cholesky: support solve with input matrices

include/eigenpy/decompositions/LDLT.hpp

 /*
- * Copyright 2020 INRIA
+ * Copyright 2020-2021 INRIA
  */
 
 #ifndef __eigenpy_decomposition_ldlt_hpp__
@@ -23,7 +23,8 @@ namespace eigenpy
     typedef _MatrixType MatrixType;
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
-    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,1,MatrixType::Options> VectorType;
+    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,1,MatrixType::Options> VectorXs;
+    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic,MatrixType::Options> MatrixXs;
     typedef Eigen::LDLT<MatrixType> Solver;
     
     template<class PyClass>
@@ -55,7 +56,7 @@ namespace eigenpy
            "Returns the LDLT decomposition matrix.",
            bp::return_internal_reference<>())
       
-      .def("rankUpdate",(Solver & (Solver::*)(const Eigen::MatrixBase<VectorType> &, const RealScalar &))&Solver::template rankUpdate<VectorType>,
+      .def("rankUpdate",(Solver & (Solver::*)(const Eigen::MatrixBase<VectorXs> &, const RealScalar &))&Solver::template rankUpdate<VectorXs>,
            bp::args("self","vector","sigma"),
            bp::return_self<>())
     
@@ -78,8 +79,10 @@ namespace eigenpy
 #endif
       .def("reconstructedMatrix",&Solver::reconstructedMatrix,bp::arg("self"),
            "Returns the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose.")
-      .def("solve",&solve<VectorType>,bp::args("self","b"),
+      .def("solve",&solve<VectorXs>,bp::args("self","b"),
            "Returns the solution x of A x = b using the current decomposition of A.")
+      .def("solve",&solve<MatrixXs>,bp::args("self","B"),
+           "Returns the solution X of A X = B using the current decomposition of A where B is a right hand side matrix.")
       
       .def("setZero",&Solver::setZero,bp::arg("self"),
            "Clear any existing decomposition.")
@@ -107,7 +110,7 @@ namespace eigenpy
     
     static MatrixType matrixL(const Solver & self) { return self.matrixL(); }
     static MatrixType matrixU(const Solver & self) { return self.matrixU(); }
-    static VectorType vectorD(const Solver & self) { return self.vectorD(); }
+    static VectorXs vectorD(const Solver & self) { return self.vectorD(); }
     
     static MatrixType transpositionsP(const Solver & self)
     {
@@ -115,8 +118,8 @@ namespace eigenpy
                                                            self.matrixL().rows());
     }
     
-    template<typename VectorType>
-    static VectorType solve(const Solver & self, const VectorType & vec)
+    template<typename MatrixOrVector>
+    static MatrixOrVector solve(const Solver & self, const MatrixOrVector & vec)
     {
       return self.solve(vec);
     }

include/eigenpy/decompositions/LLT.hpp

 /*
- * Copyright 2020 INRIA
+ * Copyright 2020-2021 INRIA
  */
 
 #ifndef __eigenpy_decomposition_llt_hpp__
@@ -23,7 +23,8 @@ namespace eigenpy
     typedef _MatrixType MatrixType;
     typedef typename MatrixType::Scalar Scalar;
     typedef typename MatrixType::RealScalar RealScalar;
-    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,1,MatrixType::Options> VectorType;
+    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,1,MatrixType::Options> VectorXs;
+    typedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic,MatrixType::Options> MatrixXs;
     typedef Eigen::LLT<MatrixType> Solver;
     
     template<class PyClass>
@@ -46,10 +47,10 @@ namespace eigenpy
            bp::return_internal_reference<>())
 
 #if EIGEN_VERSION_AT_LEAST(3,3,90)
-      .def("rankUpdate",(Solver& (Solver::*)(const VectorType &, const RealScalar &))&Solver::template rankUpdate<VectorType>,
+      .def("rankUpdate",(Solver& (Solver::*)(const VectorXs &, const RealScalar &))&Solver::template rankUpdate<VectorXs>,
            bp::args("self","vector","sigma"), bp::return_self<>())
 #else
-      .def("rankUpdate",(Solver (Solver::*)(const VectorType &, const RealScalar &))&Solver::template rankUpdate<VectorType>,
+      .def("rankUpdate",(Solver (Solver::*)(const VectorXs &, const RealScalar &))&Solver::template rankUpdate<VectorXs>,
            bp::args("self","vector","sigma"))
 #endif
       
@@ -72,8 +73,10 @@ namespace eigenpy
 #endif
       .def("reconstructedMatrix",&Solver::reconstructedMatrix,bp::arg("self"),
            "Returns the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose.")
-      .def("solve",&solve<VectorType>,bp::args("self","b"),
+      .def("solve",&solve<VectorXs>,bp::args("self","b"),
            "Returns the solution x of A x = b using the current decomposition of A.")
+      .def("solve",&solve<MatrixXs>,bp::args("self","B"),
+           "Returns the solution X of A X = B using the current decomposition of A where B is a right hand side matrix.")
       ;
     }
     
@@ -99,8 +102,8 @@ namespace eigenpy
     static MatrixType matrixL(const Solver & self) { return self.matrixL(); }
     static MatrixType matrixU(const Solver & self) { return self.matrixU(); }
     
-    template<typename VectorType>
-    static VectorType solve(const Solver & self, const VectorType & vec)
+    template<typename MatrixOrVector>
+    static MatrixOrVector solve(const Solver & self, const MatrixOrVector & vec)
     {
       return self.solve(vec);
     }

unittest/python/test_LDLT.py

 import eigenpy
-eigenpy.switchToNumpyArray()
 
 import numpy as np
 import numpy.linalg as la
@@ -16,3 +15,9 @@ D = ldlt.vectorD()
 P = ldlt.transpositionsP() 
 
 assert eigenpy.is_approx(np.transpose(P).dot(L.dot(np.diag(D).dot(np.transpose(L).dot(P)))),A)
+
+X = np.random.rand(dim,20)
+B = A.dot(X)
+X_est = ldlt.solve(B)
+assert eigenpy.is_approx(X,X_est)
+assert eigenpy.is_approx(A.dot(X_est),B)

unittest/python/test_LLT.py

 import eigenpy
-eigenpy.switchToNumpyArray()
 
 import numpy as np
 import numpy.linalg as la
@@ -12,5 +11,10 @@ A = (A + A.T)*0.5 + np.diag(10. + np.random.rand(dim))
 llt = eigenpy.LLT(A)
 
 L = llt.matrixL() 
-
 assert eigenpy.is_approx(L.dot(np.transpose(L)),A)
+
+X = np.random.rand(dim,20)
+B = A.dot(X)
+X_est = llt.solve(B)
+assert eigenpy.is_approx(X,X_est)
+assert eigenpy.is_approx(A.dot(X_est),B)