gtsam 4.2.0
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Matrix.h
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1/* ----------------------------------------------------------------------------
2
3 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
4 * Atlanta, Georgia 30332-0415
5 * All Rights Reserved
6 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
7
8 * See LICENSE for the license information
9
10 * -------------------------------------------------------------------------- */
11
23// \callgraph
24
25#pragma once
26
28#include <gtsam/base/Vector.h>
29#include <boost/tuple/tuple.hpp>
30
31#include <vector>
32
38namespace gtsam {
39
40typedef Eigen::MatrixXd Matrix;
41typedef Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> MatrixRowMajor;
42
43// Create handy typedefs and constants for square-size matrices
44// MatrixMN, MatrixN = MatrixNN, I_NxN, and Z_NxN, for M,N=1..9
45#define GTSAM_MAKE_MATRIX_DEFS(N) \
46using Matrix##N = Eigen::Matrix<double, N, N>; \
47using Matrix1##N = Eigen::Matrix<double, 1, N>; \
48using Matrix2##N = Eigen::Matrix<double, 2, N>; \
49using Matrix3##N = Eigen::Matrix<double, 3, N>; \
50using Matrix4##N = Eigen::Matrix<double, 4, N>; \
51using Matrix5##N = Eigen::Matrix<double, 5, N>; \
52using Matrix6##N = Eigen::Matrix<double, 6, N>; \
53using Matrix7##N = Eigen::Matrix<double, 7, N>; \
54using Matrix8##N = Eigen::Matrix<double, 8, N>; \
55using Matrix9##N = Eigen::Matrix<double, 9, N>; \
56static const Eigen::MatrixBase<Matrix##N>::IdentityReturnType I_##N##x##N = Matrix##N::Identity(); \
57static const Eigen::MatrixBase<Matrix##N>::ConstantReturnType Z_##N##x##N = Matrix##N::Zero();
58
59GTSAM_MAKE_MATRIX_DEFS(1)
60GTSAM_MAKE_MATRIX_DEFS(2)
61GTSAM_MAKE_MATRIX_DEFS(3)
62GTSAM_MAKE_MATRIX_DEFS(4)
63GTSAM_MAKE_MATRIX_DEFS(5)
64GTSAM_MAKE_MATRIX_DEFS(6)
65GTSAM_MAKE_MATRIX_DEFS(7)
66GTSAM_MAKE_MATRIX_DEFS(8)
67GTSAM_MAKE_MATRIX_DEFS(9)
68
69// Matrix expressions for accessing parts of matrices
70typedef Eigen::Block<Matrix> SubMatrix;
71typedef Eigen::Block<const Matrix> ConstSubMatrix;
72
73// Matrix formatting arguments when printing.
74// Akin to Matlab style.
75const Eigen::IOFormat& matlabFormat();
76
80template <class MATRIX>
81bool equal_with_abs_tol(const Eigen::DenseBase<MATRIX>& A, const Eigen::DenseBase<MATRIX>& B, double tol = 1e-9) {
82
83 const size_t n1 = A.cols(), m1 = A.rows();
84 const size_t n2 = B.cols(), m2 = B.rows();
85
86 if(m1!=m2 || n1!=n2) return false;
87
88 for(size_t i=0; i<m1; i++)
89 for(size_t j=0; j<n1; j++) {
90 if(!fpEqual(A(i,j), B(i,j), tol, false)) {
91 return false;
92 }
93 }
94 return true;
95}
96
100inline bool operator==(const Matrix& A, const Matrix& B) {
101 return equal_with_abs_tol(A,B,1e-9);
102}
103
107inline bool operator!=(const Matrix& A, const Matrix& B) {
108 return !(A==B);
109 }
110
114GTSAM_EXPORT bool assert_equal(const Matrix& A, const Matrix& B, double tol = 1e-9);
115
119GTSAM_EXPORT bool assert_inequal(const Matrix& A, const Matrix& B, double tol = 1e-9);
120
124GTSAM_EXPORT bool assert_equal(const std::list<Matrix>& As, const std::list<Matrix>& Bs, double tol = 1e-9);
125
129GTSAM_EXPORT bool linear_independent(const Matrix& A, const Matrix& B, double tol = 1e-9);
130
134GTSAM_EXPORT bool linear_dependent(const Matrix& A, const Matrix& B, double tol = 1e-9);
135
140GTSAM_EXPORT Vector operator^(const Matrix& A, const Vector & v);
141
143template<class MATRIX>
144inline MATRIX prod(const MATRIX& A, const MATRIX&B) {
145 MATRIX result = A * B;
146 return result;
147}
148
152GTSAM_EXPORT void print(const Matrix& A, const std::string& s, std::ostream& stream);
153
157GTSAM_EXPORT void print(const Matrix& A, const std::string& s = "");
158
162GTSAM_EXPORT void save(const Matrix& A, const std::string &s, const std::string& filename);
163
169GTSAM_EXPORT std::istream& operator>>(std::istream& inputStream, Matrix& destinationMatrix);
170
180template<class MATRIX>
181Eigen::Block<const MATRIX> sub(const MATRIX& A, size_t i1, size_t i2, size_t j1, size_t j2) {
182 size_t m=i2-i1, n=j2-j1;
183 return A.block(i1,j1,m,n);
184}
185
194template <typename Derived1, typename Derived2>
195void insertSub(Eigen::MatrixBase<Derived1>& fullMatrix, const Eigen::MatrixBase<Derived2>& subMatrix, size_t i, size_t j) {
196 fullMatrix.block(i, j, subMatrix.rows(), subMatrix.cols()) = subMatrix;
197}
198
202GTSAM_EXPORT Matrix diag(const std::vector<Matrix>& Hs);
203
210template<class MATRIX>
211const typename MATRIX::ConstColXpr column(const MATRIX& A, size_t j) {
212 return A.col(j);
213}
214
221template<class MATRIX>
222const typename MATRIX::ConstRowXpr row(const MATRIX& A, size_t j) {
223 return A.row(j);
224}
225
231template<class MATRIX>
232void zeroBelowDiagonal(MATRIX& A, size_t cols=0) {
233 const size_t m = A.rows(), n = A.cols();
234 const size_t k = (cols) ? std::min(cols, std::min(m,n)) : std::min(m,n);
235 for (size_t j=0; j<k; ++j)
236 A.col(j).segment(j+1, m-(j+1)).setZero();
237}
238
242inline Matrix trans(const Matrix& A) { return A.transpose(); }
243
245template <int OutM, int OutN, int OutOptions, int InM, int InN, int InOptions>
246struct Reshape {
247 //TODO replace this with Eigen's reshape function as soon as available. (There is a PR already pending : https://bitbucket.org/eigen/eigen/pull-request/41/reshape/diff)
248 typedef Eigen::Map<const Eigen::Matrix<double, OutM, OutN, OutOptions> > ReshapedType;
249 static inline ReshapedType reshape(const Eigen::Matrix<double, InM, InN, InOptions> & in) {
250 return in.data();
251 }
252};
253
255template <int M, int InOptions>
256struct Reshape<M, M, InOptions, M, M, InOptions> {
257 typedef const Eigen::Matrix<double, M, M, InOptions> & ReshapedType;
258 static inline ReshapedType reshape(const Eigen::Matrix<double, M, M, InOptions> & in) {
259 return in;
260 }
261};
262
264template <int M, int N, int InOptions>
265struct Reshape<M, N, InOptions, M, N, InOptions> {
266 typedef const Eigen::Matrix<double, M, N, InOptions> & ReshapedType;
267 static inline ReshapedType reshape(const Eigen::Matrix<double, M, N, InOptions> & in) {
268 return in;
269 }
270};
271
273template <int M, int N, int InOptions>
274struct Reshape<N, M, InOptions, M, N, InOptions> {
275 typedef typename Eigen::Matrix<double, M, N, InOptions>::ConstTransposeReturnType ReshapedType;
276 static inline ReshapedType reshape(const Eigen::Matrix<double, M, N, InOptions> & in) {
277 return in.transpose();
278 }
279};
280
281template <int OutM, int OutN, int OutOptions, int InM, int InN, int InOptions>
282inline typename Reshape<OutM, OutN, OutOptions, InM, InN, InOptions>::ReshapedType reshape(const Eigen::Matrix<double, InM, InN, InOptions> & m){
283 BOOST_STATIC_ASSERT(InM * InN == OutM * OutN);
285}
286
293GTSAM_EXPORT std::pair<Matrix,Matrix> qr(const Matrix& A);
294
300GTSAM_EXPORT void inplace_QR(Matrix& A);
301
310GTSAM_EXPORT std::list<boost::tuple<Vector, double, double> >
311weighted_eliminate(Matrix& A, Vector& b, const Vector& sigmas);
312
320GTSAM_EXPORT void householder_(Matrix& A, size_t k, bool copy_vectors=true);
321
328GTSAM_EXPORT void householder(Matrix& A, size_t k);
329
337GTSAM_EXPORT Vector backSubstituteUpper(const Matrix& U, const Vector& b, bool unit=false);
338
346//TODO: is this function necessary? it isn't used
347GTSAM_EXPORT Vector backSubstituteUpper(const Vector& b, const Matrix& U, bool unit=false);
348
356GTSAM_EXPORT Vector backSubstituteLower(const Matrix& L, const Vector& b, bool unit=false);
357
364GTSAM_EXPORT Matrix stack(size_t nrMatrices, ...);
365GTSAM_EXPORT Matrix stack(const std::vector<Matrix>& blocks);
366
377GTSAM_EXPORT Matrix collect(const std::vector<const Matrix *>& matrices, size_t m = 0, size_t n = 0);
378GTSAM_EXPORT Matrix collect(size_t nrMatrices, ...);
379
386GTSAM_EXPORT void vector_scale_inplace(const Vector& v, Matrix& A, bool inf_mask = false); // row
387GTSAM_EXPORT Matrix vector_scale(const Vector& v, const Matrix& A, bool inf_mask = false); // row
388GTSAM_EXPORT Matrix vector_scale(const Matrix& A, const Vector& v, bool inf_mask = false); // column
389
401inline Matrix3 skewSymmetric(double wx, double wy, double wz) {
402 return (Matrix3() << 0.0, -wz, +wy, +wz, 0.0, -wx, -wy, +wx, 0.0).finished();
403}
404
405template <class Derived>
406inline Matrix3 skewSymmetric(const Eigen::MatrixBase<Derived>& w) {
407 return skewSymmetric(w(0), w(1), w(2));
408}
409
411GTSAM_EXPORT Matrix inverse_square_root(const Matrix& A);
412
414GTSAM_EXPORT Matrix cholesky_inverse(const Matrix &A);
415
428GTSAM_EXPORT void svd(const Matrix& A, Matrix& U, Vector& S, Matrix& V);
429
437GTSAM_EXPORT boost::tuple<int, double, Vector>
438DLT(const Matrix& A, double rank_tol = 1e-9);
439
445GTSAM_EXPORT Matrix expm(const Matrix& A, size_t K=7);
446
447std::string formatMatrixIndented(const std::string& label, const Matrix& matrix, bool makeVectorHorizontal = false);
448
455template <int N>
457 typedef Eigen::Matrix<double, N, 1> VectorN;
458 typedef Eigen::Matrix<double, N, N> MatrixN;
459
461 VectorN operator()(const MatrixN& A, const VectorN& b,
462 OptionalJacobian<N, N* N> H1 = boost::none,
463 OptionalJacobian<N, N> H2 = boost::none) const {
464 const MatrixN invA = A.inverse();
465 const VectorN c = invA * b;
466 // The derivative in A is just -[c[0]*invA c[1]*invA ... c[N-1]*invA]
467 if (H1)
468 for (size_t j = 0; j < N; j++)
469 H1->template middleCols<N>(N * j) = -c[j] * invA;
470 // The derivative in b is easy, as invA*b is just a linear map:
471 if (H2) *H2 = invA;
472 return c;
473 }
474};
475
481template <typename T, int N>
483 enum { M = traits<T>::dimension };
484 typedef Eigen::Matrix<double, N, 1> VectorN;
485 typedef Eigen::Matrix<double, N, N> MatrixN;
486
487 // The function phi should calculate f(a)*b, with derivatives in a and b.
488 // Naturally, the derivative in b is f(a).
489 typedef std::function<VectorN(
490 const T&, const VectorN&, OptionalJacobian<N, M>, OptionalJacobian<N, N>)>
491 Operator;
492
494 MultiplyWithInverseFunction(const Operator& phi) : phi_(phi) {}
495
497 VectorN operator()(const T& a, const VectorN& b,
498 OptionalJacobian<N, M> H1 = boost::none,
499 OptionalJacobian<N, N> H2 = boost::none) const {
500 MatrixN A;
501 phi_(a, b, boost::none, A); // get A = f(a) by calling f once
502 const MatrixN invA = A.inverse();
503 const VectorN c = invA * b;
504
505 if (H1) {
506 Eigen::Matrix<double, N, M> H;
507 phi_(a, c, H, boost::none); // get derivative H of forward mapping
508 *H1 = -invA* H;
509 }
510 if (H2) *H2 = invA;
511 return c;
512 }
513
514 private:
515 const Operator phi_;
516};
517
518GTSAM_EXPORT Matrix LLt(const Matrix& A);
519
520GTSAM_EXPORT Matrix RtR(const Matrix& A);
521
522GTSAM_EXPORT Vector columnNormSquare(const Matrix &A);
523} // namespace gtsam
Special class for optional Jacobian arguments.
typedef and functions to augment Eigen's VectorXd
Global functions in a separate testing namespace.
Definition chartTesting.h:28
Vector backSubstituteLower(const Matrix &L, const Vector &b, bool unit)
backSubstitute L*x=b
Definition Matrix.cpp:367
Vector operator^(const Matrix &A, const Vector &v)
overload ^ for trans(A)*v We transpose the vectors for speed.
Definition Matrix.cpp:131
void vector_scale_inplace(const Vector &v, Matrix &A, bool inf_mask)
scales a matrix row or column by the values in a vector Arguments (Matrix, Vector) scales the columns...
Definition Matrix.cpp:482
const MATRIX::ConstRowXpr row(const MATRIX &A, size_t j)
Extracts a row view from a matrix that avoids a copy.
Definition Matrix.h:222
T expm(const Vector &x, int K=7)
Exponential map given exponential coordinates class T needs a wedge<> function and a constructor from...
Definition Lie.h:317
void save(const Matrix &A, const string &s, const string &filename)
save a matrix to file, which can be loaded by matlab
Definition Matrix.cpp:167
bool assert_equal(const Matrix &expected, const Matrix &actual, double tol)
equals with an tolerance, prints out message if unequal
Definition Matrix.cpp:43
bool linear_dependent(const Matrix &A, const Matrix &B, double tol)
check whether the rows of two matrices are linear dependent
Definition Matrix.cpp:117
void print(const Matrix &A, const string &s, ostream &stream)
print without optional string, must specify cout yourself
Definition Matrix.cpp:156
const MATRIX::ConstColXpr column(const MATRIX &A, size_t j)
Extracts a column view from a matrix that avoids a copy.
Definition Matrix.h:211
void zeroBelowDiagonal(MATRIX &A, size_t cols=0)
Zeros all of the elements below the diagonal of a matrix, in place.
Definition Matrix.h:232
list< boost::tuple< Vector, double, double > > weighted_eliminate(Matrix &A, Vector &b, const Vector &sigmas)
Imperative algorithm for in-place full elimination with weights and constraint handling.
Definition Matrix.cpp:273
Vector backSubstituteUpper(const Matrix &U, const Vector &b, bool unit)
backSubstitute U*x=b
Definition Matrix.cpp:377
bool assert_inequal(const Matrix &A, const Matrix &B, double tol)
inequals with an tolerance, prints out message if within tolerance
Definition Matrix.cpp:63
void householder(Matrix &A, size_t k)
Householder tranformation, zeros below diagonal.
Definition Matrix.cpp:354
istream & operator>>(istream &inputStream, Matrix &destinationMatrix)
Read a matrix from an input stream, such as a file.
Definition Matrix.cpp:174
void inplace_QR(Matrix &A)
QR factorization using Eigen's internal block QR algorithm.
Definition Matrix.cpp:636
void svd(const Matrix &A, Matrix &U, Vector &S, Matrix &V)
SVD computes economy SVD A=U*S*V'.
Definition Matrix.cpp:560
Matrix3 skewSymmetric(double wx, double wy, double wz)
skew symmetric matrix returns this: 0 -wz wy wz 0 -wx -wy wx 0
Definition Matrix.h:401
Eigen::Block< const MATRIX > sub(const MATRIX &A, size_t i1, size_t i2, size_t j1, size_t j2)
extract submatrix, slice semantics, i.e.
Definition Matrix.h:181
Matrix trans(const Matrix &A)
static transpose function, just calls Eigen transpose member function
Definition Matrix.h:242
bool operator!=(const Matrix &A, const Matrix &B)
inequality
Definition Matrix.h:107
boost::tuple< int, double, Vector > DLT(const Matrix &A, double rank_tol)
Direct linear transform algorithm that calls svd to find a vector v that minimizes the algebraic erro...
Definition Matrix.cpp:568
Matrix cholesky_inverse(const Matrix &A)
Return the inverse of a S.P.D.
Definition Matrix.cpp:539
MATRIX prod(const MATRIX &A, const MATRIX &B)
products using old-style format to improve compatibility
Definition Matrix.h:144
void householder_(Matrix &A, size_t k, bool copy_vectors)
Imperative version of Householder QR factorization, Golub & Van Loan p 224 version with Householder v...
Definition Matrix.cpp:327
void insertSub(Eigen::MatrixBase< Derived1 > &fullMatrix, const Eigen::MatrixBase< Derived2 > &subMatrix, size_t i, size_t j)
insert a submatrix IN PLACE at a specified location in a larger matrix NOTE: there is no size checkin...
Definition Matrix.h:195
Matrix collect(const std::vector< const Matrix * > &matrices, size_t m, size_t n)
create a matrix by concatenating Given a set of matrices: A1, A2, A3... If all matrices have the same...
Definition Matrix.cpp:443
bool linear_independent(const Matrix &A, const Matrix &B, double tol)
check whether the rows of two matrices are linear independent
Definition Matrix.cpp:103
bool fpEqual(double a, double b, double tol, bool check_relative_also)
Ensure we are not including a different version of Eigen in user code than while compiling gtsam,...
Definition Vector.cpp:42
pair< Matrix, Matrix > qr(const Matrix &A)
Householder QR factorization, Golub & Van Loan p 224, explicit version
Definition Matrix.cpp:235
Matrix diag(const std::vector< Matrix > &Hs)
Create a matrix with submatrices along its diagonal.
Definition Matrix.cpp:207
bool equal_with_abs_tol(const Eigen::DenseBase< MATRIX > &A, const Eigen::DenseBase< MATRIX > &B, double tol=1e-9)
equals with a tolerance
Definition Matrix.h:81
bool operator==(const Matrix &A, const Matrix &B)
equality is just equal_with_abs_tol 1e-9
Definition Matrix.h:100
Matrix inverse_square_root(const Matrix &A)
Use Cholesky to calculate inverse square root of a matrix.
Definition Matrix.cpp:552
A manifold defines a space in which there is a notion of a linear tangent space that can be centered ...
Definition concepts.h:30
Reshape functor.
Definition Matrix.h:246
Functor that implements multiplication of a vector b with the inverse of a matrix A.
Definition Matrix.h:456
VectorN operator()(const MatrixN &A, const VectorN &b, OptionalJacobian< N, N *N > H1=boost::none, OptionalJacobian< N, N > H2=boost::none) const
A.inverse() * b, with optional derivatives.
Definition Matrix.h:461
Functor that implements multiplication with the inverse of a matrix, itself the result of a function ...
Definition Matrix.h:482
VectorN operator()(const T &a, const VectorN &b, OptionalJacobian< N, M > H1=boost::none, OptionalJacobian< N, N > H2=boost::none) const
f(a).inverse() * b, with optional derivatives
Definition Matrix.h:497
MultiplyWithInverseFunction(const Operator &phi)
Construct with function as explained above.
Definition Matrix.h:494
OptionalJacobian is an Eigen::Ref like class that can take be constructed using either a fixed size o...
Definition OptionalJacobian.h:41