dMatrix3x3

dMatrix3x3 is a static storage container which stores a three by three matrix of double values. It is used to store deformation tensors, rotation matrices, transformation tensors, etc., as a storage unit in Storage3D container.

The data inside of the dMatrix3x3 container is manipulated using a number of dedicated methods:

Constructors

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dMatrix3x3();
Default constructor, sets matrix values to zero;

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dMatrix3x3(const dMatrix3x3& rhs);
Copy constructor, initializes the current matrix with a copy of rhs.

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dMatrix3x3(std::initializer_list<double> matinit);
Constructor, initializes the current matrix using initializer list matinit.

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static dMatrix3x3 ZeroTensor(void);
Constructs and returns zero-valued matrix.

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static dMatrix3x3 UnitTensor(void);
Constructs and returns diagonal unity matrix.

Access operators

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double& operator()(const size_t i, const size_t j);
double const& operator()(const size_t i, const size_t j) const;

Return (const) reference to the element i,j.

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double* data(void);
const double* data(void) const;
Returns (const) pointer to the first element of the vector.

Logic, arithmetic and matrix-vector operations

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bool operator==(const dMatrix3x3& rhs);
Boolean comparison operator. Returns true if element-wise difference of the two matrices is smaller than DBL_EPSILON.

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bool operator!=(const dMatrix3x3& rhs);
Boolean comparison operator. Returns true if element-wise difference of the two matrices is greater than DBL_EPSILON.

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dMatrix3x3 operator*(const double m) const;
Returns current matrix with all components multiplied by the factor m.

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dMatrix3x3 operator/(const double m) const;
Returns current matrix with all components divided by the factor m.

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dMatrix3x3 operator*(const dMatrix3x3& rhs) const;
Returns dot product of two matrices.

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dMatrix3x3 operator+(const dMatrix3x3& rhs) const;
Returns the sum of two matrices.

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dMatrix3x3 operator-(const dMatrix3x3& rhs) const;
Returns the difference of two matrices.

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dMatrix3x3 operator*(const dMatrix3x3& rhs) const;
Returns dot product of two matrices.

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dMatrix3x3& operator*=(const dMatrix3x3& rhs);
Assigns the dot product of two matrices to the current matrix.

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dMatrix3x3& operator/=(const double m);
Divides all entries of the current matrix by the factor m.

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dMatrix3x3& operator-=(const dMatrix3x3& rhs);
Subtracts matrix rhs from the current matrix.

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dMatrix3x3& operator+=(const dMatrix3x3& rhs);
Adds matrix rhs to the current matrix.

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dMatrix3x3& operator=(const dMatrix3x3& rhs);
Assigns the content of the matrix rhs to the current matrix.

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dMatrix3x3 Hadamard_product(const dMatrix3x3& rhs) const;
Returns Hadamard (component-wise) product of two matrices.

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double determinant(void) const;
Returns determinant of the current matrix.

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double double_contract(const dMatrix3x3& rhs) const;
Returns double-contraction of two matrices.

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double trace(void) const;
Returns the trace of the current matrix.

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double max(void) const;
Returns maximum element of the matrix.

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double min(void) const;
Returns minimum element of the matrix.

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double p_norm(double p);
Returns p-norm of the current matrix with the given p.

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double norm(double p);
Returns Frobenius norm of the current matrix.

Data manipulation methods

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void set(double r00, double r01, double r02,
         double r10, double r11, double r12,
         double r20, double r21, double r22)

Sets matrix elements to the correspnding values.

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void set_to_zero(void);
Sets all entries to zero.

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void set_to_unity(void);
Sets diagonal elements to one and all off-diagonal entries to zero.

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dMatrix3x3& invert();
Inverts current matrix.

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dMatrix3x3 inverted() const;
Returns inverted copy of the current matrix.

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dMatrix3x3& transpose();
Transposes current matrix.

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dMatrix3x3 transposed() const;
Returns transposed copy of the current matrix.

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dMatrix3x3& rotate(const dMatrix3x3& RotationMatrix);
Rotates current matrix using the specified RotationMatrix.

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dMatrix3x3 rotated(const dMatrix3x3& RotationMatrix) const;
Returns rotated copy of the current matrix using the specified RotationMatrix.

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dMatrix3x3& rotateU(const dMatrix3x3& RotationMatrix);
Performs left-side rotation of current matrix using the specified RotationMatrix.

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dMatrix3x3 rotatedU(const dMatrix3x3& RotationMatrix) const;
Returns left-side rotated copy of the current matrix.

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dMatrix3x3& symmetrize(void);
Symmetrizes current matrix.

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dMatrix3x3 symmetrized(void);
Returns symmetrized copy of the current matrix.

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dMatrix3x3& power_elements(double &n);
Rises all elements of the current matrix to power n.

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dMatrix3x3 powered_elements(double &n) const;
Returns copy of the current matrix with all elements resized to power n.

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dMatrix3x3 get_skew(void) const;
Return skew-symmetric copy of the current matrix.

Container properties

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constexpr size_t sizeX(void) const;
Returns first (X)-dimension of the stored matrix.

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constexpr size_t sizeY(void) const;
Returns second (Y)-dimension of the stored matrix.

MPI communication methods

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void pack(std::vector<double>& buffer);
Packs the content of the current dMatrix3x3 object into the MPI communication buffer.

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void unpack(std::vector<double>& buffer, size_t& it);
Unpacks (reads) the content of the current dMatrix3x3 object from the MPI communication buffer. The existing data in the container is overwritten.

Read/write methods

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std::string print(void) const;
Returns formatted string of the matrix values ready to print to the terminal.

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void read_ASCII(std::istream& inp);
Reads matrix content from the input stream.

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void write_ASCII(std::ostream& outp, const int precision = 16, const char sep = ' ') const;
Writes matrix content in ASCII format with the specified precision using sep as entry separator into the output stream.

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std::string get_output_string(const int precision = 16, const char sep = ' ') const;
Returns output string with matrix content in ASCII format with the specified precision using sep as entry separator.

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std::vector<double> get_vector() const;
Returns std::vector containing current matrix components.

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std::vector<float> get_vector_float() const;
Returns std::vector<float> containing current matrix components rounded to float precision.

dMatrix3x3 ​

Constructors ​

Access operators ​

Logic, arithmetic and matrix-vector operations ​

Data manipulation methods ​

Container properties ​

MPI communication methods ​

Read/write methods ​