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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.
//
// This library is free software; you can 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.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact Pavel Bochev (pbboche@sandia.gov) or
// Denis Ridzal (dridzal@sandia.gov).
//
// ************************************************************************
// @HEADER
/** \file Intrepid_ArrayTools.hpp
\brief Header file for utility class to provide array tools,
such as tensor contractions, etc.
\author Created by P. Bochev and D. Ridzal.
*/
#ifndef INTREPID_ARRAYTOOLS_HPP
#define INTREPID_ARRAYTOOLS_HPP
#include "Intrepid_ConfigDefs.hpp"
#include "Intrepid_Types.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_TestForException.hpp"
namespace Intrepid {
/** \class Intrepid::ArrayTools
\brief Utility class that provides methods for higher-order algebraic
manipulation of user-defined arrays, such as tensor contractions.
For low-order operations, see Intrepid::RealSpaceTools.
*/
class ArrayTools {
public:
/** \brief Contracts the "point" dimension P of two rank-3 containers with
dimensions (C,L,P) and (C,R,P), and returns the result in a
rank-3 container with dimensions (C,L,R).
For a fixed index "C", (C,L,R) represents a rectangular L X R matrix
where L and R may be different.
\code
C - num. integration domains dim0 in both input containers
L - num. "left" fields dim1 in "left" container
R - num. "right" fields dim1 in "right" container
P - num. integration points dim2 in both input containers
\endcode
\param outputFields [out] - Output array.
\param leftFields [in] - Left input array.
\param rightFields [in] - Right input array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInFieldsLeft, class ArrayInFieldsRight>
static void contractFieldFieldScalar(ArrayOutFields & outputFields,
const ArrayInFieldsLeft & leftFields,
const ArrayInFieldsRight & rightFields,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" and "space" dimensions P and D1 of two rank-4
containers with dimensions (C,L,P,D1) and (C,R,P,D1), and returns the
result in a rank-3 container with dimensions (C,L,R).
For a fixed index "C", (C,L,R) represents a rectangular L X R matrix
where L and R may be different.
\code
C - num. integration domains dim0 in both input containers
L - num. "left" fields dim1 in "left" container
R - num. "right" fields dim1 in "right" container
P - num. integration points dim2 in both input containers
D1- vector dimension dim3 in both input containers
\endcode
\param outputFields [out] - Output array.
\param leftFields [in] - Left input array.
\param rightFields [in] - Right input array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInFieldsLeft, class ArrayInFieldsRight>
static void contractFieldFieldVector(ArrayOutFields & outputFields,
const ArrayInFieldsLeft & leftFields,
const ArrayInFieldsRight & rightFields,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" and "space" dimensions P, D1, and D2 of two rank-5
containers with dimensions (C,L,P,D1,D2) and (C,R,P,D1,D2), and returns
the result in a rank-3 container with dimensions (C,L,R).
For a fixed index "C", (C,L,R) represents a rectangular L X R matrix
where L and R may be different.
\code
C - num. integration domains dim0 in both input containers
L - num. "left" fields dim1 in "left" container
R - num. "right" fields dim1 in "right" container
P - num. integration points dim2 in both input containers
D1- vector dimension dim3 in both input containers
D2- 2nd tensor dimension dim4 in both input containers
\endcode
\param outputFields [out] - Output array.
\param leftFields [in] - Left input array.
\param rightFields [in] - Right input array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInFieldsLeft, class ArrayInFieldsRight>
static void contractFieldFieldTensor(ArrayOutFields & outputFields,
const ArrayInFieldsLeft & leftFields,
const ArrayInFieldsRight & rightFields,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" dimensions P of a rank-3 containers and
a rank-2 container with dimensions (C,F,P) and (C,P), respectively,
and returns the result in a rank-2 container with dimensions (C,F).
For a fixed index "C", (C,F) represents a (column) vector of length F.
\code
C - num. integration domains dim0 in both input containers
F - num. fields dim1 in fields input container
P - num. integration points dim2 in fields input container and dim1 in scalar data container
\endcode
\param outputFields [out] - Output fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void contractDataFieldScalar(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" and "space" dimensions P and D of a rank-4 container and
a rank-3 container with dimensions (C,F,P,D) and (C,P,D), respectively,
and returns the result in a rank-2 container with dimensions (C,F).
For a fixed index "C", (C,F) represents a (column) vector of length F.
\code
C - num. integration domains dim0 in both input containers
F - num. fields dim1 in fields input container
P - num. integration points dim2 in fields input container and dim1 in vector data container
D - spatial (vector) dimension index dim3 in fields input container and dim2 in vector data container
\endcode
\param outputFields [out] - Output fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void contractDataFieldVector(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" and "space" dimensions P, D1 and D2 of a rank-5 container and
a rank-4 container with dimensions (C,F,P,D1,D2) and (C,P,D1,D2), respectively,
and returns the result in a rank-2 container with dimensions (C,F).
For a fixed index "C", (C,F) represents a (column) vector of length F.
\code
C - num. integration domains dim0 in both input containers
F - num. fields dim1 in fields input container
P - num. integration points dim2 in fields input container and dim1 in tensor data container
D1 - first spatial (tensor) dimension index dim3 in fields input container and dim2 in tensor data container
D2 - second spatial (tensor) dimension index dim4 in fields input container and dim3 in tensor data container
\endcode
\param outputFields [out] - Output fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void contractDataFieldTensor(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" dimensions P of rank-2 containers
with dimensions (C,P), and returns the result in a rank-1 container
with dimensions (C).
\code
C - num. integration domains dim0 in both input containers
P - num. integration points dim1 in both input containers
\endcode
\param outputData [out] - Output data array.
\param inputDataLeft [in] - Left data input array.
\param inputDataRight [in] - Right data input array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void contractDataDataScalar(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" and "space" dimensions P and D of rank-3 containers
with dimensions (C,P,D) and returns the result in a rank-1 container with dimensions (C).
\code
C - num. integration domains dim0 in both input containers
P - num. integration points dim1 in both input containers
D - spatial (vector) dimension index dim2 in both input containers
\endcode
\param outputData [out] - Output data array.
\param inputDataLeft [in] - Left data input array.
\param inputDataRight [in] - Right data input array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void contractDataDataVector(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief Contracts the "point" and "space" dimensions P, D1 and D2 of rank-4 containers
with dimensions (C,P,D1,D2) and returns the result in a rank-1 container with dimensions (C).
\code
C - num. integration domains dim0 in both input containers
P - num. integration points dim1 in both input containers
D1 - first spatial (tensor) dimension index dim2 in both input containers
D2 - second spatial (tensor) dimension index dim3 in both input containers
\endcode
\param outputData [out] - Output data array.
\param inputDataLeft [in] - Left data input array.
\param inputDataRight [in] - Right data input array.
\param compEngine [in] - Computational engine.
\param sumInto [in] - If TRUE, sum into given output array,
otherwise overwrite it. Default: FALSE.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void contractDataDataTensor(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight,
const ECompEngine compEngine,
const bool sumInto = false);
/** \brief There are two use cases:
(1) multiplies a rank-3, 4, or 5 container \a <b>inputFields</b> with dimensions (C,F,P),
(C,F,P,D1) or (C,F,P,D1,D2), representing the values of a set of scalar, vector
or tensor fields, by the values in a rank-2 container \a <b>inputData</b> indexed by (C,P),
representing the values of scalar data, OR
(2) multiplies a rank-2, 3, or 4 container \a <b>inputFields</b> with dimensions (F,P),
(F,P,D1) or (F,P,D1,D2), representing the values of a scalar, vector or a
tensor field, by the values in a rank-2 container \a <b>inputData</b> indexed by (C,P),
representing the values of scalar data;
the output value container \a <b>outputFields</b> is indexed by (C,F,P), (C,F,P,D1)
or (C,F,P,D1,D2), regardless of which of the two use cases is considered.
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\note The argument <var><b>inputFields</b></var> can be changed!
This enables in-place multiplication.
\param outputFields [out] - Output (product) fields array.
\param inputData [in] - Data (multiplying) array.
\param inputFields [in] - Input (being multiplied) fields array.
\param reciprocal [in] - If TRUE, <b>divides</b> input fields by the data
(instead of multiplying). Default: FALSE.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void scalarMultiplyDataField(ArrayOutFields & outputFields,
const ArrayInData & inputData,
ArrayInFields & inputFields,
const bool reciprocal = false);
/** \brief There are two use cases:
(1) multiplies a rank-2, 3, or 4 container \a <b>inputDataRight</b> with dimensions (C,P),
(C,P,D1) or (C,P,D1,D2), representing the values of a set of scalar, vector
or tensor data, by the values in a rank-2 container \a <b>inputDataLeft</b> indexed by (C,P),
representing the values of scalar data, OR
(2) multiplies a rank-1, 2, or 3 container \a <b>inputDataRight</b> with dimensions (P),
(P,D1) or (P,D1,D2), representing the values of scalar, vector or
tensor data, by the values in a rank-2 container \a <b>inputDataLeft</b> indexed by (C,P),
representing the values of scalar data;
the output value container \a <b>outputData</b> is indexed by (C,P), (C,P,D1) or (C,P,D1,D2),
regardless of which of the two use cases is considered.
\code
C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\note The arguments <var><b>inputDataLeft</b></var>, <var><b>inputDataRight</b></var> can be changed!
This enables in-place multiplication.
\param outputData [out] - Output data array.
\param inputDataLeft [in] - Left (multiplying) data array.
\param inputDataRight [in] - Right (being multiplied) data array.
\param reciprocal [in] - If TRUE, <b>divides</b> input fields by the data
(instead of multiplying). Default: FALSE.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void scalarMultiplyDataData(ArrayOutData & outputData,
ArrayInDataLeft & inputDataLeft,
ArrayInDataRight & inputDataRight,
const bool reciprocal = false);
/** \brief There are two use cases:
(1) dot product of a rank-3, 4 or 5 container \a <b>inputFields</b> with dimensions (C,F,P)
(C,F,P,D1) or (C,F,P,D1,D2), representing the values of a set of scalar, vector
or tensor fields, by the values in a rank-2, 3 or 4 container \a <b>inputData</b> indexed by
(C,P), (C,P,D1), or (C,P,D1,D2) representing the values of scalar, vector or
tensor data, OR
(2) dot product of a rank-2, 3 or 4 container \a <b>inputFields</b> with dimensions (F,P),
(F,P,D1) or (F,P,D1,D2), representing the values of a scalar, vector or tensor
field, by the values in a rank-2 container \a <b>inputData</b> indexed by (C,P), (C,P,D1) or
(C,P,D1,D2), representing the values of scalar, vector or tensor data;
the output value container \a <b>outputFields</b> is indexed by (C,F,P),
regardless of which of the two use cases is considered.
For input fields containers without a dimension index, this operation reduces to
scalar multiplication.
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param outputFields [out] - Output (dot product) fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void dotMultiplyDataField(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields);
/** \brief There are two use cases:
(1) dot product of a rank-2, 3 or 4 container \a <b>inputDataRight</b> with dimensions (C,P)
(C,P,D1) or (C,P,D1,D2), representing the values of a scalar, vector or a
tensor set of data, by the values in a rank-2, 3 or 4 container \a <b>inputDataLeft</b> indexed by
(C,P), (C,P,D1), or (C,P,D1,D2) representing the values of scalar, vector or
tensor data, OR
(2) dot product of a rank-2, 3 or 4 container \a <b>inputDataRight</b> with dimensions (P),
(P,D1) or (P,D1,D2), representing the values of scalar, vector or tensor
data, by the values in a rank-2 container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D1) or
(C,P,D1,D2), representing the values of scalar, vector, or tensor data;
the output value container \a <b>outputData</b> is indexed by (C,P),
regardless of which of the two use cases is considered.
For input fields containers without a dimension index, this operation reduces to
scalar multiplication.
\code
C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param outputData [out] - Output (dot product) data array.
\param inputDataLeft [in] - Left input data array.
\param inputDataRight [in] - Right input data array.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void dotMultiplyDataData(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight);
/** \brief There are two use cases:
(1) cross product of a rank-4 container \a <b>inputFields</b> with dimensions (C,F,P,D),
representing the values of a set of vector fields, on the left by the values in a rank-3
container \a <b>inputData</b> indexed by (C,P,D), representing the values of vector data, OR
(2) cross product of a rank-3 container \a <b>inputFields</b> with dimensions (F,P,D),
representing the values of a vector field, on the left by the values in a rank-3 container
\a <b>inputData</b> indexed by (C,P,D), representing the values of vector data;
the output value container \a <b>outputFields</b> is indexed by (C,F,P,D) in 3D (vector output)
and by (C,F,P) in 2D (scalar output), regardless of which of the two use cases is considered.
\code
C - num. integration domains
F - num. fields
P - num. integration points
D - spatial dimension of vector data and vector fields
\endcode
\param outputFields [out] - Output (cross product) fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void crossProductDataField(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields);
/** \brief There are two use cases:
(1) cross product of a rank-3 container \a <b>inputDataRight</b> with dimensions (C,P,D),
representing the values of a set of vector data, on the left by the values in a rank-3
container \a <b>inputDataLeft</b> indexed by (C,P,D) representing the values of vector data, OR
(2) cross product of a rank-2 container \a <b>inputDataRight</b> with dimensions (P,D),
representing the values of vector data, on the left by the values in a rank-3 container
\a <b>inputDataLeft</b> indexed by (C,P,D), representing the values of vector data;
the output value container \a <b>outputData</b> is indexed by (C,P,D) in 3D (vector output) and by
(C,P) in 2D (scalar output), regardless of which of the two use cases is considered.
\code
C - num. integration domains
P - num. integration points
D - spatial dimension of vector data and vector fields
\endcode
\param outputData [out] - Output (cross product) data array.
\param inputDataLeft [in] - Left input data array.
\param inputDataRight [in] - Right input data array.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void crossProductDataData(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight);
/** \brief There are two use cases:
(1) outer product of a rank-4 container \a <b>inputFields</b> with dimensions (C,F,P,D),
representing the values of a set of vector fields, on the left by the values in a rank-3
container \a <b>inputData</b> indexed by (C,P,D), representing the values of vector data, OR
(2) outer product of a rank-3 container \a <b>inputFields</b> with dimensions (F,P,D),
representing the values of a vector field, on the left by the values in a rank-3 container
\a <b>inputData</b> indexed by (C,P,D), representing the values of vector data;
the output value container \a <b>outputFields</b> is indexed by (C,F,P,D,D),
regardless of which of the two use cases is considered.
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param outputFields [out] - Output (outer product) fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void outerProductDataField(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields);
/** \brief There are two use cases:
(1) outer product of a rank-3 container \a <b>inputDataRight</b> with dimensions (C,P,D),
representing the values of a set of vector data, on the left by the values in a rank-3
container \a <b>inputDataLeft</b> indexed by (C,P,D) representing the values of vector data, OR
(2) outer product of a rank-2 container \a <b>inputDataRight</b> with dimensions (P,D),
representing the values of vector data, on the left by the values in a rank-3 container
\a <b>inputDataLeft</b> indexed by (C,P,D), representing the values of vector data;
the output value container \a <b>outputData</b> is indexed by (C,P,D,D),
regardless of which of the two use cases is considered.
\code
C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param outputData [out] - Output (outer product) data array.
\param inputDataLeft [in] - Left input data array.
\param inputDataRight [in] - Right input data array.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void outerProductDataData(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight);
/** \brief There are two use cases:
(1) matrix-vector product of a rank-4 container \a <b>inputFields</b> with dimensions (C,F,P,D),
representing the values of a set of vector fields, on the left by the values in a rank-2, 3, or 4
container \a <b>inputData</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data, OR
(2) matrix-vector product of a rank-3 container \a <b>inputFields</b> with dimensions (F,P,D),
representing the values of a vector field, on the left by the values in a rank-2, 3, or 4
container \a <b>inputData</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data; the output value container \a <b>outputFields</b> is
indexed by (C,F,P,D), regardless of which of the two use cases is considered.
\remarks
The rank of <b>inputData</b> implicitly defines the type of tensor data:
\li rank = 2 corresponds to a constant diagonal tensor \f$ diag(a,\ldots,a) \f$
\li rank = 3 corresponds to a nonconstant diagonal tensor \f$ diag(a_1,\ldots,a_d) \f$
\li rank = 4 corresponds to a full tensor \f$ \{a_{ij}\}\f$
\note It is assumed that all tensors are square!
\note The method is defined for spatial dimensions D = 1, 2, 3
\code
C - num. integration domains
F - num. fields
P - num. integration points
D - spatial dimension
D1* - first tensor dimensions, equals the spatial dimension D
D2** - second tensor dimension, equals the spatial dimension D
\endcode
\param outputFields [out] - Output (matrix-vector product) fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
\param transpose [in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void matvecProductDataField(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields,
const char transpose = 'N');
/** \brief There are two use cases:
(1) matrix-vector product of a rank-3 container \a <b>inputDataRight</b> with dimensions (C,P,D),
representing the values of a set of vector data, on the left by the values in a rank-2, 3, or 4
container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data, OR
(2) matrix-vector product of a rank-2 container \a <b>inputDataRight</b> with dimensions (P,D),
representing the values of vector data, on the left by the values in a rank-2, 3, or 4
container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data; the output value container \a <b>outputData</b>
is indexed by (C,P,D), regardless of which of the two use cases is considered.
\remarks
The rank of <b>inputDataLeft</b> implicitly defines the type of tensor data:
\li rank = 2 corresponds to a constant diagonal tensor \f$ diag(a,\ldots,a) \f$
\li rank = 3 corresponds to a nonconstant diagonal tensor \f$ diag(a_1,\ldots,a_d) \f$
\li rank = 4 corresponds to a full tensor \f$ \{a_{ij}\}\f$
\note It is assumed that all tensors are square!
\code
C - num. integration domains
P - num. integration points
D - spatial dimension
D1* - first tensor dimensions, equals the spatial dimension D
D2** - second tensor dimension, equals the spatial dimension D
\endcode
\param outputData [out] - Output (matrix-vector product) data array.
\param inputDataLeft [in] - Left input data array.
\param inputDataRight [in] - Right input data array.
\param transpose [in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void matvecProductDataData(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight,
const char transpose = 'N');
/** \brief There are two use cases:
(1) matrix-matrix product of a rank-5 container \a <b>inputFields</b> with dimensions (C,F,P,D1,D2),
representing the values of a set of tensor fields, on the left by the values in a rank-2, 3, or 4
container \a <b>inputData</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data, OR
(2) matrix-matrix product of a rank-4 container \a <b>inputFields</b> with dimensions (F,P,D1,D2),
representing the values of a tensor field, on the left by the values in a rank-2, 3, or 4
container \a <b>inputData</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data; the output value container \a <b>outputFields</b> is
indexed by (C,F,P,D1,D2), regardless of which of the two use cases is considered.
\remarks
The rank of <b>inputData</b> implicitly defines the type of tensor data:
\li rank = 2 corresponds to a constant diagonal tensor \f$ diag(a,\ldots,a) \f$
\li rank = 3 corresponds to a nonconstant diagonal tensor \f$ diag(a_1,\ldots,a_d) \f$
\li rank = 4 corresponds to a full tensor \f$ \{a_{ij}\}\f$
\note It is assumed that all tensors are square!
\note The method is defined for spatial dimensions D = 1, 2, 3
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1* - first spatial (tensor) dimension index
D2** - second spatial (tensor) dimension index
\endcode
\param outputFields [out] - Output (matrix-matrix product) fields array.
\param inputData [in] - Data array.
\param inputFields [in] - Input fields array.
\param transpose [in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.
*/
template<class Scalar, class ArrayOutFields, class ArrayInData, class ArrayInFields>
static void matmatProductDataField(ArrayOutFields & outputFields,
const ArrayInData & inputData,
const ArrayInFields & inputFields,
const char transpose = 'N');
/** \brief There are two use cases:
(1) matrix-matrix product of a rank-4 container \a <b>inputDataRight</b> with dimensions (C,P,D1,D2),
representing the values of a set of tensor data, on the left by the values in a rank-2, 3, or 4
container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data, OR
(2) matrix-matrix product of a rank-3 container \a <b>inputDataRight</b> with dimensions (P,D1,D2),
representing the values of tensor data, on the left by the values in a rank-2, 3, or 4
container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively,
representing the values of tensor data; the output value container \a <b>outputData</b>
is indexed by (C,P,D1,D2), regardless of which of the two use cases is considered.
\remarks
The rank of <b>inputData</b> implicitly defines the type of tensor data:
\li rank = 2 corresponds to a constant diagonal tensor \f$ diag(a,\ldots,a) \f$
\li rank = 3 corresponds to a nonconstant diagonal tensor \f$ diag(a_1,\ldots,a_d) \f$
\li rank = 4 corresponds to a full tensor \f$ \{a_{ij}\}\f$
\note It is assumed that all tensors are square!
\note The method is defined for spatial dimensions D = 1, 2, 3
\code
C - num. integration domains
P - num. integration points
D1* - first spatial (tensor) dimension index
D2** - second spatial (tensor) dimension index
\endcode
\param outputData [out] - Output (matrix-vector product) data array.
\param inputDataLeft [in] - Left input data array.
\param inputDataRight [in] - Right input data array.
\param transpose [in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.
*/
template<class Scalar, class ArrayOutData, class ArrayInDataLeft, class ArrayInDataRight>
static void matmatProductDataData(ArrayOutData & outputData,
const ArrayInDataLeft & inputDataLeft,
const ArrayInDataRight & inputDataRight,
const char transpose = 'N');
/** \brief Replicates a rank-2, 3, or 4 container with dimensions (F,P),
(F,P,D1) or (F,P,D1,D2), representing the values of a scalar, vector or a
tensor field, into an output value container of size (C,F,P),
(C,F,P,D1) or (C,F,P,D1,D2).
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param outputFields [out] - Output fields array.
\param inputFields [in] - Input fields array.
*/
template<class Scalar, class ArrayOutFields, class ArrayInFields>
static void cloneFields(ArrayOutFields & outputFields,
const ArrayInFields & inputFields);
/** \brief Multiplies a rank-2, 3, or 4 container with dimensions (F,P),
(F,P,D1) or (F,P,D1,D2), representing the values of a scalar, vector or a
tensor field, F-componentwise with a scalar container indexed by (C,F),
and stores the result in an output value container of size (C,F,P),
(C,F,P,D1) or (C,F,P,D1,D2).
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param outputFields [out] - Output fields array.
\param inputFactors [in] - Input field factors array.
\param inputFields [in] - Input fields array.
*/
template<class Scalar, class ArrayOutFields, class ArrayInFactors, class ArrayInFields>
static void cloneScaleFields(ArrayOutFields & outputFields,
const ArrayInFactors & inputFactors,
const ArrayInFields & inputFields);
/** \brief Multiplies, in place, a rank-2, 3, or 4 container with dimensions (C,F,P),
(C,F,P,D1) or (C,F,P,D1,D2), representing the values of a scalar, vector or a
tensor field, F-componentwise with a scalar container indexed by (C,F).
\code
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
\endcode
\param inoutFields [in/out] - Input / output fields array.
\param inputFactors [in] - Scaling field factors array.
*/
template<class Scalar, class ArrayInOutFields, class ArrayInFactors>
static void scaleFields(ArrayInOutFields & inoutFields,
const ArrayInFactors & inputFactors);
}; // end class ArrayTools
} // end namespace Intrepid
// include templated definitions
#include <Intrepid_ArrayToolsDefContractions.hpp>
#include <Intrepid_ArrayToolsDefScalar.hpp>
#include <Intrepid_ArrayToolsDefDot.hpp>
#include <Intrepid_ArrayToolsDefTensor.hpp>
#include <Intrepid_ArrayToolsDefCloneScale.hpp>
#endif
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