utl Namespace Reference

General utility classes and functions. More...

Classes
class	Function
	Base class for unary functions of arbitrary result and argument type. More...
class	vector
	A vector class with some added algebraic operations. More...
class	matrixBase
	Common base class for multi-dimensional (2D and 3D) matrices. More...
class	matrix
	Two-dimensional rectangular matrix with some algebraic operations. More...
class	matrix3d
	Three-dimensional rectangular matrix with some algebraic operations. More...
class	matrix4d
	Four-dimensional rectangular matrix with some algebraic operations. More...
class	Function2
	Base class for binary function of arbitrary result and argument type. More...
class	SpatialFunction
	Base class for unary spatial function of arbitrary result type. More...
class	LogStream
	Logging stream class. More...
class	Point
	Class for representing points in 3D space. More...
class	prof
	Convenience class to profile the local scope. More...
class	cmpInt
	A helper class used to search for values in an integer map. More...

Functions
template<class T >
T	trunc (T v)
	Truncate a value to zero when it is less than a given threshold. More...
template<class T >
std::istream &	operator>> (std::istream &s, vector< T > &X)
	Read the vector X from the stream s.
template<class T >
std::ostream &	operator<< (std::ostream &s, const vector< T > &X)
	Print the vector X to the stream s.
template<class T >
std::istream &	operator>> (std::istream &s, matrix< T > &A)
	Read the matrix A from the stream s.
template<class T >
std::ostream &	operator<< (std::ostream &s, const matrix< T > &A)
	Print the matrix A to the stream s. More...
template<class T >
void	writeMatlab (const char *label, const vector< T > &X, std::ostream &s=std::cout)
	Print the vector X to the stream s in matlab format.
template<class T >
void	writeMatlab (const char *label, const matrix< T > &A, std::ostream &s=std::cout)
	Print the matrix A to the stream s in matlab format.
template<class T >
std::ostream &	operator<< (std::ostream &s, const matrix3d< T > &A)
	Print the 3D matrix A to the stream s. More...
template<class T >
std::ostream &	operator<< (std::ostream &s, const matrix4d< T > &A)
	Print the 4D matrix A to the stream s. More...
Vector	operator* (const Vector &X, Real c)
	Multiplication of a vector and a scalar. More...
Vector	operator* (Real c, const Vector &X)
	Multiplication of a scalar and a vector. More...
Vector	operator/ (const Vector &X, Real d)
	Division of a vector by a scalar. More...
Vector	operator+ (const Vector &X, const Vector &Y)
	Addition of two vectors. More...
Vector	operator- (const Vector &X, const Vector &Y)
	Subtraction of two vectors. More...
Matrix	operator* (const Matrix &A, Real c)
	Multiplication of a matrix and a scalar. More...
Matrix	operator* (Real c, const Matrix &A)
	Multiplication of a scalar and a matrix. More...
Real	operator* (const Vector &X, const Vector &Y)
	Dot product of two vectors. More...
RealArray	operator* (const Matrix &A, const Vector &X)
	Multiplication of a matrix and a vector. More...
RealArray	operator* (const Vector &X, const Matrix &A)
	Multiplication of a vector and a matrix. More...
Matrix	operator* (const Matrix &A, const Matrix &B)
	Multiplication of two matrices. More...
bool	transform (Matrix &A, const Matrix &Tn)
	Congruence transformation of a symmetric matrix. More...
bool	transform (Vector &V, const Matrix &Tn, bool transpose=false)
	Congruence transformation of a vector. More...
bool	invert (Matrix &A)
	Inverts the square matrix A.
bool	solve (Matrix &A, RealArray &b, std::vector< int > *iPivot=nullptr)
	Solves the linear system of equations \( {\bf A x} = {\bf b} \). More...
void	debugPrint (const char *label, const Vector &V, int level=2)
	Debug print of given vector V, if SP_DEBUG ≥ level.
Real	Jacobian (matrix< Real > &J, matrix< Real > &dNdX, const matrix< Real > &X, const matrix< Real > &dNdu, bool computeGradient=true)
	Set up the Jacobian matrix of the coordinate mapping. More...
Real	Jacobian (matrix< Real > &J, Vec3 &t, matrix< Real > &dNdX, const matrix< Real > &X, const matrix< Real > &dNdu, size_t tangent)
	Set up the Jacobian matrix of the coordinate mapping along an edge. More...
Real	Jacobian (matrix< Real > &J, Vec3 &n, matrix< Real > &dNdX, const matrix< Real > &X, const matrix< Real > &dNdu, size_t t1, size_t t2)
	Set up the Jacobian matrix of the coordinate mapping on a boundary. More...
bool	Hessian (matrix3d< Real > &H, matrix3d< Real > &d2NdX2, const matrix< Real > &Ji, const matrix< Real > &X, const matrix3d< Real > &d2Ndu2, const matrix< Real > &dNdX, bool geoMapping=true)
	Set up the Hessian matrix of the coordinate mapping. More...
void	Hessian (const matrix3d< Real > &Hess, matrix< Real > &H)
	Convert a Hessian from a matrix3d to a matrix assuming symmetry.
void	getGmat (const matrix< Real > &Ji, const Real *du, matrix< Real > &G)
	Compute the stabilization matrix G from the Jacobian inverse. More...
bool	Hessian2 (matrix4d< Real > &d3NdX3, const matrix< Real > &Ji, const matrix4d< Real > &d3Ndu3)
	Set up third-order derivatives of the coordinate mapping. More...
void	JacobianGradient (const matrix< Real > &dudX, const matrix3d< Real > &d2Xdu2, std::vector< matrix< Real >> &dJdX)
	Calculates the derivatives of the Jacobian of the coordinate mapping. More...
void	detJacGradient (const matrix< Real > &J, const matrix< Real > &Ji, const matrix3d< Real > &H, std::vector< Real > &ddet)
	Calculates the derivatives of determinant of the Jacobian. More...
const RealFunc *	parseRealFunc (char *cline, Real A=Real(1), bool print=true)
	Creates a scalar-valued function by parsing a character string. More...
ScalarFunc *	parseTimeFunc (const char *func, const std::string &type="expression", Real eps=Real(1.0e-8))
	Creates a time function by parsing a character string. More...
VecTimeFunc *	parseVecTimeFunc (const char *func, const std::string &type)
	Creates a vector-valued time function by parsing a char string. More...
RealFunc *	parseRealFunc (const std::string &func, const std::string &type="expression", bool print=true)
	Creates a scalar-valued function by parsing a character string. More...
RealFunc *	parseExprRealFunc (const std::string &function, bool autodiff)
	Creates a scalar-valued function by parsing a character string. More...
VecFunc *	parseExprVecFunc (const std::string &function, bool autodiff)
	Creates a Vector-valued function by parsing a character string. More...
IntFunc *	parseIntFunc (const std::string &func, const std::string &type="expression")
	Creates a scalar-valued int function by parsing a character string. More...
VecFunc *	parseVecFunc (const std::string &func, const std::string &type="expression", const std::string &variables="")
	Creates a vector-valued function by parsing a character string. More...
TensorFunc *	parseTensorFunc (const std::string &func, const std::string &type)
	Creates a tensor-valued function by parsing a character string. More...
TractionFunc *	parseTracFunc (const std::string &func, const std::string &type="expression", int dir=0)
	Creates a vector-valued function defining a surface traction. More...
TractionFunc *	parseTracFunc (const tinyxml2::XMLElement *elem)
	Creates a vector-valued function defining a surface traction. More...
size_t	Pascal (int p, unsigned short int nsd)
	Returns the number of monomials in Pascal's triangle. More...
void	Pascal (int p, Real x, Real y, std::vector< Real > &phi)
	Evaluates the monomials of Pascal's triangle in 2D for order p.
void	Pascal (int p, Real x, Real y, Real z, std::vector< Real > &phi)
	Evaluates the monomials of Pascal's triangle in 3D for order p.
Real	Pos (Real x)
	Evaluates the positive ramp function \((x+|x|)/2\).
Real	Neg (Real x)
	Evaluates the negative ramp function \((x-|x|)/2\).
Real	Rad (Real x)
	Converts from degrees to radians.
bool	parseIntegers (std::vector< int > &values, const char *argv)
	Parses a character string into an integer or an integer range. More...
bool	parseVec (Vec3 &value, const char *argv)
	Parses a character string into a point vector. More...
bool	parseKnots (std::vector< Real > &xi)
	Parses a (possibly graded) sequence of knot values. More...
char *	readLine (std::istream &is)
	Reads one line, ignoring comment lines and leading blanks. More...
bool	ignoreComments (std::istream &is)
	Ignores comment lines and blank lines from an input stream. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, bool &val)
	Extracts a boolean attribute value from the specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, int &val)
	Extracts an integer attribute value from the specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, char &val, bool useIntValue=true)
	Extracts a char attribute value from the specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, size_t &val)
	Extracts a size_t attribute value from the specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, Real &val)
	Extracts a real attribute value from the specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, Vec3 &val, int ncomp=0)
	Extracts a vector attribute value from the specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, std::vector< int > &val)
	Extracts an integer vector attribute from specified XML-element. More...
int	getAttribute (const tinyxml2::XMLElement *xml, const char *att, std::string &val, bool toLower=false)
	Extracts a string attribute value from the specified XML-element. More...
const char *	getValue (const tinyxml2::XMLNode *xml, const char *tag)
	Returns the value (if any) of the specified XML-node. More...
bool	parseKnots (const tinyxml2::XMLNode *xml, std::vector< Real > &xi)
	Parses a sequence of knot values from the specified XML-node. More...
bool	renumber (int &num, int &runner, IntMap &old2new)
	Transforms the integer value num into a unique range. More...
bool	renumber (int &num, const IntMap &old2new, bool msg=false)
	Transforms the integer value num according to a given mapping. More...
int	gather (const std::vector< int > &index, size_t nr, const std::vector< Real > &in, std::vector< Real > &out, size_t offset_in=0, size_t nskip=0)
	Compresses the rows of a 2D array based on given scatter indices. More...
int	gather (const std::vector< int > &index, size_t nr, const std::vector< Real > &in, utl::matrix< Real > &out, size_t offset_in=0, size_t nskip=0)
	Compresses the rows of a 2D array based on given scatter indices. More...
int	gather (const std::vector< int > &index, size_t ir, size_t nr, const std::vector< Real > &in, std::vector< Real > &out, size_t offset_in=0, int shift_idx=0, size_t nskip=0)
	Compresses a row of a 2D array based on given scatter indices. More...
void	interleave (const std::vector< Real > &v1, const std::vector< Real > &v2, std::vector< Real > &out, size_t n1=1, size_t n2=1)
	Merges two arrays of nodal values into one array by interleaving. More...
size_t	find_closest (const std::vector< Real > &a, Real v)
	Searches for a real value in an ordered array of reals. More...
std::string	adjustRight (size_t width, const std::string &s, const std::string &suffix=" : ")
	Right-justifies the input string to the given total width.
std::set< int >	getDigits (int value)
	Splits an integer into its (unique) digits in ascending order.
int	getDirs (int ncmp)
	Makes a direction integer for given number of components.
IntMap::const_iterator	findValue (const IntMap &iMap, int iVal)
	Returns a const iterator to the entry with value iVal.
int	findKey (const IntMap &iMap, int iVal)
	Returns the key corresponding to the value iVal. More...
int	findIndex (const std::vector< int > &iVec, int iVal)
	Returns the vector index corresponding to the value iVal. More...
void	merge (std::vector< int > &a1, const std::vector< int > &a2)
	Merges integer array a2 into array a1. More...
void	merge (std::vector< Real > &a1, const std::vector< Real > &a2, const std::vector< int > &k1, const std::vector< int > &k2)
	Merges real array a2 into array a1 based on array indices. More...
Real	round (Real value, int pr)
	Rounds off value down to pr significant digits.

Variables
const char	RETAIN = 2
	Flag for vector::resize() method telling it to retain its content.
double	zero_print_tol = 1.0e-6
	Zero tolerance for printing numbers.
int	nval_per_line = 6
	Number of values to print per line.
Profiler *	profiler = nullptr
	Pointer to the one and only profiler object.

Detailed Description

General utility classes and functions.

Function Documentation

detJacGradient()

void utl::detJacGradient	(	const matrix< Real > &	J,
		const matrix< Real > &	Ji,
		const matrix3d< Real > &	H,
		std::vector< Real > &	ddet
	)

Calculates the derivatives of determinant of the Jacobian.

Parameters

[in]	J	Jacobian of the geometry mapping
[in]	Ji	Inverse jacobian of the geometry mapping
[in]	H	Hessian of the geometry mapping wrt parameters
[out]	ddet	Derivatives of the determinant

References utl::matrix< T >::multiply(), Real, and utl::matrix< T >::rows().

Referenced by MxFiniteElement::piolaGradient().

find_closest()

size_t utl::find_closest	(	const std::vector< Real > &	a,
		Real	v
	)

Searches for a real value in an ordered array of reals.

Parameters

[in]	a	The array of real values
[in]	v	The value to search for

Returns

0-based index of the closest array value.

Note

It is assumed that the array a is sorted in encreasing order on input. If this is not the case the method will deliver incorrect result.

Referenced by ASMs1DLag::evalPoint(), ASMs2DLag::evalPoint(), and ASMs3DLag::evalPoint().

findIndex()

int utl::findIndex	(	const std::vector< int > &	iVec,
		int	iVal
	)

Returns the vector index corresponding to the value iVal.

If not in the vector, -1 is returned.

Referenced by ASMbase::addLagrangeMultipliers(), ASMu2D::constrainEdge(), ASMbase::getAge(), ASMbase::getElmIndex(), ASMLRSpline::getFunctionsForElements(), ASMs2D::getNodeIndex(), ASMs3D::getNodeIndex(), ASMbase::getNodeIndex(), ASMu2DIB::integrate(), ASMbase::isElementInPartition(), ASMu1DLag::isInElementSet(), ASMu2DLag::isInElementSet(), ASMs1D::isInNodeSet(), ASMu2DLag::isInNodeSet(), ASMu2DLag::parseElemBox(), and ASMu2DLag::parseNodeBox().

findKey()

int utl::findKey	(	const IntMap &	iMap,
		int	iVal
	)

Returns the key corresponding to the value iVal.

If not in the map, the value iVal is returned.

References findValue().

Referenced by ASMbase::updateDirichlet().

gather() [1/3]

int utl::gather	(	const std::vector< int > &	index,
		size_t	ir,
		size_t	nr,
		const std::vector< Real > &	in,
		std::vector< Real > &	out,
		size_t	offset_in = 0,
		int	shift_idx = 0,
		size_t	nskip = 0
	)

Compresses a row of a 2D array based on given scatter indices.

Parameters

[in]	index	Scatter indices of the columns that should be retained
[in]	ir	Index of the row to compress
[in]	nr	Number of rows in the 2D array
[in]	in	The input array stored column-wise in a 1D array
[out]	out	The output array stored column-wise in a 1D array
[in]	offset_in	Optional start offset for the in vector
[in]	shift_idx	Optional constant shift in the scatter indices
[in]	nskip	If nonzero, skip the last nskip entries in index

gather() [2/3]

int utl::gather	(	const std::vector< int > &	index,
		size_t	nr,
		const std::vector< Real > &	in,
		std::vector< Real > &	out,
		size_t	offset_in = 0,
		size_t	nskip = 0
	)

Compresses the rows of a 2D array based on given scatter indices.

Parameters

[in]	index	Scatter indices of the columns that should be retained
[in]	nr	Number of rows in the 2D array
[in]	in	The input array stored column-wise in a 1D array
[out]	out	The output array stored column-wise in a 1D array
[in]	offset_in	Optional start offset for the in vector
[in]	nskip	If nonzero, skip the last nskip entries in index

References Real.

Referenced by IntegrandBase::evalSol1(), ASMs2Dmx::evalSolution(), ASMs3Dmx::evalSolution(), ASMs2D::evalSolution(), ASMs3D::evalSolution(), ASMu2D::evalSolution(), ASMu3D::evalSolution(), ASMs1D::evalSolution(), ASMs2Dmx::evalSolutionPiola(), SplineFields1D::gradFE(), SplineFields2D::gradFE(), SplineFields2Dmx::gradFE(), SplineFields3D::gradFE(), SplineFields3Dmx::gradFE(), SplineField2D::gradFE(), SplineField3D::gradFE(), SplineField2D::hessianFE(), SplineField3D::hessianFE(), SplineFields1D::hessianFE(), SplineFields2D::hessianFE(), SplineFields2Dmx::hessianFE(), SplineFields3D::hessianFE(), SplineFields3Dmx::hessianFE(), IntegrandBase::initElement1(), IntegrandBase::initElement2(), NormBase::initProjection(), SplineField2D::valueFE(), SplineField3D::valueFE(), SplineFields1D::valueFE(), SplineFields2D::valueFE(), SplineFields2Dmx::valueFE(), SplineFields3D::valueFE(), SplineFields3Dmx::valueFE(), SplineField2D::valueGrid(), and SplineField3D::valueGrid().

gather() [3/3]

int utl::gather	(	const std::vector< int > &	index,
		size_t	nr,
		const std::vector< Real > &	in,
		utl::matrix< Real > &	out,
		size_t	offset_in = 0,
		size_t	nskip = 0
	)

Compresses the rows of a 2D array based on given scatter indices.

Parameters

[in]	index	Scatter indices of the columns that should be retained
[in]	nr	Number of rows in the 2D array
[in]	in	The input array stored column-wise in a 1D array
[out]	out	The output array stored as a 2D matrix
[in]	offset_in	Optional start offset for the in vector
[in]	nskip	If nonzero, skip the last nskip entries in index

References utl::matrix< T >::fillColumn(), Real, and utl::matrix< T >::resize().

getAttribute() [1/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		bool &	val
	)

Extracts a boolean attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value

Returns

true if the attribute att is found in xml, otherwise false

Referenced by AnaSol::AnaSol(), MultiPatchModelGenerator1D::createG2(), MultiPatchModelGenerator2D::createG2(), DefaultGeometry1D::createG2(), DefaultGeometry2D::createG2(), MultiPatchModelGenerator3D::createG2(), DefaultGeometry3D::createG2(), MultiPatchModelGenerator1D::createGeometry(), MultiPatchModelGenerator2D::createGeometry(), MultiPatchModelGenerator3D::createGeometry(), ModelGenerator::createGeometry(), MultiPatchModelGenerator1D::MultiPatchModelGenerator1D(), MultiPatchModelGenerator2D::MultiPatchModelGenerator2D(), MultiPatchModelGenerator3D::MultiPatchModelGenerator3D(), DataExporter::OnControl(), SIMNodalConstraint< Dim >::parse(), SIMSolverTS< T1 >::parse(), HasGravityBase::parse(), AdaptiveSetup::parse(), EigenModeSIM::parse(), NewmarkSIM::parse(), NonLinSIM::parse(), SIM1D::parse(), SIM2D::parse(), SIMinput::parse(), SIMsupel::parse(), TimeStep::parse(), TextureProperties::parse(), SIMSemi3D< PlaneSolver >::parse(), SIMargsBase::parse(), SIM1D::parseBCTag(), SIM2D::parseBCTag(), SIM3D::parseBCTag(), SIMinput::parseBCTag(), SIMmultiCpl::parseConnection(), SIMoptions::parseConsoleTag(), SIMoptions::parseDiscretizationTag(), SIMinput::parseDualTag(), AnaSol::parseExpressionFunctions(), AnaSol::parseFieldFunctions(), SIM1D::parseGeometryTag(), SIM2D::parseGeometryTag(), SIM3D::parseGeometryTag(), SIMinput::parseICTag(), SIMCoupledSI< T1, T2 >::parseIterations(), parseKnots(), SIMinput::parseLinSolTag(), SIMinput::parseMaterialSet(), SIMinput::parseOutputTag(), SIMoptions::parseOutputTag(), SIMoutput::parseOutputTag(), SIMmodal::parseParams(), SIMinput::parsePatchList(), SIMinput::parsePeriodic(), SIMoptions::parseRestartTag(), SIMinput::parseTopologySet(), parseTracFunc(), LinSolParams::BlockParams::read(), ASM::readXML(), and ModelGenerator::topologySets().

getAttribute() [2/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		char &	val,
		bool	useIntValue = true
	)

Extracts a char attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value
[in]	useIntValue	If true, convert the value to an integer

Returns

true if the attribute att is found in xml, otherwise false

getAttribute() [3/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		int &	val
	)

Extracts an integer attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value

Returns

true if the attribute att is found in xml, otherwise false

getAttribute() [4/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		Real &	val
	)

Extracts a real attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value

Returns

true if the attribute att is found in xml, otherwise false

getAttribute() [5/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		size_t &	val
	)

Extracts a size_t attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value

Returns

true if the attribute att is found in xml, otherwise false

getAttribute() [6/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		std::string &	val,
		bool	toLower = false
	)

Extracts a string attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value
[in]	toLower	If true, convert return string to lower case

Returns

true if the attribute att is found in xml, otherwise false

getAttribute() [7/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		std::vector< int > &	val
	)

Extracts an integer vector attribute from specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value

Returns

true if the attribute att is found in xml, otherwise false

References parseIntegers().

getAttribute() [8/8]

int utl::getAttribute	(	const tinyxml2::XMLElement *	xml,
		const char *	att,
		Vec3 &	val,
		int	ncomp = 0
	)

Extracts a vector attribute value from the specified XML-element.

Parameters

[in]	xml	Pointer to XML-element to extract from
[in]	att	The attribute tag
[out]	val	The attribute value
[in]	ncomp	Maximum number of components to read

Returns

true if the attribute att is found in xml, otherwise false

If fewer than ncomp components specified, use the last value for the rest. If ncomp is zero, use the value zero for the missing components, if any.

References Real, and Vec3::x.

getGmat()

void utl::getGmat	(	const matrix< Real > &	Ji,
		const Real *	du,
		matrix< Real > &	G
	)

Compute the stabilization matrix G from the Jacobian inverse.

Parameters

[in]	Ji	The inverse of the Jacobian matrix
[in]	du	Element lengths in each parametric direction
[out]	G	The stabilization matrix (used in CFD simulators)

References utl::matrix< T >::cols(), Real, and utl::matrix< T >::resize().

Referenced by ASMs2D::integrate(), ASMs2Dmx::integrate(), ASMs3D::integrate(), ASMs3Dmx::integrate(), ASMu2D::integrate(), ASMu2Dmx::integrate(), ASMu3D::integrate(), and ASMu3Dmx::integrate().

getValue()

const char * utl::getValue	(	const tinyxml2::XMLNode *	xml,
		const char *	tag
	)

Returns the value (if any) of the specified XML-node.

Parameters

[in]	xml	Pointer to XML-node to extract the value from
[in]	tag	The name of the XML-element to extract the value from

This method accepts two alternative ways of specifying the value myValue :

<name>myValue</name> 

and

<name value="myValue"/> 

Referenced by SIMSolverTS< T1 >::parse(), AdaptiveSetup::parse(), EigenModeSIM::parse(), NewmarkSIM::parse(), NonLinSIM::parse(), SIMadmin::parse(), SIMoptions::parseEigSolTag(), SIMoptions::parseOutputTag(), SIMoutput::parseOutputTag(), LinSolParams::BlockParams::read(), and LinSolParams::read().

Hessian()

bool utl::Hessian	(	matrix3d< Real > &	H,
		matrix3d< Real > &	d2NdX2,
		const matrix< Real > &	Ji,
		const matrix< Real > &	X,
		const matrix3d< Real > &	d2Ndu2,
		const matrix< Real > &	dNdX,
		bool	geoMapping = true
	)

Set up the Hessian matrix of the coordinate mapping.

Parameters

[out]	H	The Hessian matrix
[out]	d2NdX2	Second order derivatives of basis functions, w.r.t. X
[in]	Ji	The inverse of the Jacobian matrix
[in]	X	Matrix of element nodal coordinates
[in]	d2Ndu2	Second order derivatives of basis functions
[in]	dNdX	First order derivatives of basis functions
[in]	geoMapping	If true, calculate geometry mapping

Returns

false if matrix dimensions are incompatible, otherwise true

If geoMapping is true, H is output, else H is input and assumed to be already calculated in a previous call.

References utl::matrixBase< T >::clear(), utl::matrix< T >::cols(), utl::matrixBase< T >::empty(), utl::matrix3d< T >::multiply(), PROFILE4, Real, utl::matrix3d< T >::resize(), and utl::matrix< T >::rows().

Referenced by SplineField::evalBasis(), LRSplineField::evalBasis(), SplineField::evalMapping(), LRSplineField::evalMapping(), ASMs2D::evalSolution(), ASMs3D::evalSolution(), ASMu2D::evalSolution(), ASMu3D::evalSolution(), ASMs1D::evalSolution(), MxFiniteElement::Hessian(), SplineFields1D::hessianFE(), ASMs1D::integrate(), ASMs2D::integrate(), ASMs3D::integrate(), ASMu2D::integrate(), and ASMu3D::integrate().

Hessian2()

bool utl::Hessian2	(	matrix4d< Real > &	d3NdX3,
		const matrix< Real > &	Ji,
		const matrix4d< Real > &	d3Ndu3
	)

Set up third-order derivatives of the coordinate mapping.

Parameters

[out]	d3NdX3	Third order derivatives of basis functions, w.r.t. X
[in]	Ji	The inverse of the Jacobian matrix
[in]	d3Ndu3	Third order derivatives of basis functions

Returns

false if matrix dimensions are incompatible, otherwise true

References utl::matrix< T >::cols(), utl::matrixBase< T >::dim(), PROFILE4, utl::matrix4d< T >::resize(), and utl::matrix< T >::rows().

Referenced by ASMs2D::evalSolution(), ASMu2D::evalSolution(), ASMs1D::evalSolution(), ASMs1D::integrate(), ASMs2D::integrate(), and ASMu2D::integrate().

ignoreComments()

bool utl::ignoreComments

(

std::istream &

is

)

Ignores comment lines and blank lines from an input stream.

Parameters

is	File stream to read from

interleave()

void utl::interleave	(	const std::vector< Real > &	v1,
		const std::vector< Real > &	v2,
		std::vector< Real > &	out,
		size_t	n1 = 1,
		size_t	n2 = 1
	)

Merges two arrays of nodal values into one array by interleaving.

Parameters

[in]	v1	The first array
[in]	v2	The second array
[out]	out	The output array
[in]	n1	Number of entries per node in first array
[in]	n2	Number of entries per node in second array

Referenced by ASMu2D::regularInterpolation(), and ASMu3D::regularInterpolation().

Jacobian() [1/3]

Real utl::Jacobian	(	matrix< Real > &	J,
		matrix< Real > &	dNdX,
		const matrix< Real > &	X,
		const matrix< Real > &	dNdu,
		bool	computeGradient = true
	)

Set up the Jacobian matrix of the coordinate mapping.

Parameters

[out]	J	The inverse of the Jacobian matrix
[out]	dNdX	First order derivatives of basis functions, w.r.t. X
[in]	X	Matrix of element nodal coordinates
[in]	dNdu	First order derivatives of basis functions
[in]	computeGradient	If false, skip calculation of dNdX

Returns

The Jacobian determinant

References utl::matrixBase< T >::clear(), utl::matrix< T >::cols(), epsZ, utl::matrix< T >::getColumn(), utl::matrix< T >::inverse(), Vec3::length(), utl::matrix< T >::multiply(), Real, and utl::matrix< T >::rows().

Referenced by ASMs1D::assembleL2matrices(), ASMs2DLag::assembleL2matrices(), ASMs3DLag::assembleL2matrices(), ASMu2D::assembleL2matrices(), ASMu3D::assembleL2matrices(), SplineField::evalMapping(), LRSplineField::evalMapping(), ASMs2DmxLag::evalSolution(), ASMs3DmxLag::evalSolution(), ASMs2DLag::evalSolution(), ASMs3DLag::evalSolution(), ASMs2DTri::evalSolution(), ASMs1DLag::evalSolution(), ASMs1DSpec::evalSolution(), ASMs2DSpec::evalSolution(), ASMs3DSpec::evalSolution(), ASMs2D::evalSolution(), ASMs3D::evalSolution(), ASMu2D::evalSolution(), ASMu3D::evalSolution(), ASMs1D::evalSolution(), ASMu2D::evaluateBasisNurbs(), LagrangeFields2D::gradFE(), LagrangeFields3D::gradFE(), SplineFields1D::gradFE(), LagrangeField3D::gradFE(), LagrangeField2D::gradFE(), SplineFields1D::hessianFE(), ASMs1D::integrate(), ASMs1DLag::integrate(), ASMs1DSpec::integrate(), ASMs2D::integrate(), ASMs2DSpec::integrate(), ASMs2DTri::integrate(), ASMs3D::integrate(), ASMs3DLag::integrate(), ASMs3DSpec::integrate(), ASMu2D::integrate(), ASMu3D::integrate(), ASMu3Dmx::integrate(), ASMs2DLag::integrate(), ASMs3D::integrateEdge(), ASMs3DLag::integrateEdge(), ASMs3DSpec::integrateEdge(), ASMs2DLag::integrateElm(), and MxFiniteElement::Jacobian().

Jacobian() [2/3]

Real utl::Jacobian	(	matrix< Real > &	J,
		Vec3 &	n,
		matrix< Real > &	dNdX,
		const matrix< Real > &	X,
		const matrix< Real > &	dNdu,
		size_t	t1,
		size_t	t2
	)

Set up the Jacobian matrix of the coordinate mapping on a boundary.

Parameters

[out]	J	The inverse of the Jacobian matrix
[out]	n	Outward-directed unit normal vector on the boundary
[out]	dNdX	1st order derivatives of basis functions, w.r.t. X
[in]	X	Matrix of element nodal coordinates
[in]	dNdu	First order derivatives of basis functions
[in]	t1	First parametric tangent direction of the boundary
[in]	t2	Second parametric tangent direction of the boundary

Returns

The surface/curve dilation of the boundary

References utl::matrixBase< T >::clear(), utl::matrix< T >::cols(), Vec3::cross(), epsZ, utl::matrix< T >::getColumn(), utl::matrix< T >::inverse(), utl::matrix< T >::multiply(), Vec3::normalize(), Real, and utl::matrix< T >::rows().

Jacobian() [3/3]

Real utl::Jacobian	(	matrix< Real > &	J,
		Vec3 &	t,
		matrix< Real > &	dNdX,
		const matrix< Real > &	X,
		const matrix< Real > &	dNdu,
		size_t	tangent
	)

Set up the Jacobian matrix of the coordinate mapping along an edge.

Parameters

[out]	J	The inverse of the Jacobian matrix
[out]	t	Unit tangent vector along the edge
[out]	dNdX	1st order derivatives of basis functions, w.r.t. X
[in]	X	Matrix of element nodal coordinates
[in]	dNdu	First order derivatives of basis functions
[in]	tangent	Parametric tangent direction along the edge

Returns

The curve dilation of the edge

References utl::matrixBase< T >::clear(), epsZ, utl::matrix< T >::getColumn(), utl::matrix< T >::inverse(), utl::matrix< T >::multiply(), Vec3::normalize(), and Real.

JacobianGradient()

void utl::JacobianGradient	(	const matrix< Real > &	dudX,
		const matrix3d< Real > &	d2Xdu2,
		std::vector< matrix< Real >> &	dJdX
	)

Calculates the derivatives of the Jacobian of the coordinate mapping.

Parameters

[in]	dudX	Derivatives of the geometry basis
[in]	d2Xdu2	Second order derivatives of the geometry basis
[out]	dJdX	Derivatives of the Jacobian wrt physical coordinates

References utl::matrix< T >::add(), utl::matrix< T >::resize(), and utl::matrix< T >::rows().

Referenced by MxFiniteElement::piolaGradient().

merge() [1/2]

void utl::merge	(	std::vector< int > &	a1,
		const std::vector< int > &	a2
	)

Merges integer array a2 into array a1.

Does not require the arrays to be sorted. The values of a2 not already in a1 are appended to a1.

Referenced by ASMs2D::addInterfaceElms(), and ASMs2D::integrate().

merge() [2/2]

void utl::merge	(	std::vector< Real > &	a1,
		const std::vector< Real > &	a2,
		const std::vector< int > &	k1,
		const std::vector< int > &	k2
	)

Merges real array a2 into array a1 based on array indices.

Does not require the arrays to be sorted. The values of a2 not already in a1 are appended to a1.

operator*() [1/8]

Matrix utl::operator*	(	const Matrix &	A,
		const Matrix &	B
	)

Multiplication of two matrices.

Returns

\( {\bf C} = {\bf A} {\bf B} \)

References utl::matrix< T >::multiply().

operator*() [2/8]

RealArray utl::operator*	(	const Matrix &	A,
		const Vector &	X
	)

Multiplication of a matrix and a vector.

Returns

\( {\bf Y} = {\bf A} {\bf X} \)

References utl::matrix< T >::multiply().

operator*() [3/8]

Matrix utl::operator*	(	const Matrix &	A,
		Real	c
	)

Multiplication of a matrix and a scalar.

Returns

\( {\bf B} = c {\bf A} \)

References utl::matrix< T >::multiply().

operator*() [4/8]

RealArray utl::operator*	(	const Vector &	X,
		const Matrix &	A
	)

Multiplication of a vector and a matrix.

Returns

\( {\bf Y} = {\bf A}^T {\bf X} \)

References utl::matrix< T >::multiply().

operator*() [5/8]

Real utl::operator* ( const Vector &  X, const Vector &  Y  )

inline

Dot product of two vectors.

Returns

\( a = {\bf X}^T {\bf Y} \)

References utl::vector< T >::dot().

operator*() [6/8]

Vector utl::operator*	(	const Vector &	X,
		Real	c
	)

Multiplication of a vector and a scalar.

Returns

\( {\bf Y} = c {\bf X} \)

operator*() [7/8]

Matrix utl::operator* ( Real  c, const Matrix &  A  )

inline

Multiplication of a scalar and a matrix.

Returns

\( {\bf B} = c {\bf A} \)

operator*() [8/8]

Vector utl::operator* ( Real  c, const Vector &  X  )

inline

Multiplication of a scalar and a vector.

Returns

\( {\bf Y} = c {\bf X} \)

operator+()

Vector utl::operator+	(	const Vector &	X,
		const Vector &	Y
	)

Addition of two vectors.

Returns

\( {\bf Z} = {\bf X} + {\bf Y} \)

References utl::vector< T >::add().

operator-()

Vector utl::operator-	(	const Vector &	X,
		const Vector &	Y
	)

Subtraction of two vectors.

Returns

\( {\bf Z} = {\bf X} - {\bf Y} \)

References utl::vector< T >::add(), and Real.

operator/()

Vector utl::operator/ ( const Vector &  X, Real  d  )

inline

Division of a vector by a scalar.

Returns

\( {\bf Y} = \frac{1}{d} {\bf X} \)

References Real.

operator<<() [1/3]

template<class T >

std::ostream& utl::operator<<	(	std::ostream &	s,
		const matrix3d< T > &	A
	)

Print the 3D matrix A to the stream s.

The matrix is printed as a set of 2D sub-matrices based on the first two indices.

References utl::matrixBase< T >::dim(), utl::matrixBase< T >::empty(), utl::matrix< T >::fill(), utl::matrixBase< T >::ptr(), and utl::matrixBase< T >::size().

operator<<() [2/3]

template<class T >

std::ostream& utl::operator<<	(	std::ostream &	s,
		const matrix4d< T > &	A
	)

Print the 4D matrix A to the stream s.

The matrix is printed as a set of 2D sub-matrices based on the first two indices.

References utl::matrixBase< T >::dim(), utl::matrixBase< T >::empty(), utl::matrix< T >::fill(), utl::matrixBase< T >::ptr(), and utl::matrixBase< T >::size().

operator<<() [3/3]

template<class T >

std::ostream& utl::operator<<	(	std::ostream &	s,
		const matrix< T > &	A
	)

Print the matrix A to the stream s.

If the matrix is symmetric, only the upper triangular part of the matrix is printed, with the diagonal elements in the first column. The global variable zero_print_tol is used as a tolerance when checking whether the matrix is symmetric or not.

References utl::matrix< T >::cols(), utl::matrix< T >::isSymmetric(), utl::matrix< T >::rows(), trunc(), and zero_print_tol.

parseExprRealFunc()

RealFunc * utl::parseExprRealFunc	(	const std::string &	function,
		bool	autodiff
	)

Creates a scalar-valued function by parsing a character string.

Parameters

[in]	function	Function expression
[in]	autodiff	If true, auto-differentiation is enabled

The implementation of this method is in the file ExprFunctions.C for encapsulation of the autodiff package.

parseExprVecFunc()

VecFunc * utl::parseExprVecFunc	(	const std::string &	function,
		bool	autodiff
	)

Creates a Vector-valued function by parsing a character string.

Parameters

[in]	function	Function expression
[in]	autodiff	If true, auto-differentiation is enabled

The implementation of this method is in the file ExprFunctions.C for encapsulation of the autodiff package.

parseIntegers()

bool utl::parseIntegers	(	std::vector< int > &	values,
		const char *	argv
	)

Parses a character string into an integer or an integer range.

Parameters

	values	The integer value(s) is/are appended to this vector
[in]	argv	Character string with integer data

An integer range is recognised through the syntax i:j.

Referenced by getAttribute(), EigenModeSIM::parse(), ASMu1DLag::parseElemSet(), ASMu2DLag::parseElemSet(), ASMs1D::parseNodeSet(), ASMsupel::parseNodeSet(), and ASMu2DLag::parseNodeSet().

parseIntFunc()

IntFunc * utl::parseIntFunc	(	const std::string &	func,
		const std::string &	type = "expression"
	)

Creates a scalar-valued int function by parsing a character string.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag

References IFEM::cout, utl::Function< Arg, Result >::evaluate(), and Real.

parseKnots() [1/2]

bool utl::parseKnots	(	const tinyxml2::XMLNode *	xml,
		std::vector< Real > &	xi
	)

Parses a sequence of knot values from the specified XML-node.

Parameters

[in]	xml	Pointer to XML-node to extract from
	xi	The knot value(s) is/are appended to this vector

References parseKnots().

parseKnots() [2/2]

bool utl::parseKnots

(

std::vector< Real > &

xi

)

Parses a (possibly graded) sequence of knot values.

Parameters

xi	The knot value(s) is/are appended to this vector

The method uses the strtok function to parse a sequence of space-separated numbers and assumes that (at least one) call to strtok with the first argument different from nullptr has been made before invoking this method.

If the first character of the first token is a digit, it is assumed that the knot values are listed explicitly by the remaining tokens. Otherwise, various mesh grading schemes are assumed with the following syntax:

• G n alpha xi1 xi2 - Geometric grading
• B n alpha xi1 xi2 - Biased geometric grading
• C n alpha xi1 xi2 - Centered geometric grading
• C5 n X1 X2 xi1 xi2 - Centred grading based on a 5th order function

In each case the starting and ending knot values, xi1 and xi2, are optional. If not specified, 0.0 and 1.0 is assumed. The 4th scheme was proposed by Tymofiy Gerasimov 14.12.2016, and is described in the file mesh-grading-function.pdf located in the doc folder.

Referenced by SIM1D::parse(), SIM2D::parse(), SIM3D::parse(), SIM1D::parseGeometryTag(), SIM2D::parseGeometryTag(), SIM3D::parseGeometryTag(), and parseKnots().

parseRealFunc() [1/2]

const RealFunc * utl::parseRealFunc	(	char *	cline,
		Real	A = Real(1),
		bool	print = true
	)

Creates a scalar-valued function by parsing a character string.

The functions are assumed on the general form

\[ f({\bf X},t) = A * g({\bf X}) * h(t) \]

The character string cline is assumed to contain first the definition of the spatial function g( X ) and then the time function h(t). Either of the two components may be omitted, for creating a space-function constant in time, or a time function constant in space.

Note

This method invokes strtok() with nullptr as first argument, assuming the initial call with a non-null string has been performed outside.

References IFEM::cout, FieldFuncBase::FIXED_LEVEL, and Real.

Referenced by SIM1D::parse(), SIM2D::parse(), SIM3D::parse(), SIMinput::parse(), SIMinput::parseBCTag(), AnaSol::parseExpressionFunctions(), SIM2D::parseGeometryTag(), SIMoutput::parseOutputTag(), parseRealFunc(), parseTracFunc(), SIMinput::setInitialConditions(), and SIMinput::setNeumann().

parseRealFunc() [2/2]

RealFunc * utl::parseRealFunc	(	const std::string &	func,
		const std::string &	type = "expression",
		bool	print = true
	)

Creates a scalar-valued function by parsing a character string.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag
[in]	print	If true, print function definition

References IFEM::cout, EvalFuncScalar< Scalar >::numError, parseRealFunc(), and Real.

parseTensorFunc()

TensorFunc * utl::parseTensorFunc	(	const std::string &	func,
		const std::string &	type
	)

Creates a tensor-valued function by parsing a character string.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag

References FieldFuncBase::FIXED_LEVEL, and splitString().

Referenced by AnaSol::parseExpressionFunctions().

parseTimeFunc()

ScalarFunc * utl::parseTimeFunc	(	const char *	func,
		const std::string &	type = "expression",
		Real	eps = Real(1.0e-8)
	)

Creates a time function by parsing a character string.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag
[in]	eps	Domain increment for calculation of numerical derivative

References IFEM::cout.

Referenced by AdaptiveSetup::parse(), SIMCoupledSI< T1, T2 >::parseIterations(), and parseTracFunc().

parseTracFunc() [1/2]

TractionFunc * utl::parseTracFunc	(	const std::string &	func,
		const std::string &	type = "expression",
		int	dir = 0
	)

Creates a vector-valued function defining a surface traction.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag
[in]	dir	Coordinate direction of the traction (0=normal direction)

References IFEM::cout, parseRealFunc(), and Real.

Referenced by SIMinput::parseBCTag(), and SIMinput::setNeumann().

parseTracFunc() [2/2]

TractionFunc * utl::parseTracFunc

(

const tinyxml2::XMLElement *

elem

)

Creates a vector-valued function defining a surface traction.

Parameters

[in]

elem

Pointer to XML-element to parse function definition from

References IFEM::cout, getAttribute(), parseRealFunc(), parseTimeFunc(), and parseVecTimeFunc().

parseVec()

bool utl::parseVec	(	Vec3 &	value,
		const char *	argv
	)

Parses a character string into a point vector.

Parameters

[out]	value	The parsed point vector
[in]	argv	Character string with data

References Real.

parseVecFunc()

VecFunc * utl::parseVecFunc	(	const std::string &	func,
		const std::string &	type = "expression",
		const std::string &	variables = ""
	)

Creates a vector-valued function by parsing a character string.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag
[in]	variables	Optional variable definition for expression functions

References IFEM::cout, FieldFuncBase::FIXED_LEVEL, EvalFuncScalar< Scalar >::numError, and splitString().

Referenced by AnaSol::parseExpressionFunctions(), and SIMinput::setNeumann().

parseVecTimeFunc()

VecTimeFunc * utl::parseVecTimeFunc	(	const char *	func,
		const std::string &	type
	)

Creates a vector-valued time function by parsing a char string.

Parameters

[in]	func	Character string to parse function definition from
[in]	type	Function definition type flag

References IFEM::cout.

Referenced by parseTracFunc().

Pascal()

size_t utl::Pascal	(	int	p,
		unsigned short int	nsd
	)

Returns the number of monomials in Pascal's triangle.

Parameters

[in]	p	Polynomial order (>= 0)
[in]	nsd	Number of spatial dimensions (2 or 3)

Referenced by Pascal().

readLine()

char * utl::readLine

(

std::istream &

is

)

Reads one line, ignoring comment lines and leading blanks.

The data read is kept in an internal static buffer.

Parameters

is	File stream to read from

Returns

Pointer to the static buffer containg the data read.

Referenced by AnaSol::AnaSol(), AdaptiveSetup::parse(), NonLinSIM::parse(), SIM1D::parse(), SIM2D::parse(), SIM3D::parse(), SIMinput::parse(), SIMoutput::parse(), TimeStep::parse(), SIMadmin::readFlat(), and ASM::readMatlab().

renumber() [1/2]

bool utl::renumber	(	int &	num,
		const IntMap &	old2new,
		bool	msg = false
	)

Transforms the integer value num according to a given mapping.

In this method the old2new mapping is not updated.

Parameters

	num	The integer value to transform, updated value on output
[in]	old2new	Mapping from old values to new values
[in]	msg	If true, give error message if given value not found

Returns

true if num was found in the old2new mapping

renumber() [2/2]

bool utl::renumber	(	int &	num,
		int &	runner,
		IntMap &	old2new
	)

Transforms the integer value num into a unique range.

This method is invoked on a series of (non-unique) values. When a value that has not been encountered before is detected, it is transformed into runner+1 and runner is incremented.

Parameters

num	The integer value to transform, updated value on output
runner	The last new value assigned
old2new	Mapping from old values to new values return true if the value of num changed

Referenced by DomainDecomposition::calcGlobalEqNumbers(), DomainDecomposition::calcGlobalNodeNumbers(), GlobalNodes::calcGlobalNodes(), ASMbase::renumberNodes(), and MPC::renumberNodes().

solve()

bool utl::solve	(	Matrix &	A,
		RealArray &	b,
		std::vector< int > *	iPivot = nullptr
	)

Solves the linear system of equations \( {\bf A x} = {\bf b} \).

If iPivot is null, the equation system is solved directly using DGESV from LAPACK. Otherwise, the matrix A is first LU-factorized using DGETRF (if iPivot[0] is zero), and then the equation system is solved using DGETRS. Therefore, it is possible to invoke this method several times to solve for more right-hand sides, if A and iPivot are retained between each call.

References utl::matrix< T >::cols(), dgesv_(), dgetrf_(), dgetrs_(), M, utl::matrixBase< T >::ptr(), Real, and utl::matrix< T >::rows().

transform() [1/2]

bool utl::transform	(	Matrix &	A,
		const Matrix &	Tn
	)

Congruence transformation of a symmetric matrix.

Parameters

	A	The matrix to be transformed
[in]	Tn	Nodal transformation matrix

The following matrix multiplication is performed by this function:

\[ {\bf A} = {\bf T}{\bf A}{\bf T}^T \]

where A is a full, symmetric matrix, and the transformation matrix T has the nodal sub-matrix Tn repeated on the diagonal and otherwise zero.

References utl::matrix< T >::cols(), utl::matrix< T >::fill(), K, M, Real, and utl::matrix< T >::rows().

Referenced by SIMsupel::recoverInternalDOFs(), and ASMsupel::transform().

transform() [2/2]

bool utl::transform	(	Vector &	V,
		const Matrix &	Tn,
		bool	transpose = false
	)

Congruence transformation of a vector.

Parameters

	V	The vector to be transformed
[in]	Tn	Nodal transformation matrix
[in]	transpose	If true, the transpose of Tn is used instead

The vector V is pre-multiplied with the transformation matrix T which has the nodal sub-matrix Tn (or its transpose) repeated on the diagonal and otherwise zero.

References utl::matrix< T >::cols(), utl::vector< T >::fill(), K, M, Real, utl::matrix< T >::rows(), and utl::vector< T >::size().

trunc()

template<class T >

T utl::trunc ( T  v )

inline

Truncate a value to zero when it is less than a given threshold.

Used when printing matrices for easy comparison with other matrices when they contain terms that are numerically zero, except for some round-off noise. The value of the global variable zero_print_tol is used as a tolerance in this method.

References zero_print_tol.

Referenced by SIMoutput::dumpPrimSol(), SIMoutput::dumpResults(), SIMoutput::dumpSolution(), SIMoutput::dumpVector(), NewmarkSIM::initAcc(), operator<<(), SIMoutput::printNRforces(), SIMbase::printSolutionSummary(), SAM::printVector(), NewmarkSIM::solutionNorms(), SIMbase::systemModes(), writeMatlab(), and NonLinSIM::~NonLinSIM().