#include <iostream>
#include <sstream>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <blitz/tinyvec-et.h>
#include <blitz/tinymat.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_eigen.h>
#include <mechsys/util/fatal.h>
#include <mechsys/util/util.h>
#include <mechsys/util/array.h>
#include <mechsys/linalg/vector.h>
#include <mechsys/linalg/matrix.h>
#include <mechsys/linalg/laexpr.h>

Namespaces
namespace	OrthoSys
	Orthogonal Cartesian system.
Typedefs
typedef LinAlg::Vector< double >	Vec_t
typedef LinAlg::Matrix< double >	Mat_t
typedef blitz::TinyMatrix < double, 3, 3 >	Mat3_t
typedef blitz::TinyVector < double, 3 >	Vec3_t
typedef blitz::TinyVector < size_t, 3 >	iVec3_t
typedef blitz::TinyVector < bool, 3 >	bVec3_t
typedef blitz::TinyVector < double, 9 >	ATensor2
	Assymmetric 2nd order tensor: for deformation gradient (F), velocity gradient (l), ...
Functions
void	dgetrf_ (const int m, const int n, double a, const int lda, int ipiv, int info)
void	dgetri_ (const int n, double a, const int lda, int ipiv, double work, const int lwork, int *info)
void	dgesvd_ (const char jobu, const char jobvt, const int M, const int N, double A, const int lda, double S, double U, const int ldu, double VT, const int ldvt, double work, const int lwork, const int info)
void	dgesv_ (int Np, int NRHSp, double A, int LDAp, int IPIVp, double B, int LDBp, int INFOp)
double	dot (Vec_t const &V, Vec_t const &W)
size_t	size (Vec_t const &V)
void	set_to_zero (Vec_t &V)
void	set_to_zero (Mat_t &M)
size_t	num_rows (Vec_t const &V)
size_t	num_rows (Mat_t const &M)
size_t	num_cols (Mat_t const &M)
String	PrintVector (Vec_t const &V, char const Fmt="%13g", Array< long > const SkipR=NULL, double Tol=1.0e-13)
String	PrintMatrix (Mat_t const &M, char const Fmt="%13g", Array< long > const SkipRC=NULL, double Tol=1.0e-13, bool NumPy=false)
void	WriteSMAT (Mat_t const &M, char const *FileKey, double Tol=1.0e-14)
double	CompareVectors (Vec_t const &A, Vec_t const &B)
double	CompareMatrices (Mat_t const &A, Mat_t const &B)
double	CheckDiagonal (Mat_t const &M, bool CheckUnitDiag=false)
double	Det (Mat_t const &M)
void	Identity (size_t NRows, Mat_t &I)
void	Svd (Mat_t const &M, Mat_t &U, Vec_t &S, Mat_t &Vt)
void	Inv (Mat_t const &M, Mat_t &Mi, double Tol=1.0e-10)
void	Sol (Mat_t &M, Vec_t &X)
void	Sol (Mat_t const &M, Vec_t const &B, Vec_t &X)
double	Norm (Vec_t const &V)
void	Dyad (Vec_t const &A, Vec_t const &B, Mat_t &M)
void	Mult (Vec_t const &A, Mat_t const &M, Vec_t &B)
void	Vec2ColMat (Vec_t const &V, Mat_t &M)
void	Eig (Mat_t &M, Vec_t &L, Mat_t *Q=NULL, bool Qtrans=false)
String	PrintVector (Vec3_t const &V, char const *Fmt="%13g", double Tol=1.0e-13)
String	PrintMatrix (Mat3_t const &M, char const *Fmt="%13g", double Tol=1.0e-13)
double	CompareVectors (Vec3_t const &A, Vec3_t const &B)
double	CompareMatrices (Mat3_t const &A, Mat3_t const &B)
void	Trans (Mat3_t const &M, Mat3_t &Mt)
double	Det (Mat3_t const &M)
void	Identity (Mat3_t &I)
void	Inv (Mat3_t const &M, Mat3_t &Mi, double Tol=1.0e-10)
void	Sol (Mat3_t const &M, Vec3_t const &B, Vec3_t &X, double Tol=1.0e-10)
void	Eig (Mat3_t &M, Vec3_t &L)
void	Eig (Mat3_t &M, Vec3_t &L, Vec3_t &V0, Vec3_t &V1, Vec3_t &V2, bool SortAsc=false, bool SortDesc=false)
double	Norm (Vec3_t const &V)
void	Dyad (Vec3_t const &A, Vec3_t const &B, Mat3_t &M)
void	Dyad (double s, Vec3_t const &A, Vec3_t const &B, Mat3_t &M)
void	Mult (Vec3_t const &A, Mat3_t const &M, Vec3_t &B)
void	Mult (Mat3_t const &A, Mat3_t const &B, Mat3_t &M)
void	set_to_zero (Vec3_t &V)
void	set_to_zero (Mat3_t &M)
int	OrthoSys::__init_ortho_sys ()
void	Ten2Mat (Vec_t const &Ten, Mat3_t &Mat)
void	Ten2Mat (Vec_t const &Ten, Mat_t &Mat)
void	Mat2Ten (Mat3_t const &Mat, Vec_t &Ten, size_t NumComponents, bool CheckSymmetry=true, double Tol=1.0e-10)
void	UnitVecDeriv (Vec_t const &n, Vec_t &nu, Mat_t &dnudn, double Tol=1.0e-8)
void	UnitVecDeriv (Vec3_t const &n, Vec3_t &nu, Mat3_t &dnudn, double Tol=1.0e-8)
void	Sym (double a, ATensor2 const &T, size_t NCp, Vec_t &S)
void	Dot (ATensor2 const &A, ATensor2 const &B, ATensor2 &C)
void	AddSkewTimesOp1 (ATensor2 const &L, Vec_t const &S, Vec_t &R, double Tol=1.0e-14)
double	Det (ATensor2 const &F)
void	CalcLCauchyGreen (ATensor2 const &F, size_t NCp, Vec_t &b, double Tol=1.0e-14)
void	Mult (Vec_t const &Sig, Vec3_t const &n, Vec3_t &t)
void	Dev (Vec_t const &Ten, Vec_t &DevTen)
double	Tra (Vec_t const &Ten)
void	Pow2 (Vec_t const &Ten, Vec_t &Ten2)
double	Det (Vec_t const &Ten)
void	Inv (Vec_t const &T, Vec_t &Ti, double Tol=1.0e-10)
void	CharInvs (Vec_t const &Ten, double &I1, double &I2, double &I3)
void	CharInvs (Vec_t const &Ten, double &I1, double &I2, double &I3, Vec_t &dI1dTen, Vec_t &dI2dTen, Vec_t &dI3dTen)
void	DerivInv (Vec_t const &A, Vec_t &Ai, Mat_t &dInvA_dA, double Tol=1.0e-10)
void	Eig (Vec_t const &Ten, Vec3_t &L, Vec3_t &V0, Vec3_t &V1, Vec3_t &V2, bool SortAsc=false, bool SortDesc=false)
void	EigenProj (Vec_t const &Ten, Vec3_t &L, Vec3_t &v0, Vec3_t &v1, Vec3_t &v2, Vec_t &P0, Vec_t &P1, Vec_t &P2, bool SortAsc=false, bool SortDesc=false)
void	EigenProjAnalytic (Vec_t const &Ten, Vec3_t &L, Vec_t &P0, Vec_t &P1, Vec_t &P2)
void	Calc_I (size_t NCp, Vec_t &I)
void	Calc_IIsym (size_t NCp, Mat_t &IIsym)
void	Calc_IdyI (size_t NCp, Mat_t &IdyI)
void	Calc_Psd (size_t NCp, Mat_t &Psd)
void	Calc_Piso (size_t NCp, Mat_t &Piso)
void	EigenProjDerivs (Vec_t const &A, Vec3_t &L, Vec3_t &v0, Vec3_t &v1, Vec3_t &v2, Vec_t &P0, Vec_t &P1, Vec_t &P2, Mat_t &dP0dA, Mat_t &dP1dA, Mat_t &dP2dA, double Pertubation=1.0e-7, double Tol=1.0e-14, bool SortAsc=false, bool SortDesc=false)
double	Calc_pcam (Vec_t const &Sig)
double	Calc_ev (Vec_t const &Eps)
double	Calc_qcam (Vec_t const &Sig)
double	Calc_ed (Vec_t const &Eps)
double	Calc_poct (Vec_t const &Sig)
double	Calc_evoct (Vec_t const &Eps)
double	Calc_qoct (Vec_t const &Sig)
double	Calc_edoct (Vec_t const &Eps)
void	Calc_pqoct (Vec_t const &Sig, double &p, double &q)
void	OctInvs (Vec_t const &Sig, double &p, double &q, double &t, double qTol=1.0e-8)
void	OctInvs (Vec_t const &Sig, double &p, double &q, Vec_t &s, double qTol=1.0e-8, bool ApplyPertub=false)
void	OctInvs (Vec_t const &Sig, double &p, double &q, double &t, double &th, Vec_t &s, double qTol=1.0e-8, Vec_t *dthdSig=NULL, bool ApplyPertub=false)
void	OctInvs (Vec3_t const &L, double &p, double &q, double &t, double qTol=1.0e-8)
void	OctInvs (Vec3_t const &L, double &p, double &q, double &t, Vec3_t &dpdL, Vec3_t &dqdL, Vec3_t &dtdL, double qTol=1.0e-8)
void	pqth2L (double p, double q, double th, Vec3_t &L, char const *Type="oct")
void	OctDerivs (Vec3_t const &L, double &p, double &q, double &t, Mat3_t &dpqthdL, double qTol=1.0e-8)
void	InvOctDerivs (Vec3_t const &Lsorted, double &p, double &q, double &t, Mat3_t &dLdpqth, double qTol=1.0e-8)
double	Phi2M (double Phi, char const *Type="oct")
double	M2Phi (double M, char const *Type="oct")
double	Calc_K (double E, double nu)
double	Calc_G (double E, double nu)
double	Calc_lam (double E, double nu)
double	Calc_G_ (double K, double nu)
double	Calc_E (double K, double G)
double	Calc_E_ (double K, double nu)
double	Calc_nu (double K, double G)
Variables
Vec3_t	OrthoSys::O
	Origin.
Vec3_t	OrthoSys::e0
Vec3_t	OrthoSys::e1
Vec3_t	OrthoSys::e2
	Basis.
Mat3_t	OrthoSys::I
	Identity.
int	OrthoSys::__dummy_init_ortho_sys = __init_ortho_sys()

Typedef Documentation

typedef blitz::TinyVector<double,9> ATensor2

Assymmetric 2nd order tensor: for deformation gradient (F), velocity gradient (l), ...

typedef blitz::TinyVector<bool,3> bVec3_t

typedef blitz::TinyVector<size_t,3> iVec3_t

typedef blitz::TinyMatrix<double,3,3> Mat3_t

3x3 Matrix.

typedef LinAlg::Matrix<double> Mat_t

typedef blitz::TinyVector<double,3> Vec3_t

3x1 Vector.

typedef LinAlg::Vector<double> Vec_t

Function Documentation

void AddSkewTimesOp1	(	ATensor2 const &	L,
		Vec_t const &	S,
		Vec_t &	R,
		double	Tol = `1.0e-14`
	)		`[inline]`

Add R to operation involving skew and symm tensors: R += w*S - S*w, in which w = skew(L) = 0.5*(L-L^T).

double Calc_E	(	double	K,
		double	G
	)		`[inline]`

Calculate E given K and G.

double Calc_E_	(	double	K,
		double	nu
	)		`[inline]`

Calculate E given K and nu.

double Calc_ed ( Vec_t const & Eps ) [inline]

double Calc_edoct ( Vec_t const & Eps ) [inline]

double Calc_ev ( Vec_t const & Eps ) [inline]

double Calc_evoct ( Vec_t const & Eps ) [inline]

double Calc_G	(	double	E,
		double	nu
	)		`[inline]`

Calculate G given E and nu.

double Calc_G_	(	double	K,
		double	nu
	)		`[inline]`

Calculate G given K and nu.

void Calc_I	(	size_t	NCp,
		Vec_t &	I
	)		`[inline]`

Initialize second order identity tensor.

void Calc_IdyI	(	size_t	NCp,
		Mat_t &	IdyI
	)		`[inline]`

Initialize IdyI fourth order tensor.

void Calc_IIsym	(	size_t	NCp,
		Mat_t &	IIsym
	)		`[inline]`

Initialize fourth order identity tensor.

double Calc_K	(	double	E,
		double	nu
	)		`[inline]`

Calculate K given E and nu.

double Calc_lam	(	double	E,
		double	nu
	)		`[inline]`

Calculate lam given E and nu.

double Calc_nu	(	double	K,
		double	G
	)		`[inline]`

Calculate nu given K and G.

double Calc_pcam ( Vec_t const & Sig ) [inline]

Derivatives of the eigenvectors of Sig w.r.t Sig (a third order tensor). NOTE: the eigevalues and eigenvectors must be given as input.

void Calc_Piso	(	size_t	NCp,
		Mat_t &	Piso
	)		`[inline]`

Initialize fourth order isotropic tensor.

double Calc_poct ( Vec_t const & Sig ) [inline]

void Calc_pqoct	(	Vec_t const &	Sig,
		double &	p,
		double &	q
	)		`[inline]`

void Calc_Psd	(	size_t	NCp,
		Mat_t &	Psd
	)		`[inline]`

Initialize fourth order symmetric-deviatoric tensor.

double Calc_qcam ( Vec_t const & Sig ) [inline]

double Calc_qoct ( Vec_t const & Sig ) [inline]

void CalcLCauchyGreen	(	ATensor2 const &	F,
		size_t	NCp,
		Vec_t &	b,
		double	Tol = `1.0e-14`
	)		`[inline]`

Calculate left Cauchy-Green tensor: b = F*F^T.

void CharInvs	(	Vec_t const &	Ten,
		double &	I1,
		double &	I2,
		double &	I3
	)		`[inline]`

Characteristic invariants of 2nd order symmetric tensor Ten.

void CharInvs	(	Vec_t const &	Ten,
		double &	I1,
		double &	I2,
		double &	I3,
		Vec_t &	dI1dTen,
		Vec_t &	dI2dTen,
		Vec_t &	dI3dTen
	)		`[inline]`

Characteristic invariants of 2nd order symmetric tensor Ten and their derivatives.

double CheckDiagonal	(	Mat_t const &	M,
		bool	CheckUnitDiag = `false`
	)		`[inline]`

Check if matrix is diagonal.

double CompareMatrices	(	Mat_t const &	A,
		Mat_t const &	B
	)		`[inline]`

Compare two matrices.

double CompareMatrices	(	Mat3_t const &	A,
		Mat3_t const &	B
	)		`[inline]`

Compare two matrices.

double CompareVectors	(	Vec_t const &	A,
		Vec_t const &	B
	)		`[inline]`

Compare two vectors.

double CompareVectors	(	Vec3_t const &	A,
		Vec3_t const &	B
	)		`[inline]`

Compare two vectors.

void DerivInv	(	Vec_t const &	A,
		Vec_t &	Ai,
		Mat_t &	dInvA_dA,
		double	Tol = `1.0e-10`
	)		`[inline]`

Derivative of the Inverse of A w.r.t A.

double Det ( Mat_t const & M ) [inline]

Determinant.

double Det ( Mat3_t const & M ) [inline]

Determinant.

double Det ( ATensor2 const & F ) [inline]

Determinant of F.

double Det ( Vec_t const & Ten ) [inline]

Determinant of 2nd order symmetric tensor Ten.

void Dev	(	Vec_t const &	Ten,
		Vec_t &	DevTen
	)		`[inline]`

Deviator of 2nd order symmetric tensor Ten.

void dgesv_	(	int *	Np,
		int *	NRHSp,
		double *	A,
		int *	LDAp,
		int *	IPIVp,
		double *	B,
		int *	LDBp,
		int *	INFOp
	)

void dgesvd_	(	const char *	jobu,
		const char *	jobvt,
		const int *	M,
		const int *	N,
		double *	A,
		const int *	lda,
		double *	S,
		double *	U,
		const int *	ldu,
		double *	VT,
		const int *	ldvt,
		double *	work,
		const int *	lwork,
		const int *	info
	)

void dgetrf_	(	const int *	m,
		const int *	n,
		double *	a,
		const int *	lda,
		int *	ipiv,
		int *	info
	)

void dgetri_	(	const int *	n,
		double *	a,
		const int *	lda,
		int *	ipiv,
		double *	work,
		const int *	lwork,
		int *	info
	)

double dot	(	Vec_t const &	V,
		Vec_t const &	W
	)		`[inline]`

void Dot	(	ATensor2 const &	A,
		ATensor2 const &	B,
		ATensor2 &	C
	)		`[inline]`

Dot product: C=A*B => C(i,j)=A(i,k)*B(k,j)

void Dyad	(	Vec_t const &	A,
		Vec_t const &	B,
		Mat_t &	M
	)		`[inline]`

Dyadic product.

void Dyad	(	Vec3_t const &	A,
		Vec3_t const &	B,
		Mat3_t &	M
	)		`[inline]`

Dyadic product.

void Dyad	(	double	s,
		Vec3_t const &	A,
		Vec3_t const &	B,
		Mat3_t &	M
	)		`[inline]`

Dyadic product multiplied by s.

void Eig	(	Mat_t &	M,
		Vec_t &	L,
		Mat_t *	Q = `NULL`,
		bool	Qtrans = `false`
	)		`[inline]`

Eigenvalues of symmetric matrix. NOTE: This function changes the matrix M.

void Eig	(	Mat3_t &	M,
		Vec3_t &	L
	)		`[inline]`

Eigenvalues. NOTE: This function changes the matrix M.

void Eig	(	Mat3_t &	M,
		Vec3_t &	L,
		Vec3_t &	V0,
		Vec3_t &	V1,
		Vec3_t &	V2,
		bool	SortAsc = `false`,
		bool	SortDesc = `false`
	)		`[inline]`

Eigenvalues and eigenvectors. NOTE: This function changes the matrix M.

void Eig	(	Vec_t const &	Ten,
		Vec3_t &	L,
		Vec3_t &	V0,
		Vec3_t &	V1,
		Vec3_t &	V2,
		bool	SortAsc = `false`,
		bool	SortDesc = `false`
	)		`[inline]`

Eigenvalues and eigenvectors of second order tensor in Mandel's basis.

void EigenProj	(	Vec_t const &	Ten,
		Vec3_t &	L,
		Vec3_t &	v0,
		Vec3_t &	v1,
		Vec3_t &	v2,
		Vec_t &	P0,
		Vec_t &	P1,
		Vec_t &	P2,
		bool	SortAsc = `false`,
		bool	SortDesc = `false`
	)		`[inline]`

Eigenprojectors of 2nd order symmetric tensor Ten.

void EigenProjAnalytic	(	Vec_t const &	Ten,
		Vec3_t &	L,
		Vec_t &	P0,
		Vec_t &	P1,
		Vec_t &	P2
	)		`[inline]`

Eigenprojectors of 2nd order symmetric tensor Ten.

void EigenProjDerivs	(	Vec_t const &	A,
		Vec3_t &	L,
		Vec3_t &	v0,
		Vec3_t &	v1,
		Vec3_t &	v2,
		Vec_t &	P0,
		Vec_t &	P1,
		Vec_t &	P2,
		Mat_t &	dP0dA,
		Mat_t &	dP1dA,
		Mat_t &	dP2dA,
		double	Pertubation = `1.0e-7`,
		double	Tol = `1.0e-14`,
		bool	SortAsc = `false`,
		bool	SortDesc = `false`
	)		`[inline]`

Derivatives of the eigenprojectors w.r.t its defining tensor.

void Identity	(	size_t	NRows,
		Mat_t &	I
	)		`[inline]`

Identity.

void Identity ( Mat3_t & I ) [inline]

Identity.

void Inv	(	Mat_t const &	M,
		Mat_t &	Mi,
		double	Tol = `1.0e-10`
	)		`[inline]`

Inverse.

void Inv	(	Mat3_t const &	M,
		Mat3_t &	Mi,
		double	Tol = `1.0e-10`
	)		`[inline]`

Inverse.

void Inv	(	Vec_t const &	T,
		Vec_t &	Ti,
		double	Tol = `1.0e-10`
	)		`[inline]`

Inverse of 2nd order symmetric tensor T.

void InvOctDerivs	(	Vec3_t const &	Lsorted,
		double &	p,
		double &	q,
		double &	t,
		Mat3_t &	dLdpqth,
		double	qTol = `1.0e-8`
	)		`[inline]`

double M2Phi	(	double	M,
		char const *	Type = `"oct"`
	)		`[inline]`

Calculate phi (friction angle at compression (degrees)) given M (max q/p at compression).

void Mat2Ten	(	Mat3_t const &	Mat,
		Vec_t &	Ten,
		size_t	NumComponents,
		bool	CheckSymmetry = `true`,
		double	Tol = `1.0e-10`
	)		`[inline]`

Creates a 2nd order symmetric tensor Ten (using Mandel's representation) based on its matrix components.

void Mult	(	Vec_t const &	A,
		Mat_t const &	M,
		Vec_t &	B
	)		`[inline]`

Left multiplication. {B} = {A}*[M]. NOTE: this is not efficient for large matrices.

void Mult	(	Vec3_t const &	A,
		Mat3_t const &	M,
		Vec3_t &	B
	)		`[inline]`

Left multiplication. {B} = {A}^T*[M].

void Mult	(	Mat3_t const &	A,
		Mat3_t const &	B,
		Mat3_t &	M
	)		`[inline]`

Matrix multiplication.

void Mult	(	Vec_t const &	Sig,
		Vec3_t const &	n,
		Vec3_t &	t
	)		`[inline]`

Multiplication of tensor's matrix by a vector (similar to Cauchy's rule). {t} = [Sig]*{n}.

double Norm ( Vec_t const & V ) [inline]

Norm.

double Norm ( Vec3_t const & V ) [inline]

Norm.

size_t num_cols ( Mat_t const & M ) [inline]

size_t num_rows ( Vec_t const & V ) [inline]

size_t num_rows ( Mat_t const & M ) [inline]

void OctDerivs	(	Vec3_t const &	L,
		double &	p,
		double &	q,
		double &	t,
		Mat3_t &	dpqthdL,
		double	qTol = `1.0e-8`
	)		`[inline]`

void OctInvs	(	Vec_t const &	Sig,
		double &	p,
		double &	q,
		double &	t,
		double	qTol = `1.0e-8`
	)		`[inline]`

Octahedral invariants of Sig.

void OctInvs	(	Vec_t const &	Sig,
		double &	p,
		double &	q,
		Vec_t &	s,
		double	qTol = `1.0e-8`,
		bool	ApplyPertub = `false`
	)		`[inline]`

Octahedral invariants of Sig (and deviator s).

void OctInvs	(	Vec_t const &	Sig,
		double &	p,
		double &	q,
		double &	t,
		double &	th,
		Vec_t &	s,
		double	qTol = `1.0e-8`,
		Vec_t *	dthdSig = `NULL`,
		bool	ApplyPertub = `false`
	)		`[inline]`

Octahedral invariants of Sig (and derivatives).

void OctInvs	(	Vec3_t const &	L,
		double &	p,
		double &	q,
		double &	t,
		double	qTol = `1.0e-8`
	)		`[inline]`

Octahedral invariants of Sig (L = principal values).

void OctInvs	(	Vec3_t const &	L,
		double &	p,
		double &	q,
		double &	t,
		Vec3_t &	dpdL,
		Vec3_t &	dqdL,
		Vec3_t &	dtdL,
		double	qTol = `1.0e-8`
	)		`[inline]`

Octahedral invariants of Sig (L = principal values). With derivatives

double Phi2M	(	double	Phi,
		char const *	Type = `"oct"`
	)		`[inline]`

Calculate M = max q/p at compression (phi: friction angle at compression (degrees)).

void Pow2	(	Vec_t const &	Ten,
		Vec_t &	Ten2
	)		`[inline]`

2nd order symmetric tensor Ten raised to the power of 2.

void pqth2L	(	double	p,
		double	q,
		double	th,
		Vec3_t &	L,
		char const *	Type = `"oct"`
	)		`[inline]`

Calc principal values given octahedral invariants. (-pi <= th(rad) <= pi)

String PrintMatrix	(	Mat_t const &	M,
		char const *	Fmt = `"%13g"`,
		Array< long > const *	SkipRC = `NULL`,
		double	Tol = `1.0e-13`,
		bool	NumPy = `false`
	)		`[inline]`

Print matrix.

String PrintMatrix	(	Mat3_t const &	M,
		char const *	Fmt = `"%13g"`,
		double	Tol = `1.0e-13`
	)		`[inline]`

Print matrix.

String PrintVector	(	Vec_t const &	V,
		char const *	Fmt = `"%13g"`,
		Array< long > const *	SkipR = `NULL`,
		double	Tol = `1.0e-13`
	)		`[inline]`

Print vector.

String PrintVector	(	Vec3_t const &	V,
		char const *	Fmt = `"%13g"`,
		double	Tol = `1.0e-13`
	)		`[inline]`

Print vector.

void set_to_zero ( Vec_t & V ) [inline]

void set_to_zero ( Mat_t & M ) [inline]

void set_to_zero ( Vec3_t & V ) [inline]

Clear vector.

void set_to_zero ( Mat3_t & M ) [inline]

Clear matrix.

size_t size ( Vec_t const & V ) [inline]

void Sol	(	Mat_t &	M,
		Vec_t &	X
	)		`[inline]`

Linear Solver. {X} = [M]^{-1}{X} (M is lost) (X initially has the contents of the right-hand side)

void Sol	(	Mat_t const &	M,
		Vec_t const &	B,
		Vec_t &	X
	)		`[inline]`

Linear Solver. {X} = [M]^{-1}{B}

void Sol	(	Mat3_t const &	M,
		Vec3_t const &	B,
		Vec3_t &	X,
		double	Tol = `1.0e-10`
	)		`[inline]`

Linear Solver. {X} = [M]^{-1}{B}

void Svd	(	Mat_t const &	M,
		Mat_t &	U,
		Vec_t &	S,
		Mat_t &	Vt
	)		`[inline]`

Singular value decomposition. M = U_mxm * D_mxn * Vt_nxn

void Sym	(	double	a,
		ATensor2 const &	T,
		size_t	NCp,
		Vec_t &	S
	)		`[inline]`

Symmetric part of a tensor multiplied by a. S = a*sym(T) = a * 0.5*(T + trn(T)).

void Ten2Mat	(	Vec_t const &	Ten,
		Mat3_t &	Mat
	)		`[inline]`

Creates the matrix representation of 2nd order symmetric tensor Ten (Mandel's representation).

void Ten2Mat	(	Vec_t const &	Ten,
		Mat_t &	Mat
	)		`[inline]`

(TinyMatrix) Creates the matrix representation of 2nd order symmetric tensor Ten (Mandel's representation).

double Tra ( Vec_t const & Ten ) [inline]

Trace of 2nd order symmetric tensor Ten.

void Trans	(	Mat3_t const &	M,
		Mat3_t &	Mt
	)		`[inline]`

Transpose.

void UnitVecDeriv	(	Vec_t const &	n,
		Vec_t &	nu,
		Mat_t &	dnudn,
		double	Tol = `1.0e-8`
	)		`[inline]`

Derivative of unit vector.

void UnitVecDeriv	(	Vec3_t const &	n,
		Vec3_t &	nu,
		Mat3_t &	dnudn,
		double	Tol = `1.0e-8`
	)		`[inline]`

Derivative of unit vector.

void Vec2ColMat	(	Vec_t const &	V,
		Mat_t &	M
	)		`[inline]`

Create column matrix from vector.

void WriteSMAT	(	Mat_t const &	M,
		char const *	FileKey,
		double	Tol = `1.0e-14`
	)		`[inline]`

Write SMatrix for vismatrix.

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