Blaze 3.9
DenseMatrix.h File Reference

Header file for utility functions for dense matrices. More...

#include <algorithm>
#include <blaze/math/Aliases.h>
#include <blaze/math/constraints/BLASCompatible.h>
#include <blaze/math/constraints/Computation.h>
#include <blaze/math/constraints/RequiresEvaluation.h>
#include <blaze/math/constraints/Triangular.h>
#include <blaze/math/constraints/UniTriangular.h>
#include <blaze/math/Epsilon.h>
#include <blaze/math/expressions/DenseMatrix.h>
#include <blaze/math/lapack/clapack/potrf.h>
#include <blaze/math/ReductionFlag.h>
#include <blaze/math/RelaxationFlag.h>
#include <blaze/math/shims/Conjugate.h>
#include <blaze/math/shims/Equal.h>
#include <blaze/math/shims/IsDefault.h>
#include <blaze/math/shims/IsDivisor.h>
#include <blaze/math/shims/IsFinite.h>
#include <blaze/math/shims/IsInf.h>
#include <blaze/math/shims/IsNaN.h>
#include <blaze/math/shims/IsOne.h>
#include <blaze/math/shims/IsReal.h>
#include <blaze/math/shims/IsZero.h>
#include <blaze/math/StorageOrder.h>
#include <blaze/math/typetraits/IsExpression.h>
#include <blaze/math/typetraits/IsDiagonal.h>
#include <blaze/math/typetraits/IsHermitian.h>
#include <blaze/math/typetraits/IsIdentity.h>
#include <blaze/math/typetraits/IsLower.h>
#include <blaze/math/typetraits/IsRestricted.h>
#include <blaze/math/typetraits/IsRowMajorMatrix.h>
#include <blaze/math/typetraits/IsScalar.h>
#include <blaze/math/typetraits/IsStrictlyLower.h>
#include <blaze/math/typetraits/IsStrictlyUpper.h>
#include <blaze/math/typetraits/IsSymmetric.h>
#include <blaze/math/typetraits/IsTriangular.h>
#include <blaze/math/typetraits/IsUniform.h>
#include <blaze/math/typetraits/IsUniLower.h>
#include <blaze/math/typetraits/IsUniTriangular.h>
#include <blaze/math/typetraits/IsUniUpper.h>
#include <blaze/math/typetraits/IsUpper.h>
#include <blaze/math/typetraits/IsZero.h>
#include <blaze/math/typetraits/RemoveAdaptor.h>
#include <blaze/math/typetraits/UnderlyingBuiltin.h>
#include <blaze/math/views/Check.h>
#include <blaze/util/algorithms/Max.h>
#include <blaze/util/Assert.h>
#include <blaze/util/EnableIf.h>
#include <blaze/util/IntegralConstant.h>
#include <blaze/util/Limits.h>
#include <blaze/util/mpl/If.h>
#include <blaze/util/NumericCast.h>
#include <blaze/util/Types.h>
#include <blaze/util/typetraits/IsBuiltin.h>
#include <blaze/util/typetraits/IsFloatingPoint.h>

Go to the source code of this file.

Functions

DenseMatrix operators
template<typename T1 , typename T2 >
auto blaze::operator== (const DenseMatrix< T1, false > &mat, T2 scalar) -> EnableIf_t< IsScalar_v< T2 >, bool >
 Equality operator for the comparison of a row-major dense matrix and a scalar value. More...
 
template<typename T1 , typename T2 >
auto blaze::operator== (const DenseMatrix< T1, true > &mat, T2 scalar) -> EnableIf_t< IsScalar_v< T2 >, bool >
 Equality operator for the comparison of a column-major dense matrix and a scalar value. More...
 
template<typename T1 , typename T2 , bool SO>
auto blaze::operator== (T1 scalar, const DenseMatrix< T2, SO > &mat) -> EnableIf_t< IsScalar_v< T1 >, bool >
 Equality operator for the comparison of a scalar value and a dense matrix. More...
 
template<typename T1 , typename T2 , bool SO>
auto blaze::operator!= (const DenseMatrix< T1, SO > &mat, T2 scalar) -> EnableIf_t< IsScalar_v< T2 >, bool >
 Inequality operator for the comparison of a dense matrix and a scalar value. More...
 
template<typename T1 , typename T2 , bool SO>
auto blaze::operator!= (T1 scalar, const DenseMatrix< T2, SO > &mat) -> EnableIf_t< IsScalar_v< T1 >, bool >
 Inequality operator for the comparison of a scalar value and a dense matrix. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator+= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Addition assignment operator for the addition of a dense matrix and a scalar value ( $ A+=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator+= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Addition assignment operator for the addition of a temporary dense matrix and a scalar value ( $ A+=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator-= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Subtraction assignment operator for the subtraction of a dense matrix and a scalar value ( $ A-=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator-= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Subtraction assignment operator for the subtraction of a temporary dense matrix and a scalar value ( $ A-=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator*= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Multiplication assignment operator for the multiplication of a dense matrix and a scalar value ( $ A*=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator*= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Multiplication assignment operator for the multiplication of a temporary dense matrix and a scalar value ( $ A*=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator/= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Division assignment operator for the division of a dense matrix by a scalar value ( $ A/=s $). More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator/= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Division assignment operator for the division of a temporary dense matrix by a scalar value ( $ A/=s $). More...
 
template<typename MT , bool SO>
MT & blaze::operator<<= (DenseMatrix< MT, SO > &mat, int count)
 Left-shift assignment operator for the uniform left-shift of a dense matrix. More...
 
template<typename MT , bool SO>
MT & blaze::operator<<= (DenseMatrix< MT, SO > &&mat, int count)
 Left-shift assignment operator for the uniform left-shift of a temporary dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator<<= (DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Left-shift assignment operator for the elementwise left-shift of a dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator<<= (DenseMatrix< MT1, SO1 > &&lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Left-shift assignment operator for the elementwise left-shift of a temporary dense matrix. More...
 
template<typename MT , bool SO>
MT & blaze::operator>>= (DenseMatrix< MT, SO > &mat, int count)
 Right-shift assignment operator for the uniform right-shift of a dense matrix. More...
 
template<typename MT , bool SO>
MT & blaze::operator>>= (DenseMatrix< MT, SO > &&mat, int count)
 Right-shift assignment operator for the uniform right-shift of a temporary dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator>>= (DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Right-shift assignment operator for the elementwise right-shift of a dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator>>= (DenseMatrix< MT1, SO1 > &&lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Right-shift assignment operator for the elementwise right-shift of a temporary dense. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator&= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Bitwise AND assignment operator for the bitwise AND of a dense matrix and a scalar value. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator&= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Bitwise AND assignment operator for the bitwise AND of a temporary dense matrix and a scalar value. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator&= (DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Bitwise AND assignment operator for the bitwise AND of a dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator&= (DenseMatrix< MT1, SO1 > &&lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Bitwise AND assignment operator for the bitwise AND of a temporary dense matrix. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator|= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Bitwise OR assignment operator for the bitwise OR of a dense matrix and a scalar value. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator|= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Bitwise OR assignment operator for the bitwise OR of a temporary dense matrix and a scalar value. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator|= (DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Bitwise OR assignment operator for the bitwise OR of a dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator|= (DenseMatrix< MT1, SO1 > &&lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Bitwise OR assignment operator for the bitwise OR of a temporary dense matrix. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator^= (DenseMatrix< MT, SO > &mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Bitwise XOR assignment operator for the bitwise XOR of a dense matrix and a scalar value. More...
 
template<typename MT , bool SO, typename ST >
auto blaze::operator^= (DenseMatrix< MT, SO > &&mat, ST scalar) -> EnableIf_t< IsScalar_v< ST >, MT & >
 Bitwise XOR assignment operator for the bitwise XOR of a temporary dense matrix and a scalar value. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator^= (DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Bitwise XOR assignment operator for the bitwise XOR of a dense matrix. More...
 
template<typename MT1 , bool SO1, typename MT2 , bool SO2>
MT1 & blaze::operator^= (DenseMatrix< MT1, SO1 > &&lhs, const DenseMatrix< MT2, SO2 > &rhs)
 Bitwise XOR assignment operator for the bitwise XOR of a temporary dense matrix. More...
 
DenseMatrix functions
template<typename MT , bool SO>
bool blaze::isnan (const DenseMatrix< MT, SO > &dm)
 Checks the given dense matrix for not-a-number elements. More...
 
template<typename MT , bool SO>
bool blaze::isinf (const DenseMatrix< MT, SO > &dm)
 Checks the given dense matrix for infinite elements. More...
 
template<typename MT , bool SO>
bool blaze::isfinite (const DenseMatrix< MT, SO > &dm)
 Checks the given dense matrix for finite elements. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isSymmetric (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is symmetric. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isHermitian (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is Hermitian. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isUniform (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a uniform matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isZero (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a zero matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isLower (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a lower triangular matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isUniLower (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a lower unitriangular matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isStrictlyLower (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a strictly lower triangular matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isUpper (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is an upper triangular matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isUniUpper (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is an upper unitriangular matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isStrictlyUpper (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a strictly upper triangular matrix. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isDiagonal (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is diagonal. More...
 
template<RelaxationFlag RF, typename MT , bool SO>
bool blaze::isIdentity (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is an identity matrix. More...
 
template<typename MT , bool SO>
bool blaze::isPositiveDefinite (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a positive definite matrix. More...
 
template<typename MT , bool SO>
size_t blaze::rank (const DenseMatrix< MT, SO > &dm)
 Computes the rank of the given dense matrix. More...
 

Detailed Description

Header file for utility functions for dense matrices.

Copyright (C) 2012-2020 Klaus Iglberger - All Rights Reserved

This file is part of the Blaze library. You can redistribute it and/or modify it under the terms of the New (Revised) BSD License. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the names of the Blaze development group nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.