Intrepid
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Intrepid::ArrayTools Class Reference

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. More...

#include <Intrepid_ArrayTools.hpp>

Classes

struct  cloneFields2
 
struct  matmatProductDataDataTempSpecLeft
 
struct  matmatProductDataDataTempSpecRight
 
struct  scalarMultiplyDataData2
 There are two use cases: (1) dot product of a rank-3, 4 or 5 container inputFields 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 inputData 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 inputFields 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 inputData 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 outputFields is indexed by (C,F,P), regardless of which of the two use cases is considered. More...
 
struct  scalarMultiplyDataField2
 

Static Public Member Functions

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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
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)
 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). More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void scalarMultiplyDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields, const bool reciprocal=false)
 There are two use cases: (1) multiplies a rank-3, 4, or 5 container inputFields 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 inputData indexed by (C,P), representing the values of scalar data, OR (2) multiplies a rank-2, 3, or 4 container inputFields 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 inputData indexed by (C,P), representing the values of scalar data; the output value container outputFields 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. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void scalarMultiplyDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight, const bool reciprocal=false)
 There are two use cases: (1) multiplies a rank-2, 3, or 4 container inputDataRight 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 inputDataLeft indexed by (C,P), representing the values of scalar data, OR (2) multiplies a rank-1, 2, or 3 container inputDataRight 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 inputDataLeft indexed by (C,P), representing the values of scalar data; the output value container outputData is indexed by (C,P), (C,P,D1) or (C,P,D1,D2), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void dotMultiplyDataField (ArrayOutFields &outputFields, const ArrayInData &inputDataLeft, const ArrayInFields &inputFields)
 There are two use cases: (1) dot product of a rank-3, 4 or 5 container inputFields 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 inputData 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 inputFields 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 inputData 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 outputFields is indexed by (C,F,P), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void dotMultiplyDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight)
 There are two use cases: (1) dot product of a rank-2, 3 or 4 container inputDataRight 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 inputDataLeft 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 inputDataRight 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 inputDataLeft 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 outputData is indexed by (C,P), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void crossProductDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields)
 There are two use cases: (1) cross product of a rank-4 container inputFields 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 inputData indexed by (C,P,D), representing the values of vector data, OR (2) cross product of a rank-3 container inputFields with dimensions (F,P,D), representing the values of a vector field, on the left by the values in a rank-3 container inputData indexed by (C,P,D), representing the values of vector data; the output value container outputFields 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. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void crossProductDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight)
 There are two use cases: (1) cross product of a rank-3 container inputDataRight 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 inputDataLeft indexed by (C,P,D) representing the values of vector data, OR (2) cross product of a rank-2 container inputDataRight with dimensions (P,D), representing the values of vector data, on the left by the values in a rank-3 container inputDataLeft indexed by (C,P,D), representing the values of vector data; the output value container outputData 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. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void outerProductDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields)
 There are two use cases: (1) outer product of a rank-4 container inputFields 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 inputData indexed by (C,P,D), representing the values of vector data, OR (2) outer product of a rank-3 container inputFields with dimensions (F,P,D), representing the values of a vector field, on the left by the values in a rank-3 container inputData indexed by (C,P,D), representing the values of vector data; the output value container outputFields is indexed by (C,F,P,D,D), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void outerProductDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight)
 There are two use cases: (1) outer product of a rank-3 container inputDataRight 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 inputDataLeft indexed by (C,P,D) representing the values of vector data, OR (2) outer product of a rank-2 container inputDataRight with dimensions (P,D), representing the values of vector data, on the left by the values in a rank-3 container inputDataLeft indexed by (C,P,D), representing the values of vector data; the output value container outputData is indexed by (C,P,D,D), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void matvecProductDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields, const char transpose= 'N')
 There are two use cases: (1) matrix-vector product of a rank-4 container inputFields 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 inputData 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 inputFields 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 inputData indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputFields is indexed by (C,F,P,D), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void matvecProductDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight, const char transpose= 'N')
 There are two use cases: (1) matrix-vector product of a rank-3 container inputDataRight 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 inputDataLeft 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 inputDataRight with dimensions (P,D), representing the values of vector data, on the left by the values in a rank-2, 3, or 4 container inputDataLeft indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputData is indexed by (C,P,D), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void matmatProductDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields, const char transpose= 'N')
 There are two use cases: (1) matrix-matrix product of a rank-5 container inputFields 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 inputData 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 inputFields 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 inputData indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputFields is indexed by (C,F,P,D1,D2), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void matmatProductDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight, const char transpose= 'N')
 There are two use cases: (1) matrix-matrix product of a rank-4 container inputDataRight 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 inputDataLeft 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 inputDataRight 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 inputDataLeft indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputData is indexed by (C,P,D1,D2), regardless of which of the two use cases is considered. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInFields >
static void cloneFields (ArrayOutFields &outputFields, const ArrayInFields &inputFields)
 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). More...
 
template<class Scalar , class ArrayOutFields , class ArrayInFactors , class ArrayInFields >
static void cloneScaleFields (ArrayOutFields &outputFields, const ArrayInFactors &inputFactors, const ArrayInFields &inputFields)
 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). More...
 
template<class Scalar , class ArrayInOutFields , class ArrayInFactors >
static void scaleFields (ArrayInOutFields &inoutFields, const ArrayInFactors &inputFactors)
 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). More...
 

Detailed Description

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.

Definition at line 71 of file Intrepid_ArrayTools.hpp.

Member Function Documentation

template<class Scalar , class ArrayOutFields , class ArrayInFields >
void Intrepid::ArrayTools::cloneFields ( ArrayOutFields &  outputFields,
const ArrayInFields &  inputFields 
)
static

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).

C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputFields[out] - Output fields array.
inputFields[in] - Input fields array.

Definition at line 51 of file Intrepid_ArrayToolsDefCloneScale.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInFactors , class ArrayInFields >
void Intrepid::ArrayTools::cloneScaleFields ( ArrayOutFields &  outputFields,
const ArrayInFactors &  inputFactors,
const ArrayInFields &  inputFields 
)
static

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).

C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputFields[out] - Output fields array.
inputFactors[in] - Input field factors array.
inputFields[in] - Input fields array.

Definition at line 136 of file Intrepid_ArrayToolsDefCloneScale.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::contractDataDataScalar ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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).

C - num. integration domains dim0 in both input containers
P - num. integration points dim1 in both input containers
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 557 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::contractDataDataTensor ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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).

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
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 665 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::contractDataDataVector ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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).

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
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 607 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::contractDataFieldScalar ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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.
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
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 267 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::contractDataFieldTensor ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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.
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
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 450 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::contractDataFieldVector ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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.
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
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 354 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInFieldsLeft , class ArrayInFieldsRight >
void Intrepid::ArrayTools::contractFieldFieldScalar ( ArrayOutFields &  outputFields,
const ArrayInFieldsLeft &  leftFields,
const ArrayInFieldsRight &  rightFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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.
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
Parameters
outputFields[out] - Output array.
leftFields[in] - Left input array.
rightFields[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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.

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
Parameters
outputFields[out] - Output array.
leftFields[in] - Left input array.
rightFields[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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.

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
Parameters
outputFields[out] - Output array.
leftFields[in] - Left input array.
rightFields[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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.

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
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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.

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
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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.

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
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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).
C - num. integration domains dim0 in both input containers
P - num. integration points dim1 in both input containers
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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).
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
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. 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).
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
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE. There are two use cases: (1) multiplies a rank-3, 4, or 5 container inputFields 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 inputData indexed by (C,P), representing the values of scalar data, OR (2) multiplies a rank-2, 3, or 4 container inputFields 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 inputData indexed by (C,P), representing the values of scalar data; the output value container outputFields 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.
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Note
The argument inputFields can be changed! This enables in-place multiplication.
Parameters
outputFields[out] - Output (product) fields array.
inputData[in] - Data (multiplying) array.
inputFields[in] - Input (being multiplied) fields array.
reciprocal[in] - If TRUE, divides input fields by the data (instead of multiplying). Default: FALSE.

Definition at line 51 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInFieldsLeft , class ArrayInFieldsRight >
void Intrepid::ArrayTools::contractFieldFieldTensor ( ArrayOutFields &  outputFields,
const ArrayInFieldsLeft &  leftFields,
const ArrayInFieldsRight &  rightFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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.
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
Parameters
outputFields[out] - Output array.
leftFields[in] - Left input array.
rightFields[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 189 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInFieldsLeft , class ArrayInFieldsRight >
void Intrepid::ArrayTools::contractFieldFieldVector ( ArrayOutFields &  outputFields,
const ArrayInFieldsLeft &  leftFields,
const ArrayInFieldsRight &  rightFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

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.
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
Parameters
outputFields[out] - Output array.
leftFields[in] - Left input array.
rightFields[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 117 of file Intrepid_ArrayToolsDefContractions.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::crossProductDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight 
)
static

There are two use cases: (1) cross product of a rank-3 container inputDataRight 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 inputDataLeft indexed by (C,P,D) representing the values of vector data, OR (2) cross product of a rank-2 container inputDataRight with dimensions (P,D), representing the values of vector data, on the left by the values in a rank-3 container inputDataLeft indexed by (C,P,D), representing the values of vector data; the output value container outputData 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.

C - num. integration domains
P - num. integration points
D - spatial dimension of vector data and vector fields
Parameters
outputData[out] - Output (cross product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.

Definition at line 238 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::crossProductDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields 
)
static

There are two use cases: (1) cross product of a rank-4 container inputFields 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 inputData indexed by (C,P,D), representing the values of vector data, OR (2) cross product of a rank-3 container inputFields with dimensions (F,P,D), representing the values of a vector field, on the left by the values in a rank-3 container inputData indexed by (C,P,D), representing the values of vector data; the output value container outputFields 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.

C - num. integration domains
F - num. fields
P - num. integration points
D - spatial dimension of vector data and vector fields
Parameters
outputFields[out] - Output (cross product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.

Definition at line 55 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::dotMultiplyDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight 
)
static

There are two use cases: (1) dot product of a rank-2, 3 or 4 container inputDataRight 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 inputDataLeft 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 inputDataRight 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 inputDataLeft 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 outputData 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.
C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputData[out] - Output (dot product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.

Definition at line 351 of file Intrepid_ArrayToolsDefDot.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::dotMultiplyDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputDataLeft,
const ArrayInFields &  inputFields 
)
static

There are two use cases: (1) dot product of a rank-3, 4 or 5 container inputFields 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 inputData 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 inputFields 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 inputData 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 outputFields 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.
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index

Parameters
outputData[out] - Output (dot product) data array.
inputDataRight[in] - Data array Right.
inputDataLeft[in] - Data Array Left.
invalRank[in] - rank inputDataRight
outvalRank[in] - rank output

Definition at line 52 of file Intrepid_ArrayToolsDefDot.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::matmatProductDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const char  transpose = 'N' 
)
static

There are two use cases: (1) matrix-matrix product of a rank-4 container inputDataRight 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 inputDataLeft 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 inputDataRight 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 inputDataLeft indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputData is indexed by (C,P,D1,D2), regardless of which of the two use cases is considered.

Remarks
The rank of inputData implicitly defines the type of tensor data:
  • rank = 2 corresponds to a constant diagonal tensor $ diag(a,\ldots,a) $
  • rank = 3 corresponds to a nonconstant diagonal tensor $ diag(a_1,\ldots,a_d) $
  • rank = 4 corresponds to a full tensor $ \{a_{ij}\}$
Note
It is assumed that all tensors are square!
The method is defined for spatial dimensions D = 1, 2, 3
C - num. integration domains
P - num. integration points
D1* - first spatial (tensor) dimension index
D2** - second spatial (tensor) dimension index
Parameters
outputData[out] - Output (matrix-vector product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.
transpose[in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.

Definition at line 1976 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::matmatProductDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const char  transpose = 'N' 
)
static

There are two use cases: (1) matrix-matrix product of a rank-5 container inputFields 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 inputData 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 inputFields 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 inputData indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputFields is indexed by (C,F,P,D1,D2), regardless of which of the two use cases is considered.

Remarks
The rank of inputData implicitly defines the type of tensor data:
  • rank = 2 corresponds to a constant diagonal tensor $ diag(a,\ldots,a) $
  • rank = 3 corresponds to a nonconstant diagonal tensor $ diag(a_1,\ldots,a_d) $
  • rank = 4 corresponds to a full tensor $ \{a_{ij}\}$
Note
It is assumed that all tensors are square!
The method is defined for spatial dimensions D = 1, 2, 3
C - num. integration domains
F - num. fields
P - num. integration points
D1* - first spatial (tensor) dimension index
D2** - second spatial (tensor) dimension index
Parameters
outputFields[out] - Output (matrix-matrix product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
transpose[in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.

Definition at line 1497 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::matvecProductDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const char  transpose = 'N' 
)
static

There are two use cases: (1) matrix-vector product of a rank-3 container inputDataRight 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 inputDataLeft 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 inputDataRight with dimensions (P,D), representing the values of vector data, on the left by the values in a rank-2, 3, or 4 container inputDataLeft indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputData is indexed by (C,P,D), regardless of which of the two use cases is considered.

Remarks
The rank of inputDataLeft implicitly defines the type of tensor data:
  • rank = 2 corresponds to a constant diagonal tensor $ diag(a,\ldots,a) $
  • rank = 3 corresponds to a nonconstant diagonal tensor $ diag(a_1,\ldots,a_d) $
  • rank = 4 corresponds to a full tensor $ \{a_{ij}\}$
Note
It is assumed that all tensors are square!
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
Parameters
outputData[out] - Output (matrix-vector product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.
transpose[in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.

Definition at line 1085 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::matvecProductDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const char  transpose = 'N' 
)
static

There are two use cases: (1) matrix-vector product of a rank-4 container inputFields 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 inputData 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 inputFields 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 inputData indexed by (C,P), (C,P,D1) or (C,P,D1,D2), respectively, representing the values of tensor data; the output value container outputFields is indexed by (C,F,P,D), regardless of which of the two use cases is considered.

Remarks
The rank of inputData implicitly defines the type of tensor data:
  • rank = 2 corresponds to a constant diagonal tensor $ diag(a,\ldots,a) $
  • rank = 3 corresponds to a nonconstant diagonal tensor $ diag(a_1,\ldots,a_d) $
  • rank = 4 corresponds to a full tensor $ \{a_{ij}\}$
Note
It is assumed that all tensors are square!
The method is defined for spatial dimensions D = 1, 2, 3
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
Parameters
outputFields[out] - Output (matrix-vector product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
transpose[in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.

Definition at line 642 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::outerProductDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight 
)
static

There are two use cases: (1) outer product of a rank-3 container inputDataRight 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 inputDataLeft indexed by (C,P,D) representing the values of vector data, OR (2) outer product of a rank-2 container inputDataRight with dimensions (P,D), representing the values of vector data, on the left by the values in a rank-3 container inputDataLeft indexed by (C,P,D), representing the values of vector data; the output value container outputData is indexed by (C,P,D,D), regardless of which of the two use cases is considered.

C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputData[out] - Output (outer product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.

Definition at line 532 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::outerProductDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields 
)
static

There are two use cases: (1) outer product of a rank-4 container inputFields 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 inputData indexed by (C,P,D), representing the values of vector data, OR (2) outer product of a rank-3 container inputFields with dimensions (F,P,D), representing the values of a vector field, on the left by the values in a rank-3 container inputData indexed by (C,P,D), representing the values of vector data; the output value container outputFields is indexed by (C,F,P,D,D), regardless of which of the two use cases is considered.

C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputFields[out] - Output (outer product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.

Definition at line 417 of file Intrepid_ArrayToolsDefTensor.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::ArrayTools::scalarMultiplyDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const bool  reciprocal = false 
)
static

There are two use cases: (1) multiplies a rank-2, 3, or 4 container inputDataRight 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 inputDataLeft indexed by (C,P), representing the values of scalar data, OR (2) multiplies a rank-1, 2, or 3 container inputDataRight 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 inputDataLeft indexed by (C,P), representing the values of scalar data; the output value container outputData is indexed by (C,P), (C,P,D1) or (C,P,D1,D2), regardless of which of the two use cases is considered.

C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Note
The arguments inputDataLeft, inputDataRight can be changed! This enables in-place multiplication.
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left (multiplying) data array.
inputDataRight[in] - Right (being multiplied) data array.
reciprocal[in] - If TRUE, divides input fields by the data (instead of multiplying). Default: FALSE.

Definition at line 501 of file Intrepid_ArrayToolsDefScalar.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::ArrayTools::scalarMultiplyDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const bool  reciprocal = false 
)
static

There are two use cases: (1) multiplies a rank-3, 4, or 5 container inputFields 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 inputData indexed by (C,P), representing the values of scalar data, OR (2) multiplies a rank-2, 3, or 4 container inputFields 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 inputData indexed by (C,P), representing the values of scalar data; the output value container outputFields 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.

C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Note
The argument inputFields can be changed! This enables in-place multiplication.
Parameters
outputFields[out] - Output (product) fields array.
inputData[in] - Data (multiplying) array.
inputFields[in] - Input (being multiplied) fields array.
reciprocal[in] - If TRUE, divides input fields by the data (instead of multiplying). Default: FALSE.

Definition at line 77 of file Intrepid_ArrayToolsDefScalar.hpp.

template<class Scalar , class ArrayInOutFields , class ArrayInFactors >
void Intrepid::ArrayTools::scaleFields ( ArrayInOutFields &  inoutFields,
const ArrayInFactors &  inputFactors 
)
static

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).

C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
inoutFields[in/out] - Input / output fields array.
inputFactors[in] - Scaling field factors array.

Definition at line 228 of file Intrepid_ArrayToolsDefCloneScale.hpp.

The documentation for this class was generated from the following files:
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