValues(), and .matrixV()
+// Eigen can map existing memory into Eigen matrices.
+float array[3];
+Map<Vector3f>(array, 3).fill(10);
+int data[4] = 1, 2, 3, 4;
+Matrix2i mat2x2(data);
+MatrixXi mat2x2 = Map<Matrix2i>(data);
+MatrixXi mat2x2 = Map<MatrixXi>(data, 2, 2);
 
- // Eigenvalue problems
- // Eigen                          // Matlab
- A.eigenvalues();                  // eig(A);
- EigenSolver<Matrix3d> eig(A);     // [vec val] = eig(A)
- eig.eigenvalues();                // diag(val)
- eig.eigenvectors();               // vec
+// Solve Ax = b. Result stored in x. Matlab: x = A \ b.
+bool solved;
+solved = A.ldlt().solve(b, &x));  // A sym. p.s.d.    #include <Eigen/Cholesky>
+solved = A.llt() .solve(b, &x));  // A sym. p.d.      #include <Eigen/Cholesky>
+solved = A.lu()  .solve(b, &x));  // Stable and fast. #include <Eigen/LU>
+solved = A.qr()  .solve(b, &x));  // No pivoting.     #include <Eigen/QR>
+solved = A.svd() .solve(b, &x));  // Stable, slowest. #include <Eigen/SVD>
+// .ldlt() -> .matrixL() and .matrixD()
+// .llt()  -> .matrixL()
+// .lu()   -> .matrixL() and .matrixU()
+// .qr()   -> .matrixQ() and .matrixR()
+// .svd()  -> .matrixU(), .singularValues(), and .matrixV()
 
-__________
-Main author: Keir Mierle
\ No newline at end of file
+// Eigenvalue problems
+// Eigen                          // Matlab
+A.eigenvalues();                  // eig(A);
+EigenSolver<Matrix3d> eig(A);     // [vec val] = eig(A)
+eig.eigenvalues();                // diag(val)
+eig.eigenvectors();               // vec