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// ************************************************************************
//
// Intrepid Package
// Copyright (2007) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// 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 name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "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 SANDIA CORPORATION OR THE
// 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.
//
// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
// Denis Ridzal (dridzal@sandia.gov), or
// Kara Peterson (kjpeter@sandia.gov)
//
// ************************************************************************
// @HEADER
/** \file Intrepid_RealSpaceTools.hpp
\brief Header file for classes providing basic linear algebra functionality in 1D, 2D and 3D.
\author Created by P. Bochev and D. Ridzal.
*/
#ifndef INTREPID_REALSPACETOOLS_HPP
#define INTREPID_REALSPACETOOLS_HPP
#include "Intrepid_ConfigDefs.hpp"
#include "Intrepid_Types.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_Assert.hpp"
#include <KokkosRank.hpp>
#ifdef HAVE_INTREPID_KOKKOSCORE
#include "Kokkos_Core.hpp"
#endif
namespace Intrepid {
/** \class Intrepid::RealSpaceTools
\brief Implementation of basic linear algebra functionality in Euclidean space.
*/
template<class Scalar>
class RealSpaceTools {
public:
/** \brief Computes absolute value of contiguous input data <b><var>inArray</var></b>
of size <b><var>size</var></b>.
\param absArray [out] - output data
\param inArray [in] - input data
\param size [in] - size
*/
static void absval(Scalar* absArray, const Scalar* inArray, const int size);
/** \brief Computes absolute value of contiguous data <b><var>inoutAbsArray</var></b>
of size <b><var>size</var></b> in place.
\param inoutAbsArray [in/out] - input/output data
\param size [in] - size
*/
static void absval(Scalar* inoutArray, const int size);
/** \brief Computes absolute value of an array.
\param outArray [out] - output array
\param inArray [in] - input array
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>absArray</var></b>) == rank(<b><var>inArray</var></b>)
\li dimensions(<b><var>absArray</var></b>) == dimensions(<b><var>inArray</var></b>)
*/
template<class ArrayAbs, class ArrayIn>
static void absval(ArrayAbs & absArray, const ArrayIn & inArray);
/** \brief Computes, in place, absolute value of an array.
\param inoutAbsArray [in/out] - input/output array
*/
template<class ArrayInOut>
static void absval(ArrayInOut & inoutAbsArray);
/** \brief Computes norm (1, 2, infinity) of the vector <b><var>inVec</var></b>
of size <b><var>dim</var></b>.
\param inVec [in] - vector
\param dim [in] - vector dimension
\param normType [in] - norm type
*/
static Scalar vectorNorm(const Scalar* inVec, const size_t dim, const ENorm normType);
/** \brief Computes norm (1, 2, infinity) of a single vector stored in
an array of rank 1.
\param inVec [in] - array representing a single vector
\param normType [in] - norm type
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>inVec</var></b>) == 1
*/
template<class ArrayIn>
static Scalar vectorNorm(const ArrayIn & inVec, const ENorm normType);
/** \brief Computes norms (1, 2, infinity) of vectors stored in a
array of total rank 2 (array of vectors), indexed by (i0, D),
or 3 (array of arrays of vectors), indexed by (i0, i1, D).
\param normArray [out] - norm array indexed by (i0) or (i0, i1)
\param inVecs [in] - array of vectors indexed by (i0, D) or (i0, i1, D)
\param normType [in] - norm type
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>normArray</var></b>) == rank(<b><var>inVecs</var></b>) - 1
\li rank(<b><var>inVecs</var></b>) == 2 or 3
\li dimensions i0, i1 of <b><var>normArray</var></b> and <b><var>inVecs</var></b> must agree
*/
template<class ArrayNorm, class ArrayIn>
static void vectorNorm(ArrayNorm & normArray, const ArrayIn & inVecs, const ENorm normType);
/* template<class ArrayNorm, class ArrayIn>
static void vectorNormTemp(ArrayNorm & normArray, const ArrayIn & inVecs, const ENorm normType);
*/
/** \brief Computes transpose of the square matrix <b><var>inMat</var></b>
of size <b><var>dim</var></b> by <b><var>dim</var></b>.
\param transposeMat [out] - matrix transpose
\param inMat [in] - matrix
\param dim [in] - matrix dimension
*/
static void transpose(Scalar* transposeMat, const Scalar* inMat, const size_t dim);
/* template<class ArrayTranspose, class ArrayIn>
static void transpose(ArrayTranspose transposeMat, const ArrayIn inMat, const size_t dim);*/
/** \brief Computes transposes of square matrices stored in
an array of total rank 2 (single matrix), indexed by (D, D),
3 (array of matrices), indexed by (i0, D, D),
or 4 (array of arrays of matrices), indexed by (i0, i1, D, D).
\param transposeMats [out] - array of transposes indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
\param inMats [in] - array of matrices indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>transposeMats</var></b>) == rank(<b><var>inMats</var></b>)
\li rank(<b><var>inMats</var></b>) == 3 or 4
\li dimensions(<b><var>transposeMats</var></b>) == dimensions(<b><var>inMats</var></b>)
\li matrices must be square
*/
template<class ArrayTranspose, class ArrayIn>
static void transpose(ArrayTranspose & transposeMats, const ArrayIn & inMats);
/* template<class ArrayTranspose, class ArrayIn>
static void transposeTemp(ArrayTranspose & transposeMats, const ArrayIn & inMats);*/
/** \brief Computes inverse of the square matrix <b><var>inMat</var></b>
of size <b><var>dim</var></b> by <b><var>dim</var></b>.
\param inverseMat [out] - matrix inverse
\param inMat [in] - matrix
\param dim [in] - matrix dimension
*/
static void inverse(Scalar* inverseMat, const Scalar* inMat, const size_t dim);
/** \brief Computes inverses of nonsingular matrices stored in
an array of total rank 2 (single matrix), indexed by (D, D),
3 (array of matrices), indexed by (i0, D, D),
or 4 (array of arrays of matrices), indexed by (i0, i1, D, D).
\param inverseMats [out] - array of inverses indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
\param inMats [in] - array of matrices indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>inverseMats</var></b>) == rank(<b><var>inMats</var></b>)
\li rank(<b><var>inMats</var></b>) == 3 or 4
\li dimensions(<b><var>inverseMats</var></b>) == dimensions(<b><var>inMats</var></b>)
\li matrices must be square
\li matrix dimensions are limited to 1, 2, and 3
*/
template<class ArrayInverse, class ArrayIn>
static void inverse(ArrayInverse & inverseMats, const ArrayIn & inMats);
static Scalar det(const Scalar* inMat, const size_t dim);
/** \brief Computes determinant of a single square matrix stored in
an array of rank 2.
\param inMat [in] - array representing a single matrix, indexed by (D, D)
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>inMats</var></b>) == 2
\li matrix dimension is limited to 1, 2, and 3
*/
template<class ArrayIn>
static Scalar det(const ArrayIn & inMat);
/** \brief Computes determinants of matrices stored in
an array of total rank 3 (array of matrices),
indexed by (i0, D, D), or 4 (array of arrays of matrices),
indexed by (i0, i1, D, D).
\param detArray [out] - array of determinants indexed by (i0) or (i0, i1)
\param inMats [in] - array of matrices indexed by (i0, D, D) or (i0, i1, D, D)
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>detArray</var></b>) == rank(<b><var>inMats</var></b>) - 2
\li rank(<b><var>inMats</var></b>) == 3 or 4
\li dimensions i0, i1 of <b><var>detArray</var></b> and <b><var>inMats</var></b> must agree
\li matrix dimensions are limited to 1, 2, and 3
*/
template<class ArrayDet, class ArrayIn>
static void det(ArrayDet & detArray, const ArrayIn & inMats);
/* #ifdef HAVE_INTREPID_KOKKOSCORE
template<class ArrayDet, class ArrayIn>
static void detTemp(ArrayDet & inverseMats, const ArrayIn & inMats);
#endif
*/
template<class ArrayDet, class ArrayIn, int matRank>
struct detTempSpec;
/** \brief Adds contiguous data <b><var>inArray1</var></b> and <b><var>inArray2</var></b>
of size <b><var>size</var></b>:\n
<b><var>sumArray</var></b> = <b><var>inArray1</var></b> + <b><var>inArray2</var></b>.
\param sumArray [out] - sum
\param inArray1 [in] - first summand
\param inArray2 [in] - second summand
\param size [in] - size of input/output data
*/
static void add(Scalar* sumArray, const Scalar* inArray1, const Scalar* inArray2, const int size);
/** \brief Adds, in place, contiguous data <b><var>inArray</var></b> into
<b><var>inoutSumArray</var></b> of size <b><var>size</var></b>:\n
<b><var>inoutSumArray</var></b> = <b><var>inoutSumArray</var></b> + <b><var>inArray</var></b>.
\param inoutSumArray [in/out] - sum / first summand
\param inArray [in] - second summand
\param size [in] - size of input/output data
*/
static void add(Scalar* inoutSumArray, const Scalar* inArray, const int size);
/** \brief Adds arrays <b><var>inArray1</var></b> and <b><var>inArray2</var></b>:\n
<b><var>sumArray</var></b> = <b><var>inArray1</var></b> + <b><var>inArray2</var></b>.
\param sumArray [out] - sum
\param inArray1 [in] - first summand
\param inArray2 [in] - second summand
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>sumArray</var></b>) == rank(<b><var>inArray1</var></b>) == rank(<b><var>inArray2</var></b>)
\li dimensions(<b><var>sumArray</var></b>) == dimensions(<b><var>inArray1</var></b>) == dimensions(<b><var>inArray2</var></b>)
*/
template<class ArraySum, class ArrayIn1, class ArrayIn2>
static void add(ArraySum & sumArray, const ArrayIn1 & inArray1, const ArrayIn2 & inArray2);
/** \brief Adds, in place, <b><var>inArray</var></b> into <b><var>inoutSumArray</var></b>:\n
<b><var>inoutSumArray</var></b> = <b><var>inoutSumArray</var></b> + <b><var>inArray</var></b>.
\param inoutSumArray [in/out] - sum/first summand
\param inArray [in] - second summand
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>inoutSumArray</var></b>) == rank(<b><var>inArray</var></b>)
\li dimensions(<b><var>inoutSumArray</var></b>) == dimensions(<b><var>inArray</var></b>)
*/
template<class ArraySum, class ArrayIn>
static void add(ArraySum & inoutSumArray, const ArrayIn & inArray);
/** \brief Subtracts contiguous data <b><var>inArray2</var></b> from <b><var>inArray1</var></b>
of size <b><var>size</var></b>:\n
<b><var>diffArray</var></b> = <b><var>inArray1</var></b> - <b><var>inArray2</var></b>.
\param diffArray [out] - difference
\param inArray1 [in] - minuend
\param inArray2 [in] - subtrahend
\param size [in] - size of input/output data
*/
static void subtract(Scalar* diffArray, const Scalar* inArray1, const Scalar* inArray2, const int size);
/** \brief Subtracts, in place, contiguous data <b><var>inArray</var></b> from
<b><var>inoutDiffArray</var></b> of size <b><var>size</var></b>:\n
<b><var>inoutDiffArray</var></b> = <b><var>inoutDiffArray</var></b> - <b><var>inArray</var></b>.
\param inoutDiffArray [in/out] - difference/minuend
\param inArray [in] - subtrahend
\param size [in] - size of input/output data
*/
static void subtract(Scalar* inoutDiffArray, const Scalar* inArray, const int size);
/** \brief Subtracts <b><var>inArray2</var></b> from <b><var>inArray1</var></b>:\n
<b><var>diffArray</var></b> = <b><var>inArray1</var></b> - <b><var>inArray2</var></b>.
\param diffArray [out] - difference
\param inArray1 [in] - minuend
\param inArray2 [in] - subtrahend
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>sumArray</var></b>) == rank(<b><var>inArray1</var></b>) == rank(<b><var>inArray2</var></b>)
\li dimensions(<b><var>sumArray</var></b>) == dimensions(<b><var>inArray1</var></b>) == dimensions(<b><var>inArray2</var></b>)
*/
template<class ArrayDiff, class ArrayIn1, class ArrayIn2>
static void subtract(ArrayDiff & diffArray, const ArrayIn1 & inArray1, const ArrayIn2 & inArray2);
/** \brief Subtracts, in place, <b><var>inArray</var></b> from <b><var>inoutDiffArray</var></b>:\n
<b><var>inoutDiffArray</var></b> = <b><var>inoutDiffArray</var></b> - <b><var>inArray</var></b>.
\param inoutDiffArray [in/out] - difference/minuend
\param inArray [in] - subtrahend
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>inoutDiffArray</var></b>) == rank(<b><var>inArray</var></b>)
\li dimensions(<b><var>inoutDiffArray</var></b>) == dimensions(<b><var>inArray</var></b>)
*/
template<class ArrayDiff, class ArrayIn>
static void subtract(ArrayDiff & inoutDiffArray, const ArrayIn & inArray);
template<class ArrayDiff, class ArrayIn>
static void subtractTemp(ArrayDiff & inoutDiffArray, const ArrayIn & inArray);
/** \brief Multiplies contiguous data <b><var>inArray</var></b> of size
<b><var>size</var></b> by a scalar (componentwise):\n
<b><var>scaledArray</var></b> = <b><var>scalar</var></b> * <b><var>inArray</var></b>.
\param scaledArray [out] - scaled array
\param inArray [in] - input array
\param size [in] - size of the input array
\param scalar [in] - multiplier
*/
static void scale(Scalar* scaledArray, const Scalar* inArray, const int size, const Scalar scalar);
/** \brief Multiplies, in place, contiguous data <b><var>inoutScaledArray</var></b> of size
<b><var>size</var></b> by a scalar (componentwise):\n
<b><var>inoutScaledArray</var></b> = <b><var>scalar</var></b> * <b><var>inoutScaledArray</var></b>.
\param inoutScaledArray [in/out] - input/scaled array
\param size [in] - size of array
\param scalar [in] - multiplier
*/
static void scale(Scalar* inoutScaledArray, const int size, const Scalar scalar);
/** \brief Multiplies array <b><var>inArray</var></b> by the scalar <b><var>scalar</var></b> (componentwise):\n
<b><var>scaledArray</var></b> = <b><var>scalar</var></b> * <b><var>inArray</var></b>.
\param scaledArray [out] - scaled array
\param inArray [in] - input array
\param scalar [in] - multiplier
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>scaledArray</var></b>) == rank(<b><var>inArray</var></b>)
\li dimensions(<b><var>scaledArray</var></b>) == dimensions(<b><var>inArray</var></b>)
*/
template<class ArrayScaled, class ArrayIn>
static void scale(ArrayScaled & scaledArray, const ArrayIn & inArray, const Scalar scalar);
/** \brief Multiplies, in place, array <b><var>inoutScaledArray</var></b> by the scalar <b><var>scalar</var></b> (componentwise):\n
<b><var>inoutScaledArray</var></b> = <b><var>scalar</var></b> * <b><var>inoutScaledArray</var></b>.
\param inoutScaledArray [in/out] - input/output array
\param scalar [in] - multiplier
*/
template<class ArrayScaled>
static void scale(ArrayScaled & inoutScaledArray, const Scalar scalar);
/** \brief Computes dot product of contiguous data <b><var>inArray1</var></b> and <b><var>inArray2</var></b>
of size <b><var>size</var></b>.
\param inArray1 [in] - first array
\param inArray2 [in] - second array
\param size [in] - size of input arrays
*/
static Scalar dot(const Scalar* inArray1, const Scalar* inArray2, const int size);
/** \brief Computes dot product of two vectors stored in
arrays of rank 1.
\param inVec1 [in] - first vector
\param inVec2 [in] - second vector
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>inVec1</var></b>) == rank(<b><var>inVec2</var></b>) == 1
\li <b><var>inVec1</var></b> and <b><var>inVec2</var></b> have same dimension
*/
template<class ArrayVec1, class ArrayVec2>
static Scalar dot(const ArrayVec1 & inVec1, const ArrayVec2 & inVec2);
/** \brief Computes dot product of vectors stored in an
array of total rank 2 (array of vectors), indexed by (i0, D),
or 3 (array of arrays of vectors), indexed by (i0, i1, D).
\param dotArray [out] - dot product array indexed by (i0) or (i0, i1)
\param inVecs1 [in] - first array of vectors indexed by (i0, D) or (i0, i1, D)
\param inVecs2 [in] - second array of vectors indexed by (i0, D) or (i0, i1, D)
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>dotArray</var></b>) == rank(<b><var>inVecs1</var></b>) - 1 == rank(<b><var>inVecs2</var></b>) - 1
\li rank(<b><var>inVecs1</var></b>) == 2 or 3
\li dimensions i0, i1 of <b><var>dotArray</var></b> and <b><var>inVecs1</var></b> / <b><var>inVecs2</var></b> must agree
*/
template<class ArrayDot, class ArrayVec1, class ArrayVec2>
static void dot(ArrayDot & dotArray, const ArrayVec1 & inVecs1, const ArrayVec2 & inVecs2);
/** \brief Matrix-vector left multiply using contiguous data:\n
<b><var>matVec</var></b> = <b><var>inMat</var></b> * <b><var>inVec</var></b>.
A single "column" vector <b><var>inVec</var></b> of size <b><var>dim</var></b> is
multiplied on the left by a square matrix <b><var>inMat</var></b> of size
<b><var>dim</var></b> by <b><var>dim</var></b>.
\param matVec [out] - matrix-vector product
\param inMat [in] - the matrix argument
\param inVec [in] - the vector argument
\param dim [in] - matrix/vector dimension
*/
static void matvec(Scalar* matVec, const Scalar* inMat, const Scalar* inVec, const size_t dim);
/** \brief Matrix-vector left multiply using multidimensional arrays:\n
<b><var>matVec</var></b> = <b><var>inMat</var></b> * <b><var>inVec</var></b>.
An array (rank 1, 2 or 3) of "column" vectors, indexed by
(D), (i0, D) or (i0, i1, D), is multiplied on the left by an
array (rank 2, 3 or 4) of square matrices, indexed by (D, D),
(i0, D, D) or (i0, i1, D, D).
\param matVec [out] - matrix-vector product indexed by (D), (i0, D) or (i0, i1, D)
\param inMat [in] - the matrix argument indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
\param inVec [in] - the vector argument indexed by (D), (i0, D) or (i0, i1, D)
\note Requirements (checked at runtime, in debug mode): \n
\li rank(<b><var>matVec</var></b>) == rank(<b><var>inVec</var></b>) == rank(<b><var>inMat</var></b>) - 1
\li dimensions(<b><var>matVec</var></b>) == dimensions(<b><var>inVec</var></b>)
\li matrix and vector dimensions D, i0 and i1 must agree
\li matrices are square
*/
template<class ArrayMatVec, class ArrayMat, class ArrayVec>
static void matvec(ArrayMatVec & matVecs, const ArrayMat & inMats, const ArrayVec & inVecs);
/** \brief Vector product using multidimensional arrays:\n
<b><var>vecProd</var></b> = <b><var>inVecLeft</var></b> x <b><var>inVecRight</var></b>
Vector multiplication of two "column" vectors stored in arrays (rank 1, 2, or 3)
indexed by (D), (i0, D) or (i0, i1, D).
\param vecProd [in] - vector product indexed by (D), (i0, D) or (i0, i1, D)
\param inLeft [in] - left vector argument indexed by (D), (i0, D) or (i0, i1, D)
\param inRight [in] - right vector argument indexed by (D), (i0, D) or (i0, i1, D)
\todo Need to decide on how to handle vecprod in 2D: is the result a vector, i.e.,
there's dimension D or a scalar?
*/
template<class ArrayVecProd, class ArrayIn1, class ArrayIn2>
static void vecprod(ArrayVecProd & vecProd, const ArrayIn1 & inLeft, const ArrayIn2 & inRight);
/* template<class ArrayVecProd, class ArrayIn1, class ArrayIn2>
static void vecprodTemp(ArrayVecProd & vecProd, const ArrayIn1 & inLeft, const ArrayIn2 & inRight); */
}; // class RealSpaceTools
} // end namespace Intrepid
// include templated definitions
#include <Intrepid_RealSpaceToolsDef.hpp>
//#include <Intrepid_RealSpaceToolsDef_Kokkos.hpp>
#endif
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