Implementation of basic linear algebra functionality in Euclidean space. More...

#include <Intrepid_RealSpaceTools.hpp>

Classes
struct	detTempSpec

Static Public Member Functions
static void	absval (Scalar absArray, const Scalar inArray, const int size)
	Computes absolute value of contiguous input data *inArray* of size *size*. More...

static void	absval (Scalar *inoutArray, const int size)
	Computes absolute value of contiguous data *inoutAbsArray* of size *size* in place. More...

template<class ArrayAbs , class ArrayIn >
static void	absval (ArrayAbs &absArray, const ArrayIn &inArray)
	Computes absolute value of an array. More...

template<class ArrayInOut >
static void	absval (ArrayInOut &inoutAbsArray)
	Computes, in place, absolute value of an array. More...

static Scalar	vectorNorm (const Scalar *inVec, const size_t dim, const ENorm normType)
	Computes norm (1, 2, infinity) of the vector *inVec* of size *dim*. More...

template<class ArrayIn >
static Scalar	vectorNorm (const ArrayIn &inVec, const ENorm normType)
	Computes norm (1, 2, infinity) of a single vector stored in an array of rank 1. More...

template<class ArrayNorm , class ArrayIn >
static void	vectorNorm (ArrayNorm &normArray, const ArrayIn &inVecs, const ENorm normType)
	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). More...

static void	transpose (Scalar transposeMat, const Scalar inMat, const size_t dim)
	Computes transpose of the square matrix *inMat* of size *dim* by *dim*. More...

template<class ArrayTranspose , class ArrayIn >
static void	transpose (ArrayTranspose &transposeMats, const ArrayIn &inMats)
	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). More...

static void	inverse (Scalar inverseMat, const Scalar inMat, const size_t dim)
	Computes inverse of the square matrix *inMat* of size *dim* by *dim*. More...

template<class ArrayInverse , class ArrayIn >
static void	inverse (ArrayInverse &inverseMats, const ArrayIn &inMats)
	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). More...

static Scalar	det (const Scalar *inMat, const size_t dim)

template<class ArrayIn >
static Scalar	det (const ArrayIn &inMat)
	Computes determinant of a single square matrix stored in an array of rank 2. More...

template<class ArrayDet , class ArrayIn >
static void	det (ArrayDet &detArray, const ArrayIn &inMats)
	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). More...

static void	add (Scalar sumArray, const Scalar inArray1, const Scalar *inArray2, const int size)
	Adds contiguous data *inArray1* and *inArray2* of size *size: sumArray* = *inArray1* + *inArray2*. More...

static void	add (Scalar inoutSumArray, const Scalar inArray, const int size)
	Adds, in place, contiguous data *inArray* into *inoutSumArray* of size *size: inoutSumArray* = *inoutSumArray* + *inArray*. More...

template<class ArraySum , class ArrayIn1 , class ArrayIn2 >
static void	add (ArraySum &sumArray, const ArrayIn1 &inArray1, const ArrayIn2 &inArray2)
	Adds arrays *inArray1* and *inArray2: sumArray* = *inArray1* + *inArray2*. More...

template<class ArraySum , class ArrayIn >
static void	add (ArraySum &inoutSumArray, const ArrayIn &inArray)
	Adds, in place, *inArray* into *inoutSumArray: inoutSumArray* = *inoutSumArray* + *inArray*. More...

static void	subtract (Scalar diffArray, const Scalar inArray1, const Scalar *inArray2, const int size)
	Subtracts contiguous data *inArray2* from *inArray1* of size *size: diffArray* = *inArray1* - *inArray2*. More...

static void	subtract (Scalar inoutDiffArray, const Scalar inArray, const int size)
	Subtracts, in place, contiguous data *inArray* from *inoutDiffArray* of size *size: inoutDiffArray* = *inoutDiffArray* - *inArray*. More...

template<class ArrayDiff , class ArrayIn1 , class ArrayIn2 >
static void	subtract (ArrayDiff &diffArray, const ArrayIn1 &inArray1, const ArrayIn2 &inArray2)
	Subtracts *inArray2* from *inArray1: diffArray* = *inArray1* - *inArray2*. More...

template<class ArrayDiff , class ArrayIn >
static void	subtract (ArrayDiff &inoutDiffArray, const ArrayIn &inArray)
	Subtracts, in place, *inArray* from *inoutDiffArray: inoutDiffArray* = *inoutDiffArray* - *inArray*. More...

template<class ArrayDiff , class ArrayIn >
static void	subtractTemp (ArrayDiff &inoutDiffArray, const ArrayIn &inArray)

static void	scale (Scalar scaledArray, const Scalar inArray, const int size, const Scalar scalar)
	Multiplies contiguous data *inArray* of size *size* by a scalar (componentwise): *scaledArray* = *scalar* * *inArray*. More...

static void	scale (Scalar *inoutScaledArray, const int size, const Scalar scalar)
	Multiplies, in place, contiguous data *inoutScaledArray* of size *size* by a scalar (componentwise): *inoutScaledArray* = *scalar* * *inoutScaledArray*. More...

template<class ArrayScaled , class ArrayIn >
static void	scale (ArrayScaled &scaledArray, const ArrayIn &inArray, const Scalar scalar)
	Multiplies array *inArray* by the scalar *scalar* (componentwise): *scaledArray* = *scalar* * *inArray*. More...

template<class ArrayScaled >
static void	scale (ArrayScaled &inoutScaledArray, const Scalar scalar)
	Multiplies, in place, array *inoutScaledArray* by the scalar *scalar* (componentwise): *inoutScaledArray* = *scalar* * *inoutScaledArray*. More...

static Scalar	dot (const Scalar inArray1, const Scalar inArray2, const int size)
	Computes dot product of contiguous data *inArray1* and *inArray2* of size *size*. More...

template<class ArrayVec1 , class ArrayVec2 >
static Scalar	dot (const ArrayVec1 &inVec1, const ArrayVec2 &inVec2)
	Computes dot product of two vectors stored in arrays of rank 1. More...

template<class ArrayDot , class ArrayVec1 , class ArrayVec2 >
static void	dot (ArrayDot &dotArray, const ArrayVec1 &inVecs1, const ArrayVec2 &inVecs2)
	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). More...

static void	matvec (Scalar matVec, const Scalar inMat, const Scalar *inVec, const size_t dim)
	Matrix-vector left multiply using contiguous data: *matVec* = *inMat* * *inVec*. More...

template<class ArrayMatVec , class ArrayMat , class ArrayVec >
static void	matvec (ArrayMatVec &matVecs, const ArrayMat &inMats, const ArrayVec &inVecs)
	Matrix-vector left multiply using multidimensional arrays: *matVec* = *inMat* * *inVec*. More...

template<class ArrayVecProd , class ArrayIn1 , class ArrayIn2 >
static void	vecprod (ArrayVecProd &vecProd, const ArrayIn1 &inLeft, const ArrayIn2 &inRight)
	Vector product using multidimensional arrays: *vecProd* = *inVecLeft* x *inVecRight* More...

Detailed Description

template<class Scalar>
class Intrepid::RealSpaceTools< Scalar >

Implementation of basic linear algebra functionality in Euclidean space.

Definition at line 68 of file Intrepid_RealSpaceTools.hpp.

Member Function Documentation

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::absval	(	Scalar *	absArray,
		const Scalar *	inArray,
		const int	size
	)

static

Computes absolute value of contiguous input data inArray of size size.

Parameters

absArray	[out] - output data
inArray	[in] - input data
size	[in] - size

Definition at line 55 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::absval	(	Scalar *	inoutArray,
		const int	size
	)

static

Computes absolute value of contiguous data inoutAbsArray of size size in place.

Parameters

inoutAbsArray	[in/out] - input/output data
size	[in] - size

Definition at line 64 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayAbs , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::absval	(	ArrayAbs &	absArray,
		const ArrayIn &	inArray
	)

static

Computes absolute value of an array.

Parameters

outArray	[out] - output array
inArray	[in] - input array

Note

Requirements (checked at runtime, in debug mode):

rank(absArray) == rank(inArray)
dimensions(absArray) == dimensions(inArray)

Definition at line 74 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayInOut >

void Intrepid::RealSpaceTools< Scalar >::absval ( ArrayInOut & inoutAbsArray )

static

Computes, in place, absolute value of an array.

Parameters

inoutAbsArray [in/out] - input/output array

Definition at line 130 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::add	(	Scalar *	sumArray,
		const Scalar *	inArray1,
		const Scalar *	inArray2,
		const int	size
	)

static

Adds contiguous data inArray1 and inArray2 of size size:
sumArray = inArray1 + inArray2.

Parameters

sumArray	[out] - sum
inArray1	[in] - first summand
inArray2	[in] - second summand
size	[in] - size of input/output data

Definition at line 1506 of file Intrepid_RealSpaceToolsDef.hpp.

Referenced by Intrepid::CellTools< Scalar >::mapToReferenceFrameInitGuess().

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::add	(	Scalar *	inoutSumArray,
		const Scalar *	inArray,
		const int	size
	)

static

Adds, in place, contiguous data inArray into inoutSumArray of size size:
inoutSumArray = inoutSumArray + inArray.

Parameters

inoutSumArray	[in/out] - sum / first summand
inArray	[in] - second summand
size	[in] - size of input/output data

Definition at line 1515 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArraySum , class ArrayIn1 , class ArrayIn2 >

void Intrepid::RealSpaceTools< Scalar >::add	(	ArraySum &	sumArray,
		const ArrayIn1 &	inArray1,
		const ArrayIn2 &	inArray2
	)

static

Adds arrays inArray1 and inArray2:
sumArray = inArray1 + inArray2.

Parameters

sumArray	[out] - sum
inArray1	[in] - first summand
inArray2	[in] - second summand

Note

Requirements (checked at runtime, in debug mode):

rank(sumArray) == rank(inArray1) == rank(inArray2)
dimensions(sumArray) == dimensions(inArray1) == dimensions(inArray2)

Definition at line 1525 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArraySum , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::add	(	ArraySum &	inoutSumArray,
		const ArrayIn &	inArray
	)

static

Adds, in place, inArray into inoutSumArray:
inoutSumArray = inoutSumArray + inArray.

Parameters

inoutSumArray	[in/out] - sum/first summand
inArray	[in] - second summand

Note

Requirements (checked at runtime, in debug mode):

rank(inoutSumArray) == rank(inArray)
dimensions(inoutSumArray) == dimensions(inArray)

Definition at line 1584 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayIn >

Scalar Intrepid::RealSpaceTools< Scalar >::det ( const ArrayIn & inMat )

static

Computes determinant of a single square matrix stored in an array of rank 2.

Parameters

inMat [in] - array representing a single matrix, indexed by (D, D)

Note

Requirements (checked at runtime, in debug mode):

rank(inMats) == 2
matrix dimension is limited to 1, 2, and 3

Definition at line 1240 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayDet , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::det	(	ArrayDet &	detArray,
		const ArrayIn &	inMats
	)

static

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).

Parameters

detArray	[out] - array of determinants indexed by (i0) or (i0, i1)
inMats	[in] - array of matrices indexed by (i0, D, D) or (i0, i1, D, D)

Note

Requirements (checked at runtime, in debug mode):

rank(detArray) == rank(inMats) - 2
rank(inMats) == 3 or 4
dimensions i0, i1 of detArray and inMats must agree
matrix dimensions are limited to 1, 2, and 3

Definition at line 1321 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

Scalar Intrepid::RealSpaceTools< Scalar >::dot	(	const Scalar *	inArray1,
		const Scalar *	inArray2,
		const int	size
	)

static

Computes dot product of contiguous data inArray1 and inArray2 of size size.

Parameters

inArray1	[in] - first array
inArray2	[in] - second array
size	[in] - size of input arrays

Definition at line 1847 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayVec1 , class ArrayVec2 >

Scalar Intrepid::RealSpaceTools< Scalar >::dot	(	const ArrayVec1 &	inVec1,
		const ArrayVec2 &	inVec2
	)

static

Computes dot product of two vectors stored in arrays of rank 1.

Parameters

inVec1	[in] - first vector
inVec2	[in] - second vector

Note

Requirements (checked at runtime, in debug mode):

rank(inVec1) == rank(inVec2) == 1
inVec1 and inVec2 have same dimension

Definition at line 1859 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayDot , class ArrayVec1 , class ArrayVec2 >

void Intrepid::RealSpaceTools< Scalar >::dot	(	ArrayDot &	dotArray,
		const ArrayVec1 &	inVecs1,
		const ArrayVec2 &	inVecs2
	)

static

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).

Parameters

dotArray	[out] - dot product array indexed by (i0) or (i0, i1)
inVecs1	[in] - first array of vectors indexed by (i0, D) or (i0, i1, D)
inVecs2	[in] - second array of vectors indexed by (i0, D) or (i0, i1, D)

Note

Requirements (checked at runtime, in debug mode):

rank(dotArray) == rank(inVecs1) - 1 == rank(inVecs2) - 1
rank(inVecs1) == 2 or 3
dimensions i0, i1 of dotArray and inVecs1 / inVecs2 must agree

Definition at line 1882 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::inverse	(	Scalar *	inverseMat,
		const Scalar *	inMat,
		const size_t	dim
	)

static

Computes inverse of the square matrix inMat of size dim by dim.

Parameters

inverseMat	[out] - matrix inverse
inMat	[in] - matrix
dim	[in] - matrix dimension

Definition at line 653 of file Intrepid_RealSpaceToolsDef.hpp.

Referenced by Intrepid::CellTools< Scalar >::setJacobianInv().

template<class Scalar >

template<class ArrayInverse , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::inverse	(	ArrayInverse &	inverseMats,
		const ArrayIn &	inMats
	)

static

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).

Parameters

inverseMats	[out] - array of inverses indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
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):

rank(inverseMats) == rank(inMats)
rank(inMats) == 3 or 4
dimensions(inverseMats) == dimensions(inMats)
matrices must be square
matrix dimensions are limited to 1, 2, and 3

Definition at line 757 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::matvec	(	Scalar *	matVec,
		const Scalar *	inMat,
		const Scalar *	inVec,
		const size_t	dim
	)

static

Matrix-vector left multiply using contiguous data:
matVec = inMat * inVec.

   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>.

Parameters

matVec	[out] - matrix-vector product
inMat	[in] - the matrix argument
inVec	[in] - the vector argument
dim	[in] - matrix/vector dimension

Definition at line 1954 of file Intrepid_RealSpaceToolsDef.hpp.

Referenced by Intrepid::CellTools< Scalar >::mapToReferenceFrameInitGuess().

template<class Scalar >

template<class ArrayMatVec , class ArrayMat , class ArrayVec >

void Intrepid::RealSpaceTools< Scalar >::matvec	(	ArrayMatVec &	matVecs,
		const ArrayMat &	inMats,
		const ArrayVec &	inVecs
	)

static

Matrix-vector left multiply using multidimensional arrays:
matVec = inMat * inVec.

   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).

Parameters

matVec	[out] - matrix-vector product indexed by (D), (i0, D) or (i0, i1, D)
inMat	[in] - the matrix argument indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
inVec	[in] - the vector argument indexed by (D), (i0, D) or (i0, i1, D)

Note

Requirements (checked at runtime, in debug mode):

rank(matVec) == rank(inVec) == rank(inMat) - 1
dimensions(matVec) == dimensions(inVec)
matrix and vector dimensions D, i0 and i1 must agree
matrices are square

Definition at line 1968 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::scale	(	Scalar *	scaledArray,
		const Scalar *	inArray,
		const int	size,
		const Scalar	scalar
	)

static

Multiplies contiguous data inArray of size size by a scalar (componentwise):
scaledArray = scalar * inArray.

Parameters

scaledArray	[out] - scaled array
inArray	[in] - input array
size	[in] - size of the input array
scalar	[in] - multiplier

Definition at line 1762 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::scale	(	Scalar *	inoutScaledArray,
		const int	size,
		const Scalar	scalar
	)

static

Multiplies, in place, contiguous data inoutScaledArray of size size by a scalar (componentwise):
inoutScaledArray = scalar * inoutScaledArray.

Parameters

inoutScaledArray	[in/out] - input/scaled array
size	[in] - size of array
scalar	[in] - multiplier

Definition at line 1771 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayScaled , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::scale	(	ArrayScaled &	scaledArray,
		const ArrayIn &	inArray,
		const Scalar	scalar
	)

static

Multiplies array inArray by the scalar scalar (componentwise):
scaledArray = scalar * inArray.

Parameters

scaledArray	[out] - scaled array
inArray	[in] - input array
scalar	[in] - multiplier

Note

Requirements (checked at runtime, in debug mode):

rank(scaledArray) == rank(inArray)
dimensions(scaledArray) == dimensions(inArray)

Definition at line 1781 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayScaled >

void Intrepid::RealSpaceTools< Scalar >::scale	(	ArrayScaled &	inoutScaledArray,
		const Scalar	scalar
	)

static

Multiplies, in place, array inoutScaledArray by the scalar scalar (componentwise):
inoutScaledArray = scalar * inoutScaledArray.

Parameters

inoutScaledArray	[in/out] - input/output array
scalar	[in] - multiplier

Definition at line 1835 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::subtract	(	Scalar *	diffArray,
		const Scalar *	inArray1,
		const Scalar *	inArray2,
		const int	size
	)

static

Subtracts contiguous data inArray2 from inArray1 of size size:
diffArray = inArray1 - inArray2.

Parameters

diffArray	[out] - difference
inArray1	[in] - minuend
inArray2	[in] - subtrahend
size	[in] - size of input/output data

Definition at line 1638 of file Intrepid_RealSpaceToolsDef.hpp.

Referenced by Intrepid::CellTools< Scalar >::mapToReferenceFrameInitGuess().

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::subtract	(	Scalar *	inoutDiffArray,
		const Scalar *	inArray,
		const int	size
	)

static

Subtracts, in place, contiguous data inArray from inoutDiffArray of size size:
inoutDiffArray = inoutDiffArray - inArray.

Parameters

inoutDiffArray	[in/out] - difference/minuend
inArray	[in] - subtrahend
size	[in] - size of input/output data

Definition at line 1647 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayDiff , class ArrayIn1 , class ArrayIn2 >

void Intrepid::RealSpaceTools< Scalar >::subtract	(	ArrayDiff &	diffArray,
		const ArrayIn1 &	inArray1,
		const ArrayIn2 &	inArray2
	)

static

Subtracts inArray2 from inArray1:
diffArray = inArray1 - inArray2.

Parameters

diffArray	[out] - difference
inArray1	[in] - minuend
inArray2	[in] - subtrahend

Note

Requirements (checked at runtime, in debug mode):

rank(sumArray) == rank(inArray1) == rank(inArray2)
dimensions(sumArray) == dimensions(inArray1) == dimensions(inArray2)

Definition at line 1657 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayDiff , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::subtract	(	ArrayDiff &	inoutDiffArray,
		const ArrayIn &	inArray
	)

static

Subtracts, in place, inArray from inoutDiffArray:
inoutDiffArray = inoutDiffArray - inArray.

Parameters

inoutDiffArray	[in/out] - difference/minuend
inArray	[in] - subtrahend

Note

Requirements (checked at runtime, in debug mode):

rank(inoutDiffArray) == rank(inArray)
dimensions(inoutDiffArray) == dimensions(inArray)

Definition at line 1710 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

void Intrepid::RealSpaceTools< Scalar >::transpose	(	Scalar *	transposeMat,
		const Scalar *	inMat,
		const size_t	dim
	)

static

Computes transpose of the square matrix inMat of size dim by dim.

Parameters

transposeMat	[out] - matrix transpose
inMat	[in] - matrix
dim	[in] - matrix dimension

Definition at line 576 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayTranspose , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::transpose	(	ArrayTranspose &	transposeMats,
		const ArrayIn &	inMats
	)

static

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).

Parameters

transposeMats	[out] - array of transposes indexed by (D, D), (i0, D, D) or (i0, i1, D, D)
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):

rank(transposeMats) == rank(inMats)
rank(inMats) == 3 or 4
dimensions(transposeMats) == dimensions(inMats)
matrices must be square

Definition at line 590 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayVecProd , class ArrayIn1 , class ArrayIn2 >

void Intrepid::RealSpaceTools< Scalar >::vecprod	(	ArrayVecProd &	vecProd,
		const ArrayIn1 &	inLeft,
		const ArrayIn2 &	inRight
	)

static

Vector product using multidimensional arrays:
vecProd = inVecLeft x inVecRight

     Vector multiplication of two "column" vectors stored in arrays (rank 1, 2, or 3)
     indexed by (D), (i0, D) or (i0, i1, D).

Parameters

vecProd	[in] - vector product indexed by (D), (i0, D) or (i0, i1, D)
inLeft	[in] - left vector argument indexed by (D), (i0, D) or (i0, i1, D)
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?

Definition at line 2039 of file Intrepid_RealSpaceToolsDef.hpp.

Referenced by Intrepid::CellTools< Scalar >::getPhysicalFaceNormals(), and Intrepid::CellTools< Scalar >::getReferenceFaceNormal().

template<class Scalar >

Scalar Intrepid::RealSpaceTools< Scalar >::vectorNorm	(	const Scalar *	inVec,
		const size_t	dim,
		const ENorm	normType
	)

static

Computes norm (1, 2, infinity) of the vector inVec of size dim.

Parameters

inVec	[in] - vector
dim	[in] - vector dimension
normType	[in] - norm type

Definition at line 139 of file Intrepid_RealSpaceToolsDef.hpp.

Referenced by Intrepid::FunctionSpaceTools::computeEdgeMeasure(), Intrepid::FunctionSpaceTools::computeFaceMeasure(), and Intrepid::CellTools< Scalar >::mapToReferenceFrameInitGuess().

template<class Scalar >

template<class ArrayIn >

Scalar Intrepid::RealSpaceTools< Scalar >::vectorNorm	(	const ArrayIn &	inVec,
		const ENorm	normType
	)

static

Computes norm (1, 2, infinity) of a single vector stored in an array of rank 1.

Parameters

inVec	[in] - array representing a single vector
normType	[in] - norm type

Note

Requirements (checked at runtime, in debug mode):

rank(inVec) == 1

Definition at line 170 of file Intrepid_RealSpaceToolsDef.hpp.

template<class Scalar >

template<class ArrayNorm , class ArrayIn >

void Intrepid::RealSpaceTools< Scalar >::vectorNorm	(	ArrayNorm &	normArray,
		const ArrayIn &	inVecs,
		const ENorm	normType
	)

static

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).

Parameters

normArray	[out] - norm array indexed by (i0) or (i0, i1)
inVecs	[in] - array of vectors indexed by (i0, D) or (i0, i1, D)
normType	[in] - norm type

Note

Requirements (checked at runtime, in debug mode):

rank(normArray) == rank(inVecs) - 1
rank(inVecs) == 2 or 3
dimensions i0, i1 of normArray and inVecs must agree

Definition at line 338 of file Intrepid_RealSpaceToolsDef.hpp.

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

http://docs.trilinos.org/r12.18/packages/intrepid/src/Shared/Intrepid_RealSpaceTools.hpp
http://docs.trilinos.org/r12.18/packages/intrepid/src/Shared/Intrepid_RealSpaceToolsDef.hpp

Classes

Static Public Member Functions

Detailed Description

template<class Scalar> class Intrepid::RealSpaceTools< Scalar >

Member Function Documentation

template<class Scalar>
class Intrepid::RealSpaceTools< Scalar >