#include "../lapack/create_matrix.h"
// test eigenpairs_symmetric_by_index(const std::pair<unsigned int,unsigned int> &, const bool)
+// for all eigenvalues with eigenvectors
#include <deal.II/base/logstream.h>
#include <deal.II/base/utilities.h>
pcout << size << " " << block_size << " " << grid->get_process_grid_rows() << " " << grid->get_process_grid_columns() << std::endl;
+ const unsigned int n_eigenvalues = size;
+ const unsigned int max_n_eigenvalues = 5;
+
// Create SPD matrices of requested size:
FullMatrix<NumberType> full_A(size);
- std::vector<NumberType> lapack_A(size*size);
+ std::vector<NumberType> eigenvalues_Lapack(size);
+ std::vector<Vector<NumberType>> s_eigenvectors_ (max_n_eigenvalues,Vector<NumberType>(size));
+ std::vector<Vector<NumberType>> p_eigenvectors_ (max_n_eigenvalues,Vector<NumberType>(size));
+ FullMatrix<NumberType> p_eigenvectors (size,size);
+
+ ScaLAPACKMatrix<NumberType> scalapack_syev (size, grid, block_size);
+ scalapack_syev.set_property(LAPACKSupport::Property::symmetric);
create_spd (full_A);
- for (unsigned int i = 0; i < size; ++i)
- for (unsigned int j = 0; j < size; ++j)
- lapack_A[i*size+j] = full_A(i,j);
+ scalapack_syev = full_A;
- std::vector<NumberType> eigenvalues_Lapack(size);
//Lapack as reference
{
+ std::vector<NumberType> lapack_A(size*size);
+ for (unsigned int i = 0; i < size; ++i)
+ for (unsigned int j = 0; j < size; ++j)
+ lapack_A[i*size+j] = full_A(i,j);
+
int info; //Variable containing information about the successfull exit of the lapack routine
char jobz = 'V'; //'V': all eigenpairs of A are computed
char uplo = 'U'; //storage format of the matrix A; not so important as matrix is symmetric
syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
AssertThrow (info==0, LAPACKSupport::ExcErrorCode("syev", info));
+ for (int i=0; i<max_n_eigenvalues; ++i)
+ for (int j=0; j<size; ++j)
+ s_eigenvectors_[i][j] = lapack_A[(size-1-i)*size+j];
+
}
- unsigned int n_eigenvalues = eigenvalues_Lapack.size(), max_n_eigenvalues=5;
- std::vector<Vector<NumberType>> s_eigenvectors_ (max_n_eigenvalues,Vector<NumberType>(size));
- for (int i=0; i<max_n_eigenvalues; ++i)
- for (int j=0; j<size; ++j)
- s_eigenvectors_[i][j] = lapack_A[(size-1-i)*size+j];
+ // the actual test:
pcout << "comparing " << max_n_eigenvalues << " eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:" << std::endl;
- std::vector<NumberType> eigenvalues_psyev;
- ScaLAPACKMatrix<NumberType> scalapack_syev (size, grid, block_size);
- scalapack_syev.set_property(LAPACKSupport::Property::symmetric);
- scalapack_syev = full_A;
- eigenvalues_psyev = scalapack_syev.eigenpairs_symmetric_by_index(std::make_pair(0,size-1),true);
- FullMatrix<NumberType> p_eigenvectors (size,size);
+ const std::vector<NumberType> eigenvalues_psyev = scalapack_syev.eigenpairs_symmetric_by_index(std::make_pair(0,size-1),true);
scalapack_syev.copy_to(p_eigenvectors);
for (unsigned int i=0; i<max_n_eigenvalues; ++i)
- {
- AssertThrow ( std::abs(eigenvalues_psyev[n_eigenvalues-i-1]-eigenvalues_Lapack[n_eigenvalues-i-1]) / std::abs(eigenvalues_Lapack[n_eigenvalues-i-1]) < tol,
- dealii::ExcInternalError());
- }
- pcout << " with respect to the given tolerance the eigenvalues coincide" << std::endl;
+ AssertThrow ( std::abs(eigenvalues_psyev[n_eigenvalues-i-1]-eigenvalues_Lapack[n_eigenvalues-i-1]) / std::abs(eigenvalues_Lapack[n_eigenvalues-i-1]) < tol,
+ ExcInternalError());
- std::vector<Vector<NumberType>> p_eigenvectors_ (max_n_eigenvalues,Vector<NumberType>(size));
- for (unsigned int i=0; i<max_n_eigenvalues; ++i)
- for (unsigned int j=0; j<size; ++j)
- p_eigenvectors_[i][j] = p_eigenvectors(j,size-1-i);
-
- //product of eigenvectors computed using Lapack and ScaLapack has to be either 1 or -1
- for (unsigned int i=0; i<max_n_eigenvalues; ++i)
- {
- NumberType product = p_eigenvectors_[i] * s_eigenvectors_[i];
-
- //the requirement for alignment of the eigenvectors has to be released (primarily for floats)
- AssertThrow (std::abs(std::abs(product)-1) < tol*10, dealii::ExcInternalError());
- }
- pcout << " with respect to the given tolerance also the eigenvectors coincide" << std::endl << std::endl;
-
- pcout << "comparing " << max_n_eigenvalues << " eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:" << std::endl;
- std::vector<NumberType> eigenvalues_psyevx_partial;
- ScaLAPACKMatrix<NumberType> scalapack_syevx_partial (size, grid, block_size);
- scalapack_syevx_partial.set_property(LAPACKSupport::Property::symmetric);
- scalapack_syevx_partial = full_A;
- eigenvalues_psyevx_partial = scalapack_syevx_partial.eigenpairs_symmetric_by_index(std::make_pair(size-max_n_eigenvalues,size-1),true);
- scalapack_syevx_partial.copy_to(p_eigenvectors);
- for (unsigned int i=eigenvalues_psyevx_partial.size()-1; i>0; --i)
- {
- if ( !(std::abs(eigenvalues_psyevx_partial[i]-eigenvalues_Lapack[size-eigenvalues_psyevx_partial.size()+i]) /
- std::abs(eigenvalues_Lapack[size-eigenvalues_psyevx_partial.size()+i]) < tol))
- {
- std::cout << "process #" << this_mpi_process << ": eigenvalues do not fit: "
- << eigenvalues_psyevx_partial[i] << " <--> " << eigenvalues_Lapack[size-eigenvalues_psyevx_partial.size()+i] << std::endl;
- }
-
- AssertThrow ( std::abs(eigenvalues_psyevx_partial[i]-eigenvalues_Lapack[size-eigenvalues_psyevx_partial.size()+i]) /
- std::abs(eigenvalues_Lapack[size-eigenvalues_psyevx_partial.size()+i]) < tol,
- dealii::ExcInternalError());
- }
pcout << " with respect to the given tolerance the eigenvalues coincide" << std::endl;
for (unsigned int i=0; i<max_n_eigenvalues; ++i)
for (unsigned int j=0; j<size; ++j)
- p_eigenvectors_[i][j] = p_eigenvectors(j,max_n_eigenvalues-1-i);
+ p_eigenvectors_[i][j] = p_eigenvectors(j,size-1-i);
//product of eigenvectors computed using Lapack and ScaLapack has to be either 1 or -1
for (unsigned int i=0; i<max_n_eigenvalues; ++i)
{
- NumberType product = p_eigenvectors_[i] * s_eigenvectors_[i];
-
- if (!(std::abs(std::abs(product)-1) < tol*10))
- {
- std::cout << "process #" << this_mpi_process << ": eigenvectors do not coincide: abs(" << product << ") != 1" << std::endl;
- }
-
+ const NumberType product = p_eigenvectors_[i] * s_eigenvectors_[i];
//the requirement for alignment of the eigenvectors has to be released (primarily for floats)
- AssertThrow (std::abs(std::abs(product)-1) < tol*10, dealii::ExcInternalError());
+ AssertThrow (std::abs(std::abs(product)-1) < tol*10,
+ ExcInternalError());
}
pcout << " with respect to the given tolerance also the eigenvectors coincide" << std::endl << std::endl;
-
- pcout << std::endl;
}
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
200 64 1 1
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 32 1 1
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 64 1 1
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 32 1 1
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 64 1 1
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
200 64 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 32 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 64 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 32 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 64 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
200 64 2 2
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 32 2 2
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 64 2 2
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 32 2 2
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 64 2 2
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
200 64 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 32 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
400 64 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 32 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
600 64 3 3
comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyev:
with respect to the given tolerance the eigenvalues coincide
with respect to the given tolerance also the eigenvectors coincide
-comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
- with respect to the given tolerance the eigenvalues coincide
- with respect to the given tolerance also the eigenvectors coincide
-
-
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 - 2018 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+#include "../tests.h"
+#include "../lapack/create_matrix.h"
+
+// test eigenpairs_symmetric_by_index(const std::pair<unsigned int,unsigned int> &, const bool)
+// for all eigenvalues without eigenvectors
+
+
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/timer.h>
+#include <deal.II/base/multithread_info.h>
+#include <deal.II/base/process_grid.h>
+
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/lapack_full_matrix.h>
+#include <deal.II/lac/lapack_templates.h>
+#include <deal.II/lac/scalapack.h>
+
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+#include <memory>
+
+
+template <typename NumberType>
+void test(const unsigned int size, const unsigned int block_size, const NumberType tol)
+{
+ MPI_Comm mpi_communicator(MPI_COMM_WORLD);
+ const unsigned int n_mpi_processes(Utilities::MPI::n_mpi_processes(mpi_communicator));
+ const unsigned int this_mpi_process(Utilities::MPI::this_mpi_process(mpi_communicator));
+
+ ConditionalOStream pcout (std::cout, (this_mpi_process ==0));
+
+ std::shared_ptr<Utilities::MPI::ProcessGrid> grid = std::make_shared<Utilities::MPI::ProcessGrid>(mpi_communicator,size,size,block_size,block_size);
+
+ pcout << size << " " << block_size << " " << grid->get_process_grid_rows() << " " << grid->get_process_grid_columns() << std::endl;
+
+ const unsigned int n_eigenvalues = size;
+ const unsigned int max_n_eigenvalues = 5;
+
+ // Create SPD matrices of requested size:
+ FullMatrix<NumberType> full_A(size);
+ std::vector<NumberType> eigenvalues_Lapack(size);
+
+ ScaLAPACKMatrix<NumberType> scalapack_syev (size, grid, block_size);
+ scalapack_syev.set_property(LAPACKSupport::Property::symmetric);
+
+ create_spd (full_A);
+ scalapack_syev = full_A;
+
+ //Lapack as reference
+ {
+ std::vector<NumberType> lapack_A(size*size);
+ for (unsigned int i = 0; i < size; ++i)
+ for (unsigned int j = 0; j < size; ++j)
+ lapack_A[i*size+j] = full_A(i,j);
+
+ int info; //Variable containing information about the successfull exit of the lapack routine
+ char jobz = 'V'; //'V': all eigenpairs of A are computed
+ char uplo = 'U'; //storage format of the matrix A; not so important as matrix is symmetric
+ int LDA = size; //leading dimension of the matrix A
+ int lwork; //length of vector/array work
+ std::vector<NumberType> work (1);
+
+ //by setting lwork to -1 a workspace query for work is done
+ //as matrix is symmetric: LDA == size of matrix
+ lwork = -1;
+ syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
+ lwork=work[0];
+ work.resize (lwork);
+ syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
+
+ AssertThrow (info==0, LAPACKSupport::ExcErrorCode("syev", info));
+ }
+
+ // the actual test:
+
+ pcout << "comparing " << max_n_eigenvalues << " eigenvalues computed using LAPACK and ScaLAPACK pdsyev:" << std::endl;
+ const std::vector<NumberType> eigenvalues_psyev = scalapack_syev.eigenpairs_symmetric_by_index(std::make_pair(0,size-1),false);
+ for (unsigned int i=0; i<max_n_eigenvalues; ++i)
+ AssertThrow ( std::abs(eigenvalues_psyev[n_eigenvalues-i-1]-eigenvalues_Lapack[n_eigenvalues-i-1]) / std::abs(eigenvalues_Lapack[n_eigenvalues-i-1]) < tol,
+ ExcInternalError());
+
+ pcout << " with respect to the given tolerance the eigenvalues coincide" << std::endl;
+}
+
+
+
+int main (int argc,char **argv)
+{
+
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, numbers::invalid_unsigned_int);
+
+ const std::vector<unsigned int> sizes = {{200,400,600}};
+ const std::vector<unsigned int> blocks = {{32,64}};
+
+ const double tol = 1e-10;
+
+ for (const auto &s : sizes)
+ for (const auto &b : blocks)
+ if (b <= s)
+ test<double>(s,b,tol);
+}
--- /dev/null
+200 32 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+200 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+200 32 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+200 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyev:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 - 2018 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+#include "../tests.h"
+#include "../lapack/create_matrix.h"
+
+// test eigenpairs_symmetric_by_index(const std::pair<unsigned int,unsigned int> &, const bool)
+// for some eigenvalues with eigenvectors
+
+
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/timer.h>
+#include <deal.II/base/multithread_info.h>
+#include <deal.II/base/process_grid.h>
+
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/lapack_full_matrix.h>
+#include <deal.II/lac/lapack_templates.h>
+#include <deal.II/lac/scalapack.h>
+
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+#include <memory>
+
+
+template <typename NumberType>
+void test(const unsigned int size, const unsigned int block_size, const NumberType tol)
+{
+ MPI_Comm mpi_communicator(MPI_COMM_WORLD);
+ const unsigned int n_mpi_processes(Utilities::MPI::n_mpi_processes(mpi_communicator));
+ const unsigned int this_mpi_process(Utilities::MPI::this_mpi_process(mpi_communicator));
+
+ ConditionalOStream pcout (std::cout, (this_mpi_process ==0));
+
+ std::shared_ptr<Utilities::MPI::ProcessGrid> grid = std::make_shared<Utilities::MPI::ProcessGrid>(mpi_communicator,size,size,block_size,block_size);
+
+ pcout << size << " " << block_size << " " << grid->get_process_grid_rows() << " " << grid->get_process_grid_columns() << std::endl;
+
+ const unsigned int n_eigenvalues = size;
+ const unsigned int max_n_eigenvalues = 5;
+
+ // Create SPD matrices of requested size:
+ FullMatrix<NumberType> full_A(size);
+ std::vector<NumberType> eigenvalues_Lapack(size);
+ std::vector<Vector<NumberType>> s_eigenvectors_ (max_n_eigenvalues,Vector<NumberType>(size));
+ std::vector<Vector<NumberType>> p_eigenvectors_ (max_n_eigenvalues,Vector<NumberType>(size));
+ FullMatrix<NumberType> p_eigenvectors (size,size);
+
+ ScaLAPACKMatrix<NumberType> scalapack_syevx (size, grid, block_size);
+ scalapack_syevx.set_property(LAPACKSupport::Property::symmetric);
+
+ create_spd (full_A);
+ scalapack_syevx = full_A;
+
+ //Lapack as reference
+ {
+ std::vector<NumberType> lapack_A(size*size);
+ for (unsigned int i = 0; i < size; ++i)
+ for (unsigned int j = 0; j < size; ++j)
+ lapack_A[i*size+j] = full_A(i,j);
+
+ int info; //Variable containing information about the successfull exit of the lapack routine
+ char jobz = 'V'; //'V': all eigenpairs of A are computed
+ char uplo = 'U'; //storage format of the matrix A; not so important as matrix is symmetric
+ int LDA = size; //leading dimension of the matrix A
+ int lwork; //length of vector/array work
+ std::vector<NumberType> work (1);
+
+ //by setting lwork to -1 a workspace query for work is done
+ //as matrix is symmetric: LDA == size of matrix
+ lwork = -1;
+ syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
+ lwork=work[0];
+ work.resize (lwork);
+ syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
+
+ AssertThrow (info==0, LAPACKSupport::ExcErrorCode("syev", info));
+ for (int i=0; i<max_n_eigenvalues; ++i)
+ for (int j=0; j<size; ++j)
+ s_eigenvectors_[i][j] = lapack_A[(size-1-i)*size+j];
+
+ }
+
+ // the actual test:
+
+ pcout << "comparing " << max_n_eigenvalues << " eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:" << std::endl;
+ const std::vector<NumberType> eigenvalues_psyevx = scalapack_syevx.eigenpairs_symmetric_by_index(std::make_pair(size-max_n_eigenvalues,size-1),true);
+ scalapack_syevx.copy_to(p_eigenvectors);
+ for (unsigned int i=eigenvalues_psyevx.size()-1; i>0; --i)
+ {
+ if ( !(std::abs(eigenvalues_psyevx[i]-eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) /
+ std::abs(eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) < tol))
+ {
+ std::cout << "process #" << this_mpi_process << ": eigenvalues do not fit: "
+ << eigenvalues_psyevx[i] << " <--> " << eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i] << std::endl;
+ }
+
+ AssertThrow ( std::abs(eigenvalues_psyevx[i]-eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) /
+ std::abs(eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) < tol,
+ ExcInternalError());
+ }
+ pcout << " with respect to the given tolerance the eigenvalues coincide" << std::endl;
+
+ // FIXME: run-time error on macOS if code between "pcout << comparing" and this line is executed.
+ // Happens at the end of the program run while freeing the MPI communicator.
+
+ for (unsigned int i=0; i<max_n_eigenvalues; ++i)
+ for (unsigned int j=0; j<size; ++j)
+ p_eigenvectors_[i][j] = p_eigenvectors(j,max_n_eigenvalues-1-i);
+
+ //product of eigenvectors computed using Lapack and ScaLapack has to be either 1 or -1
+ for (unsigned int i=0; i<max_n_eigenvalues; ++i)
+ {
+ const NumberType product = p_eigenvectors_[i] * s_eigenvectors_[i];
+ if (!(std::abs(std::abs(product)-1) < tol*10))
+ std::cout << "process #" << this_mpi_process << ": eigenvectors do not coincide: abs(" << product << ") != 1" << std::endl;
+
+ //the requirement for alignment of the eigenvectors has to be released (primarily for floats)
+ AssertThrow (std::abs(std::abs(product)-1) < tol*10,
+ ExcInternalError());
+ }
+ pcout << " with respect to the given tolerance also the eigenvectors coincide" << std::endl << std::endl;
+}
+
+
+
+int main (int argc,char **argv)
+{
+
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, numbers::invalid_unsigned_int);
+
+ const std::vector<unsigned int> sizes = {{200,400,600}};
+ const std::vector<unsigned int> blocks = {{32,64}};
+
+ const double tol = 1e-10;
+
+ for (const auto &s : sizes)
+ for (const auto &b : blocks)
+ if (b <= s)
+ test<double>(s,b,tol);
+}
--- /dev/null
+200 32 1 1
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+200 64 1 1
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 32 1 1
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 64 1 1
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 32 1 1
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 64 1 1
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
--- /dev/null
+200 32 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+200 64 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 32 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 64 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 32 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 64 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
--- /dev/null
+200 32 2 2
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+200 64 2 2
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 32 2 2
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 64 2 2
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 32 2 2
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 64 2 2
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
--- /dev/null
+200 32 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+200 64 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 32 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+400 64 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 32 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
+600 64 3 3
+comparing 5 eigenvalues and eigenvectors computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+ with respect to the given tolerance also the eigenvectors coincide
+
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 - 2018 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+#include "../tests.h"
+#include "../lapack/create_matrix.h"
+
+// test eigenpairs_symmetric_by_index(const std::pair<unsigned int,unsigned int> &, const bool)
+// for some eigenvalues without eigenvectors
+
+
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/timer.h>
+#include <deal.II/base/multithread_info.h>
+#include <deal.II/base/process_grid.h>
+
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/lapack_full_matrix.h>
+#include <deal.II/lac/lapack_templates.h>
+#include <deal.II/lac/scalapack.h>
+
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+#include <memory>
+
+
+template <typename NumberType>
+void test(const unsigned int size, const unsigned int block_size, const NumberType tol)
+{
+ MPI_Comm mpi_communicator(MPI_COMM_WORLD);
+ const unsigned int n_mpi_processes(Utilities::MPI::n_mpi_processes(mpi_communicator));
+ const unsigned int this_mpi_process(Utilities::MPI::this_mpi_process(mpi_communicator));
+
+ ConditionalOStream pcout (std::cout, (this_mpi_process ==0));
+
+ std::shared_ptr<Utilities::MPI::ProcessGrid> grid = std::make_shared<Utilities::MPI::ProcessGrid>(mpi_communicator,size,size,block_size,block_size);
+
+ pcout << size << " " << block_size << " " << grid->get_process_grid_rows() << " " << grid->get_process_grid_columns() << std::endl;
+
+ const unsigned int n_eigenvalues = size;
+ const unsigned int max_n_eigenvalues = 5;
+
+ // Create SPD matrices of requested size:
+ FullMatrix<NumberType> full_A(size);
+ std::vector<NumberType> eigenvalues_Lapack(size);
+
+ ScaLAPACKMatrix<NumberType> scalapack_syevx (size, grid, block_size);
+ scalapack_syevx.set_property(LAPACKSupport::Property::symmetric);
+
+ create_spd (full_A);
+ scalapack_syevx = full_A;
+
+ //Lapack as reference
+ {
+ std::vector<NumberType> lapack_A(size*size);
+ for (unsigned int i = 0; i < size; ++i)
+ for (unsigned int j = 0; j < size; ++j)
+ lapack_A[i*size+j] = full_A(i,j);
+
+ int info; //Variable containing information about the successfull exit of the lapack routine
+ char jobz = 'V'; //'V': all eigenpairs of A are computed
+ char uplo = 'U'; //storage format of the matrix A; not so important as matrix is symmetric
+ int LDA = size; //leading dimension of the matrix A
+ int lwork; //length of vector/array work
+ std::vector<NumberType> work (1);
+
+ //by setting lwork to -1 a workspace query for work is done
+ //as matrix is symmetric: LDA == size of matrix
+ lwork = -1;
+ syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
+ lwork=work[0];
+ work.resize (lwork);
+ syev(&jobz, &uplo, &LDA, & *lapack_A.begin(), &LDA, & *eigenvalues_Lapack.begin(), & *work.begin(), &lwork, &info);
+ AssertThrow (info==0, LAPACKSupport::ExcErrorCode("syev", info));
+ }
+
+ // the actual test:
+
+ pcout << "comparing " << max_n_eigenvalues << " eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:" << std::endl;
+ const std::vector<NumberType> eigenvalues_psyevx = scalapack_syevx.eigenpairs_symmetric_by_index(std::make_pair(size-max_n_eigenvalues,size-1),false);
+ for (unsigned int i=eigenvalues_psyevx.size()-1; i>0; --i)
+ {
+ if ( !(std::abs(eigenvalues_psyevx[i]-eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) /
+ std::abs(eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) < tol))
+ {
+ std::cout << "process #" << this_mpi_process << ": eigenvalues do not fit: "
+ << eigenvalues_psyevx[i] << " <--> " << eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i] << std::endl;
+ }
+
+ AssertThrow ( std::abs(eigenvalues_psyevx[i]-eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) /
+ std::abs(eigenvalues_Lapack[size-eigenvalues_psyevx.size()+i]) < tol,
+ ExcInternalError());
+ }
+ pcout << " with respect to the given tolerance the eigenvalues coincide" << std::endl;
+}
+
+
+
+int main (int argc,char **argv)
+{
+
+ Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, numbers::invalid_unsigned_int);
+
+ const std::vector<unsigned int> sizes = {{200,400,600}};
+ const std::vector<unsigned int> blocks = {{32,64}};
+
+ const double tol = 1e-10;
+
+ for (const auto &s : sizes)
+ for (const auto &b : blocks)
+ if (b <= s)
+ test<double>(s,b,tol);
+}
--- /dev/null
+200 32 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 1 1
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+200 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+200 32 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 2 2
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
--- /dev/null
+200 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+200 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+400 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 32 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
+600 64 3 3
+comparing 5 eigenvalues computed using LAPACK and ScaLAPACK pdsyevx:
+ with respect to the given tolerance the eigenvalues coincide
projects / dealii.git / commitdiff