Merge pull request #9804 from woodychow:optimize_cveigen

modules/core/misc/java/test/CoreTest.java

@@ -394,7 +394,13 @@ public class CoreTest extends OpenCVTestCase {
     }
 
     public void testEigen() {
-        Mat src = new Mat(3, 3, CvType.CV_32FC1, new Scalar(2.0));
+        Mat src = new Mat(3, 3, CvType.CV_32FC1) {
+            {
+                put(0, 0, 2, 0, 0);
+                put(1, 0, 0, 6, 0);
+                put(2, 0, 0, 0, 4);
+            }
+        };
         Mat eigenVals = new Mat();
         Mat eigenVecs = new Mat();
 
@@ -402,18 +408,22 @@ public class CoreTest extends OpenCVTestCase {
 
         Mat expectedEigenVals = new Mat(3, 1, CvType.CV_32FC1) {
             {
-                put(0, 0, 6, 0, 0);
-            }
-        };
-        Mat expectedEigenVecs = new Mat(3, 3, CvType.CV_32FC1) {
-            {
-                put(0, 0, 0.57735026, 0.57735026, 0.57735032);
-                put(1, 0, 0.70710677, -0.70710677, 0);
-                put(2, 0, -0.40824831, -0.40824831, 0.81649661);
+                put(0, 0, 6, 4, 2);
             }
         };
         assertMatEqual(eigenVals, expectedEigenVals, EPS);
-        assertMatEqual(eigenVecs, expectedEigenVecs, EPS);
+
+        // check by definition
+        double eps = 1e-3;
+        for(int i = 0; i < 3; i++)
+        {
+            Mat vec = eigenVecs.row(i).t();
+            Mat lhs = new Mat(3, 1, CvType.CV_32FC1);
+            Core.gemm(src, vec, 1.0, new Mat(), 1.0, lhs);
+            Mat rhs = new Mat(3, 1, CvType.CV_32FC1);
+            Core.gemm(vec, eigenVals.row(i), 1.0, new Mat(), 1.0, rhs);
+            assertMatEqual(lhs, rhs, eps);
+        }
     }
 
     public void testExp() {
@@ -1326,7 +1336,8 @@ public class CoreTest extends OpenCVTestCase {
         Mat vectors = new Mat();
 
         Core.PCACompute(data, mean, vectors);
-
+        //System.out.println(mean.dump());
+        //System.out.println(vectors.dump());
         Mat mean_truth = new Mat(1, 4, CvType.CV_32F) {
             {
                 put(0, 0, 2, 4, 4, 8);
@@ -1338,7 +1349,21 @@ public class CoreTest extends OpenCVTestCase {
             }
         };
         assertMatEqual(mean_truth, mean, EPS);
-        assertMatEqual(vectors_truth, vectors, EPS);
+
+        // eigenvectors are normalized (length = 1),
+        // but direction is unknown (v and -v are both eigen vectors)
+        // so this direct check doesn't work:
+        // assertMatEqual(vectors_truth, vectors, EPS);
+        for(int i = 0; i < 3; i++)
+        {
+            Mat vec0 = vectors_truth.row(i);
+            Mat vec1 = vectors.row(i);
+            Mat vec1_ = new Mat();
+            Core.subtract(new Mat(1, 4, CvType.CV_32F, new Scalar(0)), vec1, vec1_);
+            double scale1 = Core.norm(vec0, vec1);
+            double scale2 = Core.norm(vec0, vec1_);
+            assertTrue(Math.min(scale1, scale2) < EPS);
+        }
     }
 
     public void testPCAComputeMatMatMatInt() {
@@ -1365,7 +1390,20 @@ public class CoreTest extends OpenCVTestCase {
             }
         };
         assertMatEqual(mean_truth, mean, EPS);
-        assertMatEqual(vectors_truth, vectors, EPS);
+        // eigenvectors are normalized (length = 1),
+        // but direction is unknown (v and -v are both eigen vectors)
+        // so this direct check doesn't work:
+        // assertMatEqual(vectors_truth, vectors, EPS);
+        for(int i = 0; i < 1; i++)
+        {
+            Mat vec0 = vectors_truth.row(i);
+            Mat vec1 = vectors.row(i);
+            Mat vec1_ = new Mat();
+            Core.subtract(new Mat(1, 4, CvType.CV_32F, new Scalar(0)), vec1, vec1_);
+            double scale1 = Core.norm(vec0, vec1);
+            double scale2 = Core.norm(vec0, vec1_);
+            assertTrue(Math.min(scale1, scale2) < EPS);
+        }
     }
 
     public void testPCAProject() {

modules/core/src/lapack.cpp

@@ -43,6 +43,12 @@
 #include "precomp.hpp"
 #include <limits>
 
+#ifdef HAVE_EIGEN
+#include <Eigen/Core>
+#include <Eigen/Eigenvalues>
+#include "opencv2/core/eigen.hpp"
+#endif
+
 #if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700
 #pragma float_control(precise, on)
 #endif
@@ -1396,6 +1402,47 @@ bool cv::eigen( InputArray _src, OutputArray _evals, OutputArray _evects )
         v = _evects.getMat();
     }
 
+#ifdef HAVE_EIGEN
+    const bool evecNeeded = _evects.needed();
+    const int esOptions = evecNeeded ? Eigen::ComputeEigenvectors : Eigen::EigenvaluesOnly;
+    _evals.create(n, 1, type);
+    cv::Mat evals = _evals.getMat();
+    if ( type == CV_64F )
+    {
+        Eigen::MatrixXd src_eig, zeros_eig;
+        cv::cv2eigen(src, src_eig);
+
+        Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> es;
+        es.compute(src_eig, esOptions);
+        if ( es.info() == Eigen::Success )
+        {
+            cv::eigen2cv(es.eigenvalues().reverse().eval(), evals);
+            if ( evecNeeded )
+            {
+                cv::Mat evects = _evects.getMat();
+                cv::eigen2cv(es.eigenvectors().rowwise().reverse().transpose().eval(), v);
+            }
+            return true;
+        }
+    } else { // CV_32F
+        Eigen::MatrixXf src_eig, zeros_eig;
+        cv::cv2eigen(src, src_eig);
+
+        Eigen::SelfAdjointEigenSolver<Eigen::MatrixXf> es;
+        es.compute(src_eig, esOptions);
+        if ( es.info() == Eigen::Success )
+        {
+            cv::eigen2cv(es.eigenvalues().reverse().eval(), evals);
+            if ( evecNeeded )
+            {
+                cv::eigen2cv(es.eigenvectors().rowwise().reverse().transpose().eval(), v);
+            }
+            return true;
+        }
+    }
+    return false;
+#else
+
     size_t elemSize = src.elemSize(), astep = alignSize(n*elemSize, 16);
     AutoBuffer<uchar> buf(n*astep + n*5*elemSize + 32);
     uchar* ptr = alignPtr((uchar*)buf, 16);
@@ -1408,6 +1455,7 @@ bool cv::eigen( InputArray _src, OutputArray _evals, OutputArray _evects )
 
     w.copyTo(_evals);
     return ok;
+#endif
 }
 
 namespace cv

modules/core/test/test_eigen.cpp

@@ -59,7 +59,7 @@ using namespace std;
 #define MESSAGE_ERROR_DIFF_1 "Accuracy of eigen values computing less than required."
 #define MESSAGE_ERROR_DIFF_2 "Accuracy of eigen vectors computing less than required."
 #define MESSAGE_ERROR_ORTHO "Matrix of eigen vectors is not orthogonal."
-#define MESSAGE_ERROR_ORDER "Eigen values are not sorted in ascending order."
+#define MESSAGE_ERROR_ORDER "Eigen values are not sorted in descending order."
 
 const int COUNT_NORM_TYPES = 3;
 const int NORM_TYPE[COUNT_NORM_TYPES] = {cv::NORM_L1, cv::NORM_L2, cv::NORM_INF};
@@ -164,8 +164,8 @@ void Core_EigenTest_32::run(int) { check_full(CV_32FC1); }
 void Core_EigenTest_64::run(int) { check_full(CV_64FC1); }
 
 Core_EigenTest::Core_EigenTest()
-: eps_val_32(1e-3f), eps_vec_32(12e-3f),
-  eps_val_64(1e-4f), eps_vec_64(1e-3f), ntests(100) {}
+: eps_val_32(1e-3f), eps_vec_32(1e-3f),
+  eps_val_64(1e-4f), eps_vec_64(1e-4f), ntests(100) {}
 Core_EigenTest::~Core_EigenTest() {}
 
 bool Core_EigenTest::check_pair_count(const cv::Mat& src, const cv::Mat& evalues, int low_index, int high_index)
@@ -234,7 +234,7 @@ bool Core_EigenTest::check_orthogonality(const cv::Mat& U)
 
     for (int i = 0; i < COUNT_NORM_TYPES; ++i)
     {
-        double diff = cvtest::norm(UUt, E, NORM_TYPE[i]);
+        double diff = cvtest::norm(UUt, E, NORM_TYPE[i] | cv::NORM_RELATIVE);
         if (diff > eps_vec)
         {
             std::cout << endl; std::cout << "Checking orthogonality of matrix " << U << ": ";
@@ -257,7 +257,7 @@ bool Core_EigenTest::check_pairs_order(const cv::Mat& eigen_values)
                 if (!(eigen_values.at<float>(i, 0) > eigen_values.at<float>(i+1, 0)))
                 {
                 std::cout << endl; std::cout << "Checking order of eigen values vector " << eigen_values << "..." << endl;
-                std::cout << "Pair of indexes with non ascending of eigen values: (" << i << ", " << i+1 << ")." << endl;
+                std::cout << "Pair of indexes with non descending of eigen values: (" << i << ", " << i+1 << ")." << endl;
                 std::cout << endl;
                 CV_Error(CORE_EIGEN_ERROR_ORDER, MESSAGE_ERROR_ORDER);
                 return false;
@@ -272,9 +272,9 @@ bool Core_EigenTest::check_pairs_order(const cv::Mat& eigen_values)
                 if (!(eigen_values.at<double>(i, 0) > eigen_values.at<double>(i+1, 0)))
                 {
                     std::cout << endl; std::cout << "Checking order of eigen values vector " << eigen_values << "..." << endl;
-                    std::cout << "Pair of indexes with non ascending of eigen values: (" << i << ", " << i+1 << ")." << endl;
+                    std::cout << "Pair of indexes with non descending of eigen values: (" << i << ", " << i+1 << ")." << endl;
                     std::cout << endl;
-                    CV_Error(CORE_EIGEN_ERROR_ORDER, "Eigen values are not sorted in ascending order.");
+                    CV_Error(CORE_EIGEN_ERROR_ORDER, "Eigen values are not sorted in descending order.");
                     return false;
                 }
 
@@ -307,43 +307,28 @@ bool Core_EigenTest::test_pairs(const cv::Mat& src)
 
     cv::Mat eigen_vectors_t; cv::transpose(eigen_vectors, eigen_vectors_t);
 
-    cv::Mat src_evec(src.rows, src.cols, type);
-    src_evec = src*eigen_vectors_t;
+    // Check:
+    // src * eigenvector = eigenval * eigenvector
+    cv::Mat lhs(src.rows, src.cols, type);
+    cv::Mat rhs(src.rows, src.cols, type);
 
-    cv::Mat eval_evec(src.rows, src.cols, type);
+    lhs = src*eigen_vectors_t;
 
-    switch (type)
+    for (int i = 0; i < src.cols; ++i)
     {
-    case CV_32FC1:
-        {
-            for (int i = 0; i < src.cols; ++i)
-            {
-                cv::Mat tmp = eigen_values.at<float>(i, 0) * eigen_vectors_t.col(i);
-                for (int j = 0; j < src.rows; ++j) eval_evec.at<float>(j, i) = tmp.at<float>(j, 0);
-            }
-
-            break;
-        }
-
-    case CV_64FC1:
+        double eigenval = 0;
+        switch (type)
         {
-            for (int i = 0; i < src.cols; ++i)
-            {
-                cv::Mat tmp = eigen_values.at<double>(i, 0) * eigen_vectors_t.col(i);
-                for (int j = 0; j < src.rows; ++j) eval_evec.at<double>(j, i) = tmp.at<double>(j, 0);
-            }
-
-            break;
+        case CV_32FC1: eigenval = eigen_values.at<float>(i, 0); break;
+        case CV_64FC1: eigenval = eigen_values.at<double>(i, 0); break;
         }
-
-    default:;
+        cv::Mat rhs_v = eigenval * eigen_vectors_t.col(i);
+        rhs_v.copyTo(rhs.col(i));
     }
 
-    cv::Mat disparity = src_evec - eval_evec;
-
     for (int i = 0; i < COUNT_NORM_TYPES; ++i)
     {
-        double diff = cvtest::norm(disparity, NORM_TYPE[i]);
+        double diff = cvtest::norm(lhs, rhs, NORM_TYPE[i] | cv::NORM_RELATIVE);
         if (diff > eps_vec)
         {
             std::cout << endl; std::cout << "Checking accuracy of eigen vectors computing for matrix " << src << ": ";
@@ -372,7 +357,7 @@ bool Core_EigenTest::test_values(const cv::Mat& src)
 
     for (int i = 0; i < COUNT_NORM_TYPES; ++i)
     {
-        double diff = cvtest::norm(eigen_values_1, eigen_values_2, NORM_TYPE[i]);
+        double diff = cvtest::norm(eigen_values_1, eigen_values_2, NORM_TYPE[i] | cv::NORM_RELATIVE);
         if (diff > eps_val)
         {
             std::cout << endl; std::cout << "Checking accuracy of eigen values computing for matrix " << src << ": ";
@@ -419,7 +404,7 @@ static void testEigen(const Mat_<T>& src, const Mat_<T>& expected_eigenvalues, b
     SCOPED_TRACE(runSymmetric ? "cv::eigen" : "cv::eigenNonSymmetric");
 
     int type = traits::Type<T>::value;
-    const T eps = 1e-6f;
+    const T eps = src.type() == CV_32F ? 1e-4f : 1e-6f;
 
     Mat eigenvalues, eigenvectors, eigenvalues0;