MatrixRUTC - Right Upper Triangular matrix.

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Ravl - Math - Linear Algebra - MatrixRUTC

MatrixRUTC

Right Upper Triangular matrix.

include	"Ravl/MatrixRUT.hh"
Created:	24/01/2001
Source file:	Ravl/Math/LinearAlgebra/General/MatrixRUT.hh
User Level:	Normal
Library:	RavlMath
In Scope:	RavlN

Comments:
This class contains functions optimised for working with Right Upper Triangular matrix's. The lower right is assumed to be zero. Most of the operations on this matrix ignore the contents of the lower part, and it is not garanteed to contain zero's. To ensure this use 'ZeroLowerLeft()', this MUST be done before using matrix operators that are not part of this class.

The matrix MUST be square.

Parent Classes:

MatrixC

Methods:

MatrixRUTC(): Default constructor.
MatrixRUTC(UIntT size): Create a new matrix of size * size.
MatrixRUTC(const MatrixC & oth): Base constructor.
MatrixRUTC(const SArray2dC<RealT> & oth): Base constructor.
MatrixRUTC Inverse() const: Calculate the inverse of a upper right triangular matrix.
an invalid matrix is returned if this matrix is singular. This can be tested for by IsValid().
bool InverseIP(): Calculate the inverse of a upper right triangular matrix. In place.
NOTE: The result is not upper triangular. False is returned if matrix is singular, true otherwise.
void AddOuterProduct(const VectorC & vec): Add outer product of 'vec' with itself to this matrix.
void AddOuterProduct(const VectorC & vec,RealT a): Add outer product of 'vec' with itself to this matrix multiplied by a
const MatrixRUTC & operator +=(const MatrixRUTC & mat): Add another right upper matrix to this one.
const MatrixRUTC & operator -=(const MatrixRUTC & mat): Subtract another right upper matrix from this one.
const MatrixRUTC & operator *=(RealT val): Multiply by a constant.
const MatrixRUTC & operator /=(RealT val): Divide by a constant.
void ZeroLowerLeft(): Fill the lower left part of the matrix with zero's.
Note: This is an in place operation.
void MakeSymmetric(): Make this matrix symmetric.
Copy the upper right triangle to the lower left. Note: this is an in-place operation.
RealT Det() const: Calculate the determinant of the matrix.
Very quick, Just the product of the diagonal.

#include "Ravl/Matrix.hh"

bool IsReal() const: Test if matrix only contains real values.
This will return false if either nan's (Not an number) or infinite values are found.
MatrixC Inverse() const: Calculate the inverse of this matrix.
an invalid matrix is returned if this matrix is singular.
bool InverseIP(): Calculate the inverse of this matrix in place.
Returns false if matrix is singular.
Notes: The matrix must be square
If the matrix is not stored in a continous area of memory a slightly different routine is used to do the inversion.
MatrixC PseudoInverse(RealT thresh = 1 e - 5) const: Do a pseudo inverse
Uses singular value decomposition to decompose the matrix, and sets the singular values smaller than 'thesh' to zero.
RealT Det() const: Calculate the determinant of the matrix.

#include "Ravl/TMatrix.hh"

operator TFMatrixC<RealT,N,M>(): Convert to fixed size matrix.
SizeT Rows() const: Return the number of rows
SizeT Cols() const: Return the number of columns
TMatrixC<RealT> operator *(RealT val) const: Multiply by a constant.
TVectorC<RealT> operator *(const TVectorC<RealT> & vector) const: Multiplication "TVectorC" = "This" * vector
TMatrixC<RealT> operator *(const TMatrixC<RealT> & mat) const: Multiplication "result" = "this" * "mat"
TMatrixC<RealT> MulT(const TMatrixC<RealT> & B) const: Multiplication A * B.T()
TMatrixC<RealT> TMul(const TMatrixC<RealT> & B) const: Multiplication A.T() * B
TVectorC<RealT> TMul(const TVectorC<RealT> & vec) const: Multiplication A.T() * vec
TMatrixC<RealT> AAT() const: Return A * A.T().
TMatrixC<RealT> ATA() const: Return A.T() * A.
TMatrixC<RealT> T() const: Get transpose of matrix.
static TMatrixC<RealT> Identity(UIntT n): Returns an identity matrx of n by n.
NB. This is a static function and should be called MatrixC::Identity(n). where n is the size of the matrix.
const TMatrixC<RealT> & SetDiagonal(const TVectorC<RealT> & d): Set the diagonal of this matrix.
If d.Size() != Cols() an error is given.
const TMatrixC<RealT> & AddDiagonal(const TVectorC<RealT> & d): Add a vector to the diagonal of this matrix.
If d.Size() != Cols() an error is given.
TMatrixC<RealT> SubMatrix(SizeT size1,SizeT size2): Get sub matrix of size1,size2.
The creates a new access, but does not copy the data itself. The matrix always starts from 0,0.
RealT SumOfAbs() const: Sum the absolute values of all members of the matrix.
const TMatrixC<RealT> & AddOuterProduct(const TVectorC<RealT> & vec1,const TVectorC<RealT> & vec2): Add outer product of vec1 and vec2 to this matrix.
const TMatrixC<RealT> & AddOuterProduct(const TVectorC<RealT> & vec1,const TVectorC<RealT> & vec2,const RealT & a): Add outer product of vec1 and vec2 multiplied by a to this matrix .
const TMatrixC<RealT> & SetSmallToBeZero(const RealT & min): Set values smaller than 'min' to zero in vector.
void SwapRows(int i,int j): Swap two rows in the matrix.

#include "Ravl/SArray2d.hh"

SArray2dC<RealT> Copy() const: Copy array.

Special operations

Buffer2dC<RealT> & Buffer(): Access base data buffer.
Experts only!
const Buffer2dC<RealT> & Buffer() const: Constant access base data buffer.
Experts only!
SArray1dC<RealT> AsVector(bool alwaysCopy = false): Access 2d array as 1d vector.
This will only copy the data if the data isn't continuous or alwaysCopy is true, this can make it much more effecient than a straigh copy.
SArray2dC<RealT> operator +(const SArray2dC<RealT> & arr) const: Sums 2 numerical arrays. The operator returns the result as a new array.
SArray2dC<RealT> operator -(const SArray2dC<RealT> & arr) const: Subtracts 2 numerical arrays. The operator returns the result as a new array.
SArray2dC<RealT> operator *(const SArray2dC<RealT> & arr) const: Mutliplies 2 numerical arrays. The operator returns the result as a new array.
SArray2dC<RealT> operator /(const SArray2dC<RealT> & arr) const: Devides 2 numerical arrays. The operator returns the result as a new array.
SArray2dC<RealT> operator *(const RealT & number) const: Multiplys the array by the 'number'. The operator returns the result as a new array.
SArray2dC<RealT> operator /(const RealT & number) const: Divides all array items by the 'number'. The operator returns the result as a new array.
SArray2dC<RealT> operator +(const RealT & number) const: Adds 'number' to the array. The operator returns the result as a new array.
SArray2dC<RealT> operator -(const RealT & number) const: Subtracts 'number' from all array items. The operator returns the result as a new array.
const SArray2dC<RealT> & operator +=(const SArray2dC<RealT> & arr): Adds the 2nd array to this array.
const SArray2dC<RealT> & operator -=(const SArray2dC<RealT> & arr): Subtracts the 2nd array from this array.
const SArray2dC<RealT> & operator *=(const SArray2dC<RealT> & arr): Multiplies the 2nd array to this array.
const SArray2dC<RealT> & operator /=(const SArray2dC<RealT> & arr): Divides the 2nd array from this array.
const SArray2dC<RealT> & operator +=(const RealT & number): Adds 'number' to all array items.
const SArray2dC<RealT> & operator -=(const RealT & number): Subtracts 'number' from all array items.
const SArray2dC<RealT> & operator *=(const RealT & number): Multiplies the array by the 'number'.
const SArray2dC<RealT> & operator /=(const RealT & number): Divides the array elements by the 'number'.
RealT SumSqr() const: Calculate the sum of the squares of all the elements in the array
RealT Sum() const: Returns the sum all elements of the array.
Slice1dC<RealT> Diagonal(): Take a slice along the diagonal of the array.
SArray1dC<RealT> SliceRow(IndexC i): Access row as 1d array.
NB. Changes made to the slice will also affect this array!
Slice1dC<RealT> SliceColumn(IndexC i): Access columb as 1d slice.
NB. Changes made to the slice will also affect this array!
void SetColumn(IndexC i,const SArray1dC<RealT> & val): Set the values in the column i to those in 'val'.
'val' must have a size equal to the number of rows.
void SetRow(IndexC i,const SArray1dC<RealT> & val): Set the values in the row i to those in 'val'.
'val' must have a size equal to the number of columns
void BuildAccess(UIntT offset = 0,UIntT stride = 0)

#include "Ravl/SBfAcc2d.hh"

bool Contains(const Index2dC & i) const: Does this buffer contain the index i ?
Returns true if yes.
RealT & operator [](const Index2dC & i): access to the item array[(i)]
const RealT & operator [](const Index2dC & i) const: return the item array[(i)]
SizeBufferAccessC<RealT> operator [](IndexC i): access to the item array[(i)]
const SizeBufferAccessC<RealT> operator [](IndexC i) const: return the item array[(i)]
SizeT Size1() const: Size.
SizeT Size2() const: Size.
UIntT Size() const: Get the total number of elements in the array.
void Fill(const RealT & d): Fill array with value.
IntT Stride() const: Get the stide of the 2d array.
bool IsContinuous() const: Test if the array is allocated in a continous area of memory.
Note: this only checks the first two rows follow each other in memory, this may miss other discontunities.

#include "Ravl/SBfAcc.hh"

const SizeBufferAccessC<BufferAccessC<DataT>> & operator =(BufferAccessC<DataT> * bp): Changes the reference element to the element pointed by 'bp'. Access to the object --------------------
BufferAccessC<DataT> * DataStart() const: Returns the address of the first element of the buffer.
SizeT Size() const: Returns the number of elements of the array.
IndexRangeC Limits() const: Returns the usable range of indeces expressed by this object.
IndexRangeC Range() const: Returns the usable range of indeces expressed by this object.
IndexC IMin() const: Returns the minimum index of the range of this access.
IndexC IMax() const: Returns the maximum index of the range of this access.
const BufferAccessC<DataT> & operator [](const IndexC i) const: Read-only access to the ('i'+1)-th element of the buffer.
BufferAccessC<DataT> & operator [](const IndexC i): Read-write access to the ('i'+1)-th element of the buffer.
const SizeBufferAccessC<BufferAccessC<DataT>> & SAccess(void) const: Returns this object. Logical functions -----------------
bool IsEmpty() const: Returns TRUE if the size of the array is zero.
bool Contains(IndexC i) const: Returns TRUE if the array contains an item with the index 'i'. Modifications of the access ---------------------------
SizeT ShrinkHigh(SizeT k): Changes the number of elements by subtracting the last 'k' elements.
const SizeBufferAccessC<BufferAccessC<DataT>> & Swap(SizeBufferAccessC<BufferAccessC<DataT>> & a): Exchanges the contents of this buffer with buffer 'a'.
void Attach(const SizeBufferAccessC<BufferAccessC<DataT>> & b): Changes this buffer access to have the same access rights as 'b'.
void Attach(const BufferAccessC<BufferAccessC<DataT>> & b,SizeT size): Changes this buffer access to have the access rights as 'b' limited for 'size' elements.
SizeBufferAccessC<BufferAccessC<DataT>> operator +(SizeT i) const: Creates the new access object shifted 'i' elements to the right (towards next elements). The size is descreased to fit the the original range of this access. Modifications of the buffer contents ------------------------------------
void Fill(const BufferAccessC<DataT> & d): 'd' value is assigned to all elements of the buffer.
void CopyFrom(const SizeBufferAccessC<BufferAccessC<DataT>> & oth): Copy contents of another buffer into this one.
NB. Buffers MUST be the same length.
void Reverse(): Reverse the order of elements in this array in place.
SizeBufferAccessC<BufferAccessC<DataT>> BufferFrom(UIntT first): Get an access for this buffer starting from the 'first' element to the end of the buffer.
SizeBufferAccessC<BufferAccessC<DataT>> BufferFrom(UIntT first,UIntT len): Get an access for this buffer starting from the 'first' element for 'len' elements.
An error will be generated if the requested buffer isn't contains within this one.
bool operator ==(const SizeBufferAccessC<BufferAccessC<DataT>> & ba) const: Are two accesses the same ?
SizeBufferAccessC<BufferAccessC<DataT>> Copy(void) const: Returns a physical copy of this access pointing to the physical copy of the accessed buffer in the range accessible by this access. The new copy is necessary to attach to reference counted buffer or to delete at the end of the life of this object.

#include "Ravl/BufferAccess.hh"

BufferAccessC<DataT> * ReferenceElm() const: Returns the pointer to the reference element of the attached buffer. The reference element need not to be the valid element of the buffer.
void * ReferenceVoid() const: Returns the pointer to the reference element of the attached buffer. The reference element need not to be the valid element of the buffer. The function is intended to be used in printing.
bool IsValid() const: Returns TRUE if this buffer access is not a default access object.
const BufferAccessC<DataT> & operator [](const IndexC i) const: Read-only access to the ('i'+1)-th element of the buffer.
BufferAccessC<DataT> & operator [](const IndexC i): Read-write access to the ('i'+1)-th element of the buffer.
const BufferAccessC<BufferAccessC<DataT>> & operator +=(IndexC ind): Inplace Add index to start position.
const BufferAccessC<BufferAccessC<DataT>> & operator -=(IndexC ind): Inplace Subtract index from start position.
BufferAccessC<BufferAccessC<DataT>> operator -(IndexC ind) const: Substract value from position, and return it as a new value.
BufferAccessC<BufferAccessC<DataT>> operator +(IndexC ind) const: Substract value from position, and return it as a new value.
bool operator ==(const BufferAccessC<BufferAccessC<DataT>> & ba) const: Are two accesses the same ?
bool operator !=(const BufferAccessC<BufferAccessC<DataT>> & ba) const: Are two accesses the same ?

Maintainer:Charles Galambos, Created: 24/01/2001, Documentation by CxxDoc: Tue Aug 13 09:59:30 2002