chrono::ChMatrix< Real > Class Template Reference

Description

template<class Real = double> class chrono::ChMatrix< Real >

A base class for matrix objects (tables of NxM numbers). To access elements, the indexes start from zero, and you must indicate first row, then column, that is: m(2,4) means the element at 3rd row, 5th column. This is an abstract class, so you cannot instantiate objects from it: you must rather create matrices using the specialized child classes like ChMatrixDynamic, ChMatrixNM, ChMatrix33 and so on; all of them have this same base class. Warning: for optimization reasons, not all functions will check about boundaries of element indexes and matrix sizes (in some cases, if sizes are wrong, debug asserts are used).

Further info at the Mathematical objects in Chrono manual page.

#include <ChMatrix.h>

Inheritance diagram for chrono::ChMatrix< Real >:

Public Member Functions

Real & operator() (const int row, const int col)
Parenthesis () operator, to access a single element of the matrix, by supplying the row and the column (indexes start from 0). More...

const Real & operator() (const int row, const int col) const

Real & operator() (const int el)
Parenthesis () operator, to access a single element of the matrix, by supplying the ordinal of the element (indexes start from 0). More...

const Real & operator() (const int el) const

Real * operator[] (const int row)
The [] operator returns the address of the n-th row. More...

const Real * operator[] (const int row) const

ChMatrix< Real > & operator*= (const Real factor)
Multiplies this matrix by a factor, in place.

template<class RealB >
ChMatrix< Real > & operator+= (const ChMatrix< RealB > &matbis)
Increments this matrix by another matrix, in place.

template<class RealB >
ChMatrix< Real > & operator-= (const ChMatrix< RealB > &matbis)
Decrements this matrix by another matrix, in place.

bool operator== (const ChMatrix< Real > &other)
Matrices are equal?

bool operator!= (const ChMatrix< Real > &other)
Matrices are not equal?

virtual ChMatrix< Real > & operator= (const ChMatrix< Real > &matbis)
Assignment operator.

template<class RealB >
ChMatrix< Real > & operator= (const ChMatrix< RealB > &matbis)

void SetElement (int row, int col, Real elem)

Real GetElement (int row, int col)
Gets the element at row,col position. More...

Real GetElement (int row, int col) const

void SetElementN (int index, Real elem)
Sets the Nth element, counting row after row.

Real GetElementN (int index)
Gets the Nth element, counting row after row.

const Real GetElementN (int index) const

Real & Element (int row, int col)
Access a single element of the matrix, by supplying the row and the column (indexes start from 0). More...

const Real & Element (int row, int col) const

Real & ElementN (int index)
Access a single element of the matrix, the Nth element, counting row after row. More...

const Real & ElementN (int index) const

Access directly the "Real* address" buffer. More...

const Real * GetAddress () const

int GetRows () const
Gets the number of rows.

int GetColumns () const
Gets the number of columns.

virtual void Resize (int nrows, int ncols)
Reallocate memory for a new size. VIRTUAL! Must be implemented by child classes!

void SwapColumns (int a, int b)
Swaps the columns a and b.

void SwapRows (int a, int b)
Swap the rows a and b.

void FillDiag (Real sample)
Fill the diagonal elements, given a sample. More...

void FillElem (Real sample)
Fill the matrix with the same value in all elements.

void FillRandom (Real max, Real min)
Fill the matrix with random float numbers, falling within the "max"/"min" range. More...

virtual void Reset ()
Resets the matrix to zero (warning: simply sets memory to 0 bytes!)

void Reset (int nrows, int ncols)
Reset to zeroes and (if needed) changes the size to have row and col.

void SetIdentity ()
Reset to identity matrix (ones on diagonal, zero elsewhere)

template<class RealB >
void CopyFromMatrix (const ChMatrix< RealB > &matra)
Copy a matrix "matra" into this matrix. More...

template<class RealB >
void CopyFromMatrixT (const ChMatrix< RealB > &matra)
Copy the transpose of matrix "matra" into this matrix. More...

template<class RealB >
void CopyTUpMatrix (const ChMatrix< RealB > &matra)
Copy the transposed upper triangular part of "matra" in the lower triangular part of this matrix. More...

template<class RealB >
void CopyTLwMatrix (const ChMatrix< RealB > &matra)
Copy the transposed lower triangulat part of "matra" in the upper triangular part of this matrix. More...

virtual void ArchiveOUT (ChArchiveOut &marchive)
Method to allow serialization of transient data in archives.

virtual void ArchiveIN (ChArchiveIn &marchive)
Method to allow de serialization of transient data from archives.

void StreamOUT (ChStreamOutAscii &mstream)
Method to allow serializing transient data into in ascii as a readable item, for example "chrono::GetLog() << myobject;" ***OBSOLETE***.

void StreamOUTdenseMatlabFormat (ChStreamOutAscii &mstream)
Method to allow serializing transient data into an ascii stream (ex. More...

void MatrNeg ()
Changes the sign of all the elements of this matrix, in place.

template<class RealB , class RealC >
void MatrAdd (const ChMatrix< RealB > &matra, const ChMatrix< RealC > &matrb)
Sum two matrices, and stores the result in "this" matrix: [this]=[A]+[B].

template<class RealB , class RealC >
void MatrSub (const ChMatrix< RealB > &matra, const ChMatrix< RealC > &matrb)
Subtract two matrices, and stores the result in "this" matrix: [this]=[A]-[B].

template<class RealB >
void MatrInc (const ChMatrix< RealB > &matra)
Increments this matrix with another matrix A, as: [this]+=[A].

void MatrInc (Real val)
Increments this matrix by val, as [this]+=val.

template<class RealB >
void MatrDec (const ChMatrix< RealB > &matra)
Decrements this matrix with another matrix A, as: [this]-=[A].

void MatrScale (Real factor)
Scales a matrix, multiplying all elements by a constant value: [this]*=f.

template<class RealB >
void MatrScale (const ChMatrix< RealB > &matra)
Scales a matrix, multiplying all element by all other elements of matra (it is not the classical matrix multiplication!)

void MatrDivScale (Real factor)
Scales a matrix, dividing all elements by a constant value: [this]/=f.

template<class RealB >
void MatrDivScale (const ChMatrix< RealB > &matra)
Scales a matrix, dividing all element by all other elements of matra (it is not the classical matrix multiplication!)

template<class RealB , class RealC >
void MatrMultiply (const ChMatrix< RealB > &matra, const ChMatrix< RealC > &matrb)
Multiplies two matrices, and stores the result in "this" matrix: [this]=[A]*[B].

template<class RealB , class RealC >
void MatrMultiplyT (const ChMatrix< RealB > &matra, const ChMatrix< RealC > &matrb)
Multiplies two matrices (the second is considered transposed): [this]=[A]*[B]' Faster than doing B.MatrTranspose(); result.MatrMultiply(A,B); Note: no check on mistaken size of this!

template<class RealB , class RealC >
void MatrTMultiply (const ChMatrix< RealB > &matra, const ChMatrix< RealC > &matrb)
Multiplies two matrices (the first is considered transposed): [this]=[A]'*[B] Faster than doing A.MatrTranspose(); result.MatrMultiply(A,B);.

void MatrTranspose ()
Transpose this matrix in place.

Real Det ()
Returns the determinant of the matrix. More...

void MatrInverse ()
Returns the inverse of the matrix. More...

bool Equals (const ChMatrix< Real > &other) const
Returns true if vector is identical to other matrix.

bool Equals (const ChMatrix< Real > &other, Real tol) const
Returns true if vector equals another vector, within a tolerance 'tol'.

template<class RealB >
ChVector< Real > Matr34_x_Quat (const ChQuaternion< RealB > &qua)
Multiplies this 3x4 matrix by a quaternion, as v=[G]*q The matrix must be 3x4. More...

template<class RealB >
ChQuaternion< Real > Matr34T_x_Vect (const ChVector< RealB > &va)
Multiplies this 3x4 matrix (transposed) by a vector, as q=[G]'*v The matrix must be 3x4. More...

template<class RealB >
ChQuaternion< Real > Matr44_x_Quat (const ChQuaternion< RealB > &qua)
Multiplies this 4x4 matrix (transposed) by a quaternion, The matrix must be 4x4. More...

void MatrXq_SemiTranspose ()
Transposes only the lower-right 3x3 submatrix of a hemisymmetric 4x4 matrix, used when the 4x4 matrix is a "star" matrix [q] coming from a quaternion q: the non commutative quat. More...

void MatrXq_SemiNeg ()
Change the sign of the 2nd, 3rd and 4th columns of a 4x4 matrix, The product between a quaternion q1 and the conjugate of q2 (q2'), is: q1 x q2' = [q1]*q2' = [q1sn]*q2 where [q1sn] is the semi-negation of the 4x4 matrix [q1]. More...

Real NormInf () const
Gets the norm infinite of the matrix, i.e. More...

Real NormTwo () const
Gets the norm two of the matrix, i.e. More...

Real Max () const
Finds max value among the values of the matrix.

Real Min () const
Finds min value among the values of the matrix.

void LinInterpolate (const ChMatrix< Real > &matra, const ChMatrix< Real > &matrb, Real mx)
Linear interpolation of two matrices. More...

void RowColInterp (Real vmin, Real vmax, Real umin, Real umax)
Fills a matrix or a vector with a bilinear interpolation, from corner values (as a u-v patch). More...

template<class RealB >
void PasteMatrix (const ChMatrix< RealB > &matra, int insrow, int inscol)
Paste a matrix "matra" into "this", inserting at location insrow-inscol. More...

template<class RealB >
void PasteSumMatrix (const ChMatrix< RealB > &matra, int insrow, int inscol)
Paste a matrix "matra" into "this", inserting at location insrow-inscol and performing a sum with the preexisting values. More...

template<class RealB >
void PasteTranspMatrix (const ChMatrix< RealB > &matra, int insrow, int inscol)
Paste a matrix "matra", transposed, into "this", inserting at location insrow-inscol. More...

template<class RealB >
void PasteSumTranspMatrix (const ChMatrix< RealB > &matra, int insrow, int inscol)
Paste a matrix "matra", transposed, into "this", inserting at location insrow-inscol and performing a sum with the preexisting values. More...

template<class RealB >
void PasteClippedMatrix (const ChMatrix< RealB > &matra, int cliprow, int clipcol, int nrows, int ncolumns, int insrow, int inscol)
Paste a clipped portion of the matrix "matra" into "this", inserting the clip (of size nrows, ncolumns) at the location insrow-inscol. More...

template<class RealB >
void PasteClippedMatrixToVector (const ChMatrix< RealB > &matra, int cliprow, int clipcol, int nrows, int ncolumns, int insindex)
Paste a clipped portion of the matrix "matra" into "this", where "this" is a vector (of ChMatrix type), inserting the clip (of size nrows, ncolumns) at the location insindex. More...

template<class RealB >
void PasteClippedVectorToMatrix (const ChMatrix< RealB > &matra, int cliprow, int clipcol, int nrows, int ncolumns, int insindex)
Paste a clipped portion of a vector into "this", where "this" is a matrix (of ChMatrix type), inserting the clip (of size nrows, ncolumns) at the location insindex. More...

template<class RealB >
void PasteSumClippedMatrix (const ChMatrix< RealB > &matra, int cliprow, int clipcol, int nrows, int ncolumns, int insrow, int inscol)
Paste a clipped portion of the matrix "matra" into "this", performing a sum with preexisting values, inserting the clip (of size nrows, ncolumns) at the location insrow-inscol. More...

template<class RealB >
void PasteVector (const ChVector< RealB > &va, int insrow, int inscol)
Paste a vector "va" into the matrix.

template<class RealB >
void PasteSumVector (const ChVector< RealB > &va, int insrow, int inscol)
Paste a vector "va" into the matrix, summing it with preexisting values.

template<class RealB >
void PasteSubVector (const ChVector< RealB > &va, int insrow, int inscol)
Paste a vector "va" into the matrix, subtracting it from preexisting values.

template<class RealB >
void PasteQuaternion (const ChQuaternion< RealB > &qa, int insrow, int inscol)
Paste a quaternion into the matrix.

template<class RealB >
void PasteSumQuaternion (const ChQuaternion< RealB > &qa, int insrow, int inscol)
Paste a quaternion into the matrix, summing it with preexisting values.

template<class RealB >
void PasteCoordsys (const ChCoordsys< RealB > &cs, int insrow, int inscol)
Paste a coordsys into the matrix.

ChVector< Real > ClipVector (int insrow, int inscol) const
Returns the vector clipped from insrow, inscol.

ChQuaternion< Real > ClipQuaternion (int insrow, int inscol) const
Returns the quaternion clipped from insrow, inscol.

ChCoordsys< Real > ClipCoordsys (int insrow, int inscol) const
Returns the coordsys clipped from insrow, inscol.

template<class RealB >
void Set_Xq_matrix (const ChQuaternion< RealB > &q)
Fills a 4x4 matrix as the "star" matrix, representing quaternion cross product. More...

Static Public Member Functions

template<class RealB , class RealC >
static Real MatrDot (const ChMatrix< RealB > &ma, const ChMatrix< RealC > &mb)
Computes dot product between two column-matrices (vectors) with same size. More...

int rows = 1

int columns = 1

Member Function Documentation

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::CopyFromMatrix ( const ChMatrix< RealB > & matra )

Copy a matrix "matra" into this matrix.

Note that the destination matrix will be resized if necessary.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::CopyFromMatrixT ( const ChMatrix< RealB > & matra )

Copy the transpose of matrix "matra" into this matrix.

Note that the destination matrix will be resized if necessary.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::CopyTLwMatrix ( const ChMatrix< RealB > & matra )

Copy the transposed lower triangulat part of "matra" in the upper triangular part of this matrix.

(matra must be square) Note that the destination matrix will be resized if necessary.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::CopyTUpMatrix ( const ChMatrix< RealB > & matra )

Copy the transposed upper triangular part of "matra" in the lower triangular part of this matrix.

(matra must be square) Note that the destination matrix will be resized if necessary.

template<class Real = double>
 Real chrono::ChMatrix< Real >::Det ( )

Returns the determinant of the matrix.

Note! This method must be used only with max 4x4 matrices, otherwise it throws an exception.

template<class Real = double>
 Real& chrono::ChMatrix< Real >::Element ( int row, int col )

Access a single element of the matrix, by supplying the row and the column (indexes start from 0).

Value is returned by reference, so it can be modified, like in m.Element(1,2)=10.

template<class Real = double>
 Real& chrono::ChMatrix< Real >::ElementN ( int index )

Access a single element of the matrix, the Nth element, counting row after row.

Value is returned by reference, so it can be modified, like in m.Element(5)=10.

template<class Real = double>
 void chrono::ChMatrix< Real >::FillDiag ( Real sample )

Fill the diagonal elements, given a sample.

Note that the matrix must already be square (no check for rectangular matrices!), and the extra-diagonal elements are not modified -this function does not set them to 0-

template<class Real = double>
 void chrono::ChMatrix< Real >::FillRandom ( Real max, Real min )

Fill the matrix with random float numbers, falling within the "max"/"min" range.

template<class Real = double>
 Real* chrono::ChMatrix< Real >::GetAddress ( )

Access directly the "Real* address" buffer.

Warning! this is a low level function, it should be used in rare cases, if really needed!

template<class Real = double>
 Real chrono::ChMatrix< Real >::GetElement ( int row, int col )

Gets the element at row,col position.

Indexes start with zero. The return value is a copy of original value. Use Element() instead if you want to access directly by reference the original element.

template<class Real = double>
 void chrono::ChMatrix< Real >::LinInterpolate ( const ChMatrix< Real > & matra, const ChMatrix< Real > & matrb, Real mx )

Linear interpolation of two matrices.

Parameter mx must be 0...1. [this] =(1-x)[A]+ (x)[B] Matrices must have the same size!!

template<class Real = double>
template<class RealB >
 ChVector chrono::ChMatrix< Real >::Matr34_x_Quat ( const ChQuaternion< RealB > & qua )

Multiplies this 3x4 matrix by a quaternion, as v=[G]*q The matrix must be 3x4.

Returns
The result of the multiplication, i.e. a vector.
template<class Real = double>
template<class RealB >
 ChQuaternion chrono::ChMatrix< Real >::Matr34T_x_Vect ( const ChVector< RealB > & va )

Multiplies this 3x4 matrix (transposed) by a vector, as q=[G]'*v The matrix must be 3x4.

Returns
The result of the multiplication, i.e. a quaternion.
template<class Real = double>
template<class RealB >
 ChQuaternion chrono::ChMatrix< Real >::Matr44_x_Quat ( const ChQuaternion< RealB > & qua )

Multiplies this 4x4 matrix (transposed) by a quaternion, The matrix must be 4x4.

Returns
The result of the multiplication, i.e. a quaternion.
template<class Real = double>
template<class RealB , class RealC >
 static Real chrono::ChMatrix< Real >::MatrDot ( const ChMatrix< RealB > & ma, const ChMatrix< RealC > & mb )
static

Computes dot product between two column-matrices (vectors) with same size.

Returns a scalar value.

template<class Real = double>
 void chrono::ChMatrix< Real >::MatrInverse ( )

Returns the inverse of the matrix.

Note! This method must be used only with max 4x4 matrices, otherwise it throws an exception.

template<class Real = double>
 void chrono::ChMatrix< Real >::MatrXq_SemiNeg ( )

Change the sign of the 2nd, 3rd and 4th columns of a 4x4 matrix, The product between a quaternion q1 and the conjugate of q2 (q2'), is: q1 x q2' = [q1]*q2' = [q1sn]*q2 where [q1sn] is the semi-negation of the 4x4 matrix [q1].

template<class Real = double>
 void chrono::ChMatrix< Real >::MatrXq_SemiTranspose ( )

Transposes only the lower-right 3x3 submatrix of a hemisymmetric 4x4 matrix, used when the 4x4 matrix is a "star" matrix [q] coming from a quaternion q: the non commutative quat.

product is: q1 x q2 = [q1]*q2 = [q2st]*q1 where [q2st] is the "semi-transpose of [q2].

template<class Real = double>
 Real chrono::ChMatrix< Real >::NormInf ( ) const

Gets the norm infinite of the matrix, i.e.

the max. of its elements in absolute value.

template<class Real = double>
 Real chrono::ChMatrix< Real >::NormTwo ( ) const

Gets the norm two of the matrix, i.e.

the square root of the sum of the elements squared.

template<class Real = double>
 Real& chrono::ChMatrix< Real >::operator() ( const int row, const int col )

Parenthesis () operator, to access a single element of the matrix, by supplying the row and the column (indexes start from 0).

For example: m(3,5) gets the element at the 4th row, 6th column. Value is returned by reference, so it can be modified, like in m(1,2)=10.

template<class Real = double>
 Real& chrono::ChMatrix< Real >::operator() ( const int el )

Parenthesis () operator, to access a single element of the matrix, by supplying the ordinal of the element (indexes start from 0).

For example: m(3) gets the 4th element, counting row by row. Mostly useful if the matrix is Nx1 sized (i.e. a N-element vector). Value is returned by reference, so it can be modified, like in m(1,2)=10.

template<class Real = double>
 Real* chrono::ChMatrix< Real >::operator[] ( const int row )

The [] operator returns the address of the n-th row.

This is mostly for compatibility with old matrix programming styles (2d array-like) where to access an element at row i, column j, one can write mymatrix[i][j].

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteClippedMatrix ( const ChMatrix< RealB > & matra, int cliprow, int clipcol, int nrows, int ncolumns, int insrow, int inscol )

Paste a clipped portion of the matrix "matra" into "this", inserting the clip (of size nrows, ncolumns) at the location insrow-inscol.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteClippedMatrixToVector ( const ChMatrix< RealB > & matra, int cliprow, int clipcol, int nrows, int ncolumns, int insindex )

Paste a clipped portion of the matrix "matra" into "this", where "this" is a vector (of ChMatrix type), inserting the clip (of size nrows, ncolumns) at the location insindex.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteClippedVectorToMatrix ( const ChMatrix< RealB > & matra, int cliprow, int clipcol, int nrows, int ncolumns, int insindex )

Paste a clipped portion of a vector into "this", where "this" is a matrix (of ChMatrix type), inserting the clip (of size nrows, ncolumns) at the location insindex.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteMatrix ( const ChMatrix< RealB > & matra, int insrow, int inscol )

Paste a matrix "matra" into "this", inserting at location insrow-inscol.

Normal copy for insrow=inscol=0

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteSumClippedMatrix ( const ChMatrix< RealB > & matra, int cliprow, int clipcol, int nrows, int ncolumns, int insrow, int inscol )

Paste a clipped portion of the matrix "matra" into "this", performing a sum with preexisting values, inserting the clip (of size nrows, ncolumns) at the location insrow-inscol.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteSumMatrix ( const ChMatrix< RealB > & matra, int insrow, int inscol )

Paste a matrix "matra" into "this", inserting at location insrow-inscol and performing a sum with the preexisting values.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteSumTranspMatrix ( const ChMatrix< RealB > & matra, int insrow, int inscol )

Paste a matrix "matra", transposed, into "this", inserting at location insrow-inscol and performing a sum with the preexisting values.

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::PasteTranspMatrix ( const ChMatrix< RealB > & matra, int insrow, int inscol )

Paste a matrix "matra", transposed, into "this", inserting at location insrow-inscol.

Normal copy for insrow=inscol=0

template<class Real = double>
 void chrono::ChMatrix< Real >::RowColInterp ( Real vmin, Real vmax, Real umin, Real umax )

Fills a matrix or a vector with a bilinear interpolation, from corner values (as a u-v patch).

template<class Real = double>
template<class RealB >
 void chrono::ChMatrix< Real >::Set_Xq_matrix ( const ChQuaternion< RealB > & q )

Fills a 4x4 matrix as the "star" matrix, representing quaternion cross product.

That is, given two quaternions a and b, aXb= [Astar]*b

template<class Real = double>
 void chrono::ChMatrix< Real >::StreamOUTdenseMatlabFormat ( ChStreamOutAscii & mstream )

Method to allow serializing transient data into an ascii stream (ex.

a file) as a Matlab .dat file (all numbers in a row, separated by space, then CR)