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rdMtx Class Reference

A class for performing vector and matrix operations. More...

#include <rdMtx.h>

List of all members.

Static Public Member Functions

double Angle (const double *aV1, const double *aV2)

Find the angle between two vectors: theta = acos( aV1*aV2/(|aV1|*|aV2|)).

double Normalize (int aN, const double aV[], double rV[])

Normalize a vector.

double Magnitude (int aN, const double aV[])

Compute the magnitude of a vector.

double DotProduct (int aN, const double aV1[], const double aV2[])

Compute the dot product of two vectors.

int CrossProduct (double *aV1, double *aV2, double *aV)

Compute the cross product of two vectors.

void Interpolate (int aN, double aT1, double *aY1, double aT2, double *aY2, double t, double *aY)

Linearly interpolate or extrapolate an array of data.

double Interpolate (double aT1, double aY1, double aT2, double aY2, double t)

Linearly interpolate or extrapolate two data points.

void Translate (double aX, double aY, double aZ, const double aP[3], double rP[3])

Translate a point by a specified amount.

void Rotate (int aXYZ, double aRadians, const double aP[3], double rP[3])

Rotate a point about the X, Y, or Z axis by a specified amount.

void Rotate (const double aAxis[3], double aRadians, const double aP[3], double rP[3])

Rotate a point about a specified axis by a specified amount.

void RotateDeg (int aXYZ, double aDegrees, const double aP[3], double rP[3])

Rotate a point about the X axis by a specified amount.

void RotateDeg (const double aAxis[3], double aDegrees, const double aP[3], double rP[3])

Rotate a point about a specified axis by a specified amount.

int Identity (int aNR, double *rI)

Assign a square matrix to the identidy matrix: rI = I.

int Assign (int aNR, int aNC, double aScalar, double *rM)

Assign all elements of a matrix to a specified value: rMij = aScalar.

int Assign (int aNR, int aNC, const double *aM, double *rM)

Assign two matrices: rM = aM.

int Add (int aNR, int aNC, const double *aM1, double aScalar, double *aM)

Add a scalar to a matrix.

int Add (int aNR, int aNC, const double *aM1, const double *aM2, double *aM)

Add two matrices.

int Subtract (int aNR, int aNC, const double *aM1, const double *aM2, double *aM)

Subtract two matrices.

int Multiply (int aNR, int aNC, const double *aM, double aScalar, double *rM)

Multiply a matrix by a scalar.

int Multiply (int aNR1, int aNCR, int aNC2, const double *aM1, const double *aM2, double *aM)

Multiply two matrices.

int Invert (int aN, const double *aM, double *aMInv)

Compute the inverse of a matrix.

int Transpose (int aNR, int aNC, const double *aM, double *aMT)

Transpose a matrix.

void Print (int aNR, int aNC, const double *aM, int aPrecision=8)

Print a matrix.

int FindIndex (int aStartIndex, double aTime, int aNT, double *aT)

Starting at aIndex, move through the array aT and find the index of the element whose value is closest to but less than aTime.

int FindIndexLess (int aNX, double *aX, double aValue)

Scan from the beginning of the array, aX, and find the index of the element such that the element's value is less than or equal to aValue and the next element's value is greater than aValue.

int FindIndexGreater (int aNX, double *aX, double aValue)

Scan from the end of the array, aX, and find the index of the element such that the element's value is greater than or equal to aValue and such that the next element's value is less than aValue.

int ComputeIndex (int i2, int n1, int i1)

Compute the index for an element of a three dimensional matrix as though the matrix were laid out in one dimension.

int ComputeIndex (int i3, int n2, int i2, int n1, int i1)

Compute the index for an element of a three dimensional matrix as though the matrix were laid out in one dimension.

void GetDim3 (int n3, int n2, int n1, int i2, int i1, double *m, double *a)

Get elements *,i2,i1 of a three dimensional matrix as an array, where * varies along the 3rd dimension, i2 the 2nd, and i1 the 1st.

void SetDim3 (int n3, int n2, int n1, int i2, int i1, double *m, double *a)

Set elements *,i2,i1 of a three dimensional matrix to the values in array a, where * varies along the 3rd dimension, i2 the 2nd, and i1 the 1st.

int EnsureWorkSpaceCapacity (int aN)

Ensure that the work space is at least of size aN.

int EnsurePointerSpaceCapacity (int aN)

Ensure that the pointer spaces is at least of size aN.

void FreeWorkAndPointerSpaces ()

Free the work and pointer spaces.

Static Private Attributes

int _PSpaceSize = 0

int _WSpaceSize = 0

double ** _P1Space = NULL

double ** _P2Space = NULL

double * _WSpace = NULL

Detailed Description

A class for performing vector and matrix operations.

Most all the methods in this class are static.

Member Function Documentation

int rdMtx::Add ( int aNR,

int aNC,

const double * aM1,

const double * aM2,

double * aM

) [static]

Add two matrices.
If the arguments are not valid, then a -1 is returned. Othersise, 0 is returned.
It is permissible for aM to coincide with either aM1 or aM2.

int rdMtx::Add ( int aNR,

int aNC,

const double * aM1,

double aScalar,

double * aM

) [static]

Add a scalar to a matrix.
If the arguments are not valid, then a -1 is returned. Othersise, 0 is returned.
It is permissible for aM to coincide with aM1.

double rdMtx::Angle ( const double * aV1,

const double * aV2

) [static]

Find the angle between two vectors: theta = acos( aV1*aV2/(|aV1|*|aV2|)).

Parameters:

aV1 Vector 1.

aV2 Vector 2.

Returns:
Angle between two vectors in radians.

int rdMtx::Assign ( int aNR,

int aNC,

const double * aM,

double * rM

) [static]

Assign two matrices: rM = aM.

Parameters:

aNR Number of rows in the matrices.

aNC Number of columns in the matrices.

aM Input matrix.

rM Ouput matrix (rM = aM).

Returns:
0 on success, -1 on error.

int rdMtx::Assign ( int aNR,

int aNC,

double aScalar,

double * rM

) [static]

Assign all elements of a matrix to a specified value: rMij = aScalar.
It is permissible for

Parameters:

aNR Number of rows in the matrix.

aNC Number of columns in the matrix.

aScalar Scalar value to which to set the element of the matrix.

rM Ouput matrix (rMij = aScalar for all i,j).

Returns:
0 on success, -1 on error.

int rdMtx::CrossProduct ( double * aV1,

double * aV2,

double * aV

) [static]

Compute the cross product of two vectors.
If the arguments are not valid (aR=aS=NULL), -1 is returned.

double rdMtx::DotProduct ( int aN,

const double aV1[],

const double aV2[]

) [static]

Compute the dot product of two vectors.
If the arguments are not valid (aV1=aV2=NULL), 0.0 is returned.

int rdMtx::EnsurePointerSpaceCapacity ( int aN ) [static]

Ensure that the pointer spaces is at least of size aN.
If the capacity could not be increased to aN, -1 is returned. Otherwise, 0 is returned.

int rdMtx::EnsureWorkSpaceCapacity ( int aN ) [static]

Ensure that the work space is at least of size aN.
If the capacity could not be increased to aN, -1 is returned. Otherwise, 0 is returned.

int rdMtx::FindIndex ( int aStartIndex,

double aTime,

int aNT,

double * aT

) [static]

Starting at aIndex, move through the array aT and find the index of the element whose value is closest to but less than aTime.
It is assumed that the array aT is monotonically increasing and has at least 2 elements.
If aTime lies outside the interval of aT, the index of either the first point or second to last point is returned depending on whether aTime is below or above the interval of aT.
-1 is if an error is encountered.

int rdMtx::FindIndexGreater ( int aNX,

double * aX,

double aValue

) [static]

Scan from the end of the array, aX, and find the index of the element such that the element's value is greater than or equal to aValue and such that the next element's value is less than aValue.
If no value in the array is less than aValue, the index of the first element in the array is returned.
If no value in the array is greater than or equal to aValue, -1 is returned.

int rdMtx::FindIndexLess ( int aNX,

double * aX,

double aValue

) [static]

Scan from the beginning of the array, aX, and find the index of the element such that the element's value is less than or equal to aValue and the next element's value is greater than aValue.
If no value in the array is greater than aValue, the index of the last element in the array is returned.
If no value in the array is less than or equal to aValue, -1 is returned.

void rdMtx::GetDim3 ( int n3,

int n2,

int n1,

int i2,

int i1,

double * m,

double * a

) [static]

Get elements *,i2,i1 of a three dimensional matrix as an array, where * varies along the 3rd dimension, i2 the 2nd, and i1 the 1st.
The first dimension is the dimension which varies most rapidly when the data is laid out in a one dimensional array, and the second dimension is the one which varies second most rapidly, and so on.
For now, it is assumed that parameter a has enough memory allocated to hold the array.

int rdMtx::Identity ( int aNR,

double * rI

) [static]

Assign a square matrix to the identidy matrix: rI = I.
The matrix must be square.

Parameters:

aN Dimension of the matrix (aN=nRows, aN=nCols).

rI Ouput identity matrix (rI = I).

Returns:
0 on success, -1 on error.

int rdMtx::Invert ( int aN,

const double * aM,

double * aMInv

) [static]

Compute the inverse of a matrix.
If the arguments are not valid (aM==NULL), then -1 is returned. If the matrix is not invertible, then -2 is returned. Othersise, 0 is returned.
It is permissible for aM to overlap in memory with aMInv.

double rdMtx::Magnitude ( int aN,

const double aV[]

) [static]

Compute the magnitude of a vector.

Parameters:

aV Vector.

Returns:
Square root of the dot product aV*aV.

int rdMtx::Multiply ( int aNR1,

int aNCR,

int aNC2,

const double * aM1,

const double * aM2,

double * aM

) [static]

Multiply two matrices.
If the arguments are not valid (aM1,aM2,aM==NULL), then a -1 is returned. Othersise, 0 is returned.
It is permissible for aM to overlap with either aM1 or aM2.

int rdMtx::Multiply ( int aNR,

int aNC,

const double * aM,

double aScalar,

double * rM

) [static]

Multiply a matrix by a scalar.
It is permissible for aM and rM to coincide in memory.

Parameters:

aNR Number of rows in aM.

aNC Number of columns in aM.

aM Matirx laid out in memory as aM[aNR][aNC].

aScalar Scalar value by which to multiply aM.

rM Result of aScalar * aM.

Returns:
-1 if an error is encountered, 0 otherwise.

double rdMtx::Normalize ( int aN,

const double aV[],

double rV[]

) [static]

Normalize a vector.
If aV has a magnitude of zero, all elements of rV are set to 0.0. It is permissible for aV and rV to coincide in memory.

Parameters:

aV Vector to be normalized.

rV Result of the normalization.

Returns:
Magnitude of aV.

void rdMtx::Rotate ( const double aAxis[3],

double aRadians,

const double aP[3],

double rP[3]

) [static]

Rotate a point about a specified axis by a specified amount.

Parameters:

aAxis Axis about which to rotate. The axis is not assumed to be a unit vector; however, if the axis is the zero vector, no rotation is performed.

aRadians Amount of rotation in radians.

aP Point to rotate.

rP Rotated point. aP and rP may coincide in memory.

void rdMtx::Rotate ( int aXYZ,

double aRadians,

const double aP[3],

double rP[3]

) [static]

Rotate a point about the X, Y, or Z axis by a specified amount.

Parameters:

aXYZ Specify whether to rotate about the X (aXYZ=0), Y (aXYZ=1), or Z (aXYZ=2) axes. If aXYZ is not 0, 1, or 2, no rotation is performed.

aRadians Amount of rotation in radians.

aP Point to rotate.

rP Rotated point. aP and rP may coincide in memory.

void rdMtx::RotateDeg ( const double aAxis[3],

double aDegrees,

const double aP[3],

double rP[3]

) [static]

Rotate a point about a specified axis by a specified amount.

Parameters:

aAxis Axis about which to rotate.

aDegrees Amount of rotation in degrees.

aP Point to rotate.

rP Rotated point. aP and rP may coincide in memory.

void rdMtx::RotateDeg ( int aXYZ,

double aDegrees,

const double aP[3],

double rP[3]

) [static]

Rotate a point about the X axis by a specified amount.

Parameters:

aXYZ Specify whether to rotate about the X (aXYZ=0), Y (aXYZ=1), or Z (aXYZ=2) axis. If aXYZ is not 0, 1, or 2, no rotation is performed.

aDegrees Amount of rotation in degrees.

aP Point to rotate.

rP Rotated point. aP and rP may coincide in memory.

void rdMtx::SetDim3 ( int n3,

int n2,

int n1,

int i2,

int i1,

double * m,

double * a

) [static]

Set elements *,i2,i1 of a three dimensional matrix to the values in array a, where * varies along the 3rd dimension, i2 the 2nd, and i1 the 1st.
The first dimension is the dimension which varies most rapidly when the data is laid out in a one dimensional array, and the second dimension is the one which varies second most rapidly, and so on.

int rdMtx::Subtract ( int aNR,

int aNC,

const double * aM1,

const double * aM2,

double * aM

) [static]

Subtract two matrices.
If the arguments are not valid, then a -1 is returned. Othersise, 0 is returned.
It is permissible for aM to coincide with either aM1 or aM2.

void rdMtx::Translate ( double aX,

double aY,

double aZ,

const double aP[3],

double rP[3]

) [static]

Translate a point by a specified amount.

Parameters:

aX Amount to translate in the X direction.

aY Amount to translate in the Y direction.

aZ Amount to translate in the Z direction.

aP Point to translate.

rP Translated point. aP and rP may coincide in memory.

int rdMtx::Transpose ( int aNR,

int aNC,

const double * aM,

double * aMT

) [static]

Transpose a matrix.
If the arguments are invalid (e.g.,aM==NULL), then a -1 is returned. Othersise, 0 is returned.
It is permissible for aM to overlap in memory with aMT.

The documentation for this class was generated from the following files:

rdMtx.h
rdMtx.cpp

Generated on Wed Aug 20 02:17:12 2003 for Simulation Software by

1.3


Static Public Member Functions
double	Angle (const double aV1, const double aV2)
	Find the angle between two vectors: theta = acos( aV1aV2/(\|aV1\|\|aV2\|)).
double	Normalize (int aN, const double aV[], double rV[])
	Normalize a vector.
double	Magnitude (int aN, const double aV[])
	Compute the magnitude of a vector.
double	DotProduct (int aN, const double aV1[], const double aV2[])
	Compute the dot product of two vectors.
int	CrossProduct (double aV1, double aV2, double *aV)
	Compute the cross product of two vectors.
void	Interpolate (int aN, double aT1, double aY1, double aT2, double aY2, double t, double *aY)
	Linearly interpolate or extrapolate an array of data.
double	Interpolate (double aT1, double aY1, double aT2, double aY2, double t)
	Linearly interpolate or extrapolate two data points.
void	Translate (double aX, double aY, double aZ, const double aP[3], double rP[3])
	Translate a point by a specified amount.
void	Rotate (int aXYZ, double aRadians, const double aP[3], double rP[3])
	Rotate a point about the X, Y, or Z axis by a specified amount.
void	Rotate (const double aAxis[3], double aRadians, const double aP[3], double rP[3])
	Rotate a point about a specified axis by a specified amount.
void	RotateDeg (int aXYZ, double aDegrees, const double aP[3], double rP[3])
	Rotate a point about the X axis by a specified amount.
void	RotateDeg (const double aAxis[3], double aDegrees, const double aP[3], double rP[3])
	Rotate a point about a specified axis by a specified amount.
int	Identity (int aNR, double *rI)
	Assign a square matrix to the identidy matrix: rI = I.
int	Assign (int aNR, int aNC, double aScalar, double *rM)
	Assign all elements of a matrix to a specified value: rMij = aScalar.
int	Assign (int aNR, int aNC, const double aM, double rM)
	Assign two matrices: rM = aM.
int	Add (int aNR, int aNC, const double aM1, double aScalar, double aM)
	Add a scalar to a matrix.
int	Add (int aNR, int aNC, const double aM1, const double aM2, double *aM)
	Add two matrices.
int	Subtract (int aNR, int aNC, const double aM1, const double aM2, double *aM)
	Subtract two matrices.
int	Multiply (int aNR, int aNC, const double aM, double aScalar, double rM)
	Multiply a matrix by a scalar.
int	Multiply (int aNR1, int aNCR, int aNC2, const double aM1, const double aM2, double *aM)
	Multiply two matrices.
int	Invert (int aN, const double aM, double aMInv)
	Compute the inverse of a matrix.
int	Transpose (int aNR, int aNC, const double aM, double aMT)
	Transpose a matrix.
void	Print (int aNR, int aNC, const double *aM, int aPrecision=8)
	Print a matrix.
int	FindIndex (int aStartIndex, double aTime, int aNT, double *aT)
	Starting at aIndex, move through the array aT and find the index of the element whose value is closest to but less than aTime.
int	FindIndexLess (int aNX, double *aX, double aValue)
	Scan from the beginning of the array, aX, and find the index of the element such that the element's value is less than or equal to aValue and the next element's value is greater than aValue.
int	FindIndexGreater (int aNX, double *aX, double aValue)
	Scan from the end of the array, aX, and find the index of the element such that the element's value is greater than or equal to aValue and such that the next element's value is less than aValue.
int	ComputeIndex (int i2, int n1, int i1)
	Compute the index for an element of a three dimensional matrix as though the matrix were laid out in one dimension.
int	ComputeIndex (int i3, int n2, int i2, int n1, int i1)
	Compute the index for an element of a three dimensional matrix as though the matrix were laid out in one dimension.
void	GetDim3 (int n3, int n2, int n1, int i2, int i1, double m, double a)
	Get elements ,i2,i1 of a three dimensional matrix as an array, where * varies along the 3rd dimension, i2 the 2nd, and i1 the 1st.*
void	SetDim3 (int n3, int n2, int n1, int i2, int i1, double m, double a)
	Set elements ,i2,i1 of a three dimensional matrix to the values in array a, where * varies along the 3rd dimension, i2 the 2nd, and i1 the 1st.*
int	EnsureWorkSpaceCapacity (int aN)
	Ensure that the work space is at least of size aN.
int	EnsurePointerSpaceCapacity (int aN)
	Ensure that the pointer spaces is at least of size aN.
void	FreeWorkAndPointerSpaces ()
	Free the work and pointer spaces.
Static Private Attributes
int	_PSpaceSize = 0
int	_WSpaceSize = 0
double **	_P1Space = NULL
double **	_P2Space = NULL
double *	_WSpace = NULL