Schur

DESCRIPTION

@@ -1,14 +1,15 @@
 Package: EigenR
 Type: Package
 Title: Complex Matrix Algebra with 'Eigen'
-Version: 1.2.3
+Version: 1.2.3.9000
 Author: Stéphane Laurent
 Maintainer: Stéphane Laurent <laurent_step@outlook.fr>
 Description: Matrix algebra using the 'Eigen' C++ library: determinant, rank, inverse, pseudo-inverse, kernel and image, QR decomposition, Cholesky decomposition, linear least-squares problems. Also provides matrix functions such as exponential, logarithm, power, sine and cosine. Complex matrices are supported.
 License: GPL-3
 Imports: Rcpp (>= 1.0.5)
-LinkingTo: Rcpp, RcppEigen
-RoxygenNote: 7.1.2
+LinkingTo: Rcpp, RcppEigen (>= 0.3.4.0.0)
+RoxygenNote: 7.3.1
 Encoding: UTF-8
 URL: https://github.com/stla/EigenR
 BugReports: https://github.com/stla/EigenR/issues
+SystemRequirements: C++ 17

NAMESPACE

@@ -5,6 +5,7 @@ export(Eigen_QR)
 export(Eigen_UtDU)
 export(Eigen_absdet)
 export(Eigen_chol)
+export(Eigen_complexSchur)
 export(Eigen_cos)
 export(Eigen_cosh)
 export(Eigen_det)
@@ -22,6 +23,8 @@ export(Eigen_pinverse)
 export(Eigen_pow)
 export(Eigen_range)
 export(Eigen_rank)
+export(Eigen_realQZ)
+export(Eigen_realSchur)
 export(Eigen_sin)
 export(Eigen_sinh)
 export(Eigen_sqrt)

NEWS.md

@@ -1,7 +1,13 @@
+# EigenR 1.3.0
+
+New features: Schur decomposition, QZ decomposition (only for real matrices).
+
+
 # EigenR 1.2.3
 
 Fixed a mistake in `Eigen_UtDU`.
 
+
 # EigenR 1.2.2
 
 No change for the user.

R/EigenR.R

@@ -681,6 +681,7 @@ Eigen_sqrt <- function(M){
 #'
 #' @return A list with the \code{Q}, \code{Z}, \code{S} and \code{T} matrices.
 #' @export
+#' @details See \href{https://eigen.tuxfamily.org/dox/classEigen_1_1RealQZ.html}{Eigen::RealQZ}.
 #'
 #' @examples
 #' library(EigenR)
@@ -713,11 +714,15 @@ Eigen_realQZ <- function(A, B) {
 #'
 #' @return A list with the \code{T} and \code{U} matrices.
 #' @export
+#' @details See \href{https://eigen.tuxfamily.org/dox/classEigen_1_1RealSchur.html}{Eigen::RealSchur}.
 #'
 #' @examples
 #' library(EigenR)
 #' M <- cbind(c(3, 2, 3), c(1, 1, 1), c(5, 0, -2))
 #' schur <- Eigen_realSchur(M)
+#' T <- schur$T
+#' U <- schur$U
+#' M - U %*% T %*% t(U)
 Eigen_realSchur <- function(M) {
   stopifnot(isSquareMatrix(M), isReal(M))
   EigenR_realSchur(M)
@@ -731,11 +736,15 @@ Eigen_realSchur <- function(M) {
 #'
 #' @return A list with the \code{T} and \code{U} matrices.
 #' @export
+#' @details See \href{https://eigen.tuxfamily.org/dox/classEigen_1_1ComplexSchur.html}{Eigen::ComplexSchur}.
 #'
 #' @examples
 #' library(EigenR)
 #' M <- cbind(c(3, 2i, 1+3i), c(1, 1i, 1), c(5, 0, -2i))
 #' schur <- Eigen_complexSchur(M)
+#' T <- schur$T
+#' U <- schur$U
+#' M - U %*% T %*% t(Conj(U))
 Eigen_complexSchur <- function(M) {
   stopifnot(isSquareMatrix(M), isRealOrComplex(M))
   schur <- EigenR_complexSchur(Re(M), Im(M))

R/RcppExports.R

@@ -209,6 +209,18 @@ EigenR_rank_cplx <- function(Re, Im) {
     .Call('_EigenR_EigenR_rank_cplx', PACKAGE = 'EigenR', Re, Im)
 }
 
+EigenR_realQZ <- function(A, B) {
+    .Call('_EigenR_EigenR_realQZ', PACKAGE = 'EigenR', A, B)
+}
+
+EigenR_realSchur <- function(M) {
+    .Call('_EigenR_EigenR_realSchur', PACKAGE = 'EigenR', M)
+}
+
+EigenR_complexSchur <- function(Re, Im) {
+    .Call('_EigenR_EigenR_complexSchur', PACKAGE = 'EigenR', Re, Im)
+}
+
 EigenR_isInjective_real <- function(M) {
     .Call('_EigenR_EigenR_isInjective_real', PACKAGE = 'EigenR', M)
 }

src/Makevars

@@ -4,4 +4,4 @@
 
 ## With R 3.1.0 or later, you can uncomment the following line to tell R to 
 ## enable compilation with C++11 (or even C++14) where available
-CXX_STD = CXX11
+CXX_STD = CXX17

src/Makevars.win

@@ -4,4 +4,4 @@
 
 ## With R 3.1.0 or later, you can uncomment the following line to tell R to 
 ## enable compilation with C++11 (or even C++14) where available
-CXX_STD = CXX11
+CXX_STD = CXX17

src/RcppExports.cpp

@@ -630,6 +630,41 @@ BEGIN_RCPP
     return rcpp_result_gen;
 END_RCPP
 }
+// EigenR_realQZ
+Rcpp::List EigenR_realQZ(const Eigen::MatrixXd& A, const Eigen::MatrixXd& B);
+RcppExport SEXP _EigenR_EigenR_realQZ(SEXP ASEXP, SEXP BSEXP) {
+BEGIN_RCPP
+    Rcpp::RObject rcpp_result_gen;
+    Rcpp::RNGScope rcpp_rngScope_gen;
+    Rcpp::traits::input_parameter< const Eigen::MatrixXd& >::type A(ASEXP);
+    Rcpp::traits::input_parameter< const Eigen::MatrixXd& >::type B(BSEXP);
+    rcpp_result_gen = Rcpp::wrap(EigenR_realQZ(A, B));
+    return rcpp_result_gen;
+END_RCPP
+}
+// EigenR_realSchur
+Rcpp::List EigenR_realSchur(const Eigen::MatrixXd& M);
+RcppExport SEXP _EigenR_EigenR_realSchur(SEXP MSEXP) {
+BEGIN_RCPP
+    Rcpp::RObject rcpp_result_gen;
+    Rcpp::RNGScope rcpp_rngScope_gen;
+    Rcpp::traits::input_parameter< const Eigen::MatrixXd& >::type M(MSEXP);
+    rcpp_result_gen = Rcpp::wrap(EigenR_realSchur(M));
+    return rcpp_result_gen;
+END_RCPP
+}
+// EigenR_complexSchur
+Rcpp::List EigenR_complexSchur(const Eigen::MatrixXd& Re, const Eigen::MatrixXd& Im);
+RcppExport SEXP _EigenR_EigenR_complexSchur(SEXP ReSEXP, SEXP ImSEXP) {
+BEGIN_RCPP
+    Rcpp::RObject rcpp_result_gen;
+    Rcpp::RNGScope rcpp_rngScope_gen;
+    Rcpp::traits::input_parameter< const Eigen::MatrixXd& >::type Re(ReSEXP);
+    Rcpp::traits::input_parameter< const Eigen::MatrixXd& >::type Im(ImSEXP);
+    rcpp_result_gen = Rcpp::wrap(EigenR_complexSchur(Re, Im));
+    return rcpp_result_gen;
+END_RCPP
+}
 // EigenR_isInjective_real
 bool EigenR_isInjective_real(const Eigen::MatrixXd& M);
 RcppExport SEXP _EigenR_EigenR_isInjective_real(SEXP MSEXP) {
@@ -753,6 +788,9 @@ static const R_CallMethodDef CallEntries[] = {
     {"_EigenR_EigenR_QR_cplx", (DL_FUNC) &_EigenR_EigenR_QR_cplx, 2},
     {"_EigenR_EigenR_rank_real", (DL_FUNC) &_EigenR_EigenR_rank_real, 1},
     {"_EigenR_EigenR_rank_cplx", (DL_FUNC) &_EigenR_EigenR_rank_cplx, 2},
+    {"_EigenR_EigenR_realQZ", (DL_FUNC) &_EigenR_EigenR_realQZ, 2},
+    {"_EigenR_EigenR_realSchur", (DL_FUNC) &_EigenR_EigenR_realSchur, 1},
+    {"_EigenR_EigenR_complexSchur", (DL_FUNC) &_EigenR_EigenR_complexSchur, 2},
     {"_EigenR_EigenR_isInjective_real", (DL_FUNC) &_EigenR_EigenR_isInjective_real, 1},
     {"_EigenR_EigenR_isInjective_cplx", (DL_FUNC) &_EigenR_EigenR_isInjective_cplx, 2},
     {"_EigenR_EigenR_isSurjective_real", (DL_FUNC) &_EigenR_EigenR_isSurjective_real, 1},

src/Schur.cpp

@@ -0,0 +1,22 @@
+#include "EigenR.h"
+
+// [[Rcpp::export]]
+Rcpp::List EigenR_realSchur(const Eigen::MatrixXd& M) {
+  Eigen::RealSchur<Eigen::MatrixXd> schur(M); 
+  const Eigen::MatrixXd U = schur.matrixU();
+  const Eigen::MatrixXd T = schur.matrixT();
+  return Rcpp::List::create(Rcpp::Named("T") = T,
+                            Rcpp::Named("U") = U);
+}
+
+// [[Rcpp::export]]
+Rcpp::List EigenR_complexSchur(const Eigen::MatrixXd& Re, 
+                               const Eigen::MatrixXd& Im) {
+  const Eigen::MatrixXcd M = matricesToMatrixXcd(Re, Im);
+  Eigen::ComplexSchur<Eigen::MatrixXcd> schur(M.rows());
+  schur.compute(M);
+  const Eigen::MatrixXcd U = schur.matrixU();
+  const Eigen::MatrixXcd T = schur.matrixT();
+  return Rcpp::List::create(Rcpp::Named("U") = cplxMatrixToList(U),
+                            Rcpp::Named("T") = cplxMatrixToList(T));
+}