matrixArrayCalcs defines various utility functions for use with Matrix objects and array objects. More...

#include "myOutput.h"
#include "math.h"
#include "string.h"
#include <fstream>
#include <newmatap.h>
#include <newmatio.h>

Macros
#define	isnan(a) ((fabs(a) >= 90000) \|\| (a != a))

#define	sign(a) ((a > 0) - (a < 0))

#define	PI 3.14159265358979

Functions
int	minVal (const int *values, const int numValues)

int	maxVal (const int *values, const int numValues)

Matrix	conv2 (const Matrix &A, const Matrix &H)

void	interp2 (double xpts, double ypts, const Matrix Z, double xi, double yi, double *zi, int numPts)

void	interp2mat (double xpts, double ypts, const Matrix Z, double xi, double yi, Matrix &zi)

void	nearestInterp (double xpts, double ypts, const Matrix &zvals, double xi, double yi, double &zi, int xIndices, int yIndices, ColumnVector &Weights)

bool	findNearestValid (const Matrix &zvals, int &xIndex, int &yIndex)

void	bilinearInterp (double xpts, double ypts, const Matrix &zvals, double xi, double yi, double &zi, int xIndices, int yIndices, ColumnVector &Weights)

void	bicubicInterp (double xpts, double ypts, const Matrix &zvals, double xi, double yi, double &zi, int xIndices, int yIndices, ColumnVector &Weights)

void	splineInterp (double xpts, double ypts, const Matrix &zvals, double xi, double yi, double &zi, int xIndices, int yIndices, ColumnVector &Weights)

void	nearestInterp_mat (double xpts, double ypts, const Matrix &zvals, double xi, double yi, Matrix &zi, Matrix &var)

void	bilinearInterp_mat (double xpts, double ypts, const Matrix &zvals, double xi, double yi, Matrix &zi, Matrix &var)

void	bicubicInterp_mat (double xpts, double ypts, const Matrix &zvals, double xi, double yi, Matrix &zi, Matrix &var)

void	splineInterp_mat (double xpts, double ypts, const Matrix &zvals, double xi, double yi, Matrix &zi, Matrix &var)

int	closestPt (double key, const double *base, size_t nmemb)

int	closestPtUniformArray (double key, double firstVal, double lastVal, size_t nmemb)

int	lowerBound (double val, const double *vec, int numVals)

double	unif (double mean, double halfInterval)

double	unif_zeroMean (const double &halfInterval)

double	unif_zeroOne ()

double	randn (double mean, double stddev)

double	randn_zeroMean (const double &stddev)

char *	charCat (char dest, const char front, const char *back)

double	computeKLdiv_gaussian_mat (double xpts, double ypts, const Matrix &refPDF, double *mu, const Matrix &Cov)

SymmetricMatrix	computeMatrixSqrt (const SymmetricMatrix &A)

void	computeArrayCrossProd (double a, double b, double *result)

Detailed Description

matrixArrayCalcs defines various utility functions for use with Matrix objects and array objects.

Author: Debbie Meduna

Date: 01/01/08

Macro Definition Documentation

#define isnan ( a ) ((fabs(a) >= 90000) || (a != a))

#define PI 3.14159265358979

#define sign ( a ) ((a > 0) - (a < 0))

Function Documentation

void bicubicInterp	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double	xi,
		double	yi,
		double &	zi,
		int *	xIndices,
		int *	yIndices,
		ColumnVector &	Weights
	)

Uses bicubic interpolation to determine zi at the point (xi,yi) from the set of data xpts, ypts, and zvals. If zvals is size m x n, xpts is size m x 1 and ypts is size n x 1. The function modifies the the entries in xIndices, yIndices and W. xIndices and yIndices are px1 arrays containing the indices of xpts and ypts used to generate zi. The method used for bicubic interpolation is very similar to that described in Numerical Recipes in C++. If a 4x4 bounding box does not exist for the current (xi,yi) data point, OR the interpolated point is NaN, bilinearInterp() is used.

void bicubicInterp_mat	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double *	xi,
		double *	yi,
		Matrix &	zi,
		Matrix &	var
	)

Interpolates all points in the vectors xi, yi to fill the matrix zi using the data in xpts, ypts and Z. Calls bicubicInterp() for each point in the xi and yi arrays to perform this interpolation.

void bilinearInterp	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double	xi,
		double	yi,
		double &	zi,
		int *	xIndices,
		int *	yIndices,
		ColumnVector &	Weights
	)

Uses bilinear interpolation to determine zi at the point (xi,yi) from the set of data xpts, ypts, and zvals. If zvals is size m x n, xpts is size m x 1 and ypts is size n x 1. The function modifies the the entries in xIndices, yIndices and W. xIndices and yIndices are 4x1 arrays containing the indices of xpts and ypts used to generate zi. W is a 4x1 column vector of corresponding weights where: zi = sum_i W(i,1)*zvals(xIndices[i]+1,yIndices[i]+1). If a 2x2 bounding box does not exist for the current (xi,yi) data point (i.e., it is out of the bounds of Z), OR the interpolated point is NaN, nearestInterp() is used.

void bilinearInterp_mat	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double *	xi,
		double *	yi,
		Matrix &	zi,
		Matrix &	var
	)

Interpolates all points in the vectors xi, yi to fill the matrix zi using the data in xpts, ypts and Z. Calls bilinearInterp() for each point in the xi and yi arrays to perform this interpolation.

char* charCat	(	char *	dest,
		const char *	front,
		const char *	back
	)

This function is used to concatenate two character arrays (front and back) into a new character array, dest. This differs from the C standard function strcat() in that the returned character array is an entirely new location in memory, separate from the front and back arrays. The length of the dest char array must be greater than or equal to the sum of the lengths of the front and back arrays.

int closestPt	(	double	key,
		const double *	base,
		size_t	nmemb
	)

Finds the index into the array "pts" which is closest to "value". This function is copied from the function nearest() in mapio.cpp.

int closestPtUniformArray	(	double	key,
		double	firstVal,
		double	lastVal,
		size_t	nmemb
	)

inline

Finds the index closest to "value" for the array whose first element is "firstVal", last element is "lastVal", and has size "nmemb". This function assumes that the array specified is uniformly spaced and takes advantage of this to perform a faster search than closestPt().

void computeArrayCrossProd	(	double *	a,
		double *	b,
		double *	result
	)

inline

This function computes the cross product: array1 x array2, and returns the result in result. The arrays are assumed to have 3 elements.

double computeKLdiv_gaussian_mat	(	double *	xpts,
		double *	ypts,
		const Matrix &	refPDF,
		double *	mu,
		const Matrix &	Cov
	)

This function computes the KL divergence between a proposal distribution and a Gaussian distribution with mean vector mu and covariance C. The proposal distribution is described by the matrix P, with corresponding (x,y) values given in the vectors xpts and ypts.

SymmetricMatrix computeMatrixSqrt ( const SymmetricMatrix & A )

This function computes the matrix square root of the given matrix, A. The given matrix and the returned matrix are both symmetric matrices. The sqrt is computed by first performing the eigenvalue decomposition of the matrix A, square rooting the resulting eigenvalues, and reconstructing the matrix to get Asqrt.

Matrix conv2	(	const Matrix &	A,
		const Matrix &	H
	)

Computes the 2D convolution of A with filter matrix H. The returned matrix B is the same size as A. H is assumed to be smaller than A.

bool findNearestValid	(	const Matrix &	zvals,
		int &	xIndex,
		int &	yIndex
	)

Finds the nearest valid (non-NaN) point in the grid zvals to the point (xIndex, yIndex). Replaces xIndex and yIndex with the indices corresponding to this found location. Returns a boolean indicating if a non-NaN point was successfully found.

void interp2	(	double *	xpts,
		double *	ypts,
		const Matrix	Z,
		double *	xi,
		double *	yi,
		double *	zi,
		int	numPts
	)

Interpolates the matrix Z to the (x,y) point pairs in arrays xi and yi. N indicates the number of point pairs to be interpolated. The arrays xpts and ypts contain the (x,y) values corresponding to entries in matrix Z. If Z is size m x n, xpts is size m x 1 and ypts is size n x 1. Bilinear interpolation is used for this function.

void interp2mat	(	double *	xpts,
		double *	ypts,
		const Matrix	Z,
		double *	xi,
		double *	yi,
		Matrix &	zi
	)

Interpolates the matrix Z to a new matrix zi over the (x,y) points in the arrays xi and yi. Nx and Ny indicates the length of these arrays. The arrays xpts and ypts contain the (x,y) values corresponding to entries in matrix Z. If Z is size m x n, xpts is size m x 1 and ypts is size n x 1. This function calls interp2() for performing interpolations.

int lowerBound	(	double	val,
		const double *	vec,
		int	numVals
	)

Finds the lowest index into the array "vec" which bounds the value "val". This function does NOT check that the returned index is a valid index into the array.

int maxVal	(	const int *	values,
		const int	numValues
	)

Finds and returns the maximum number in the integer array values.

int minVal	(	const int *	values,
		const int	numValues
	)

Rounds the number given to the nearest integer and returns the integer.

Finds and returns the minimum number in the integer array values.

void nearestInterp	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double	xi,
		double	yi,
		double &	zi,
		int *	xIndices,
		int *	yIndices,
		ColumnVector &	Weights
	)

Uses nearest-neighbor interpolation to determine zi at the point (xi,yi) from the set of data xpts, ypts, and zvals. If zvals is size m x n, xpts is size m x 1 and ypts is size n x 1. The function modifies the the entries in xIndices, yIndices and W. xIndices and yIndices are px1 arrays containing the indices of xpts and ypts used to generate zi. W is a px1 matrix of corresponding weights where: zi = sum_i W(i,1)*zvals(xIndices[i]+1,yIndices[i]+1). If the nearest point is NaN, the closest non-NaN point is found.

void nearestInterp_mat	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double *	xi,
		double *	yi,
		Matrix &	zi,
		Matrix &	var
	)

Interpolates all points in the vectors xi, yi to fill the matrix zi using the data in xpts, ypts and Z. Calls nearestInterp() for each point in the xi and yi arrays to perform this interpolation.

double randn	(	double	mean,
		double	stddev
	)

Uses a polar form Box-Muller Transform to generate a pseudorandom number from a gaussian distribution with specificied mean and standard deviation. Generates two random numbers for each call and stores the unused number for the next call to this function.

double randn_zeroMean ( const double & stddev )

inline

Uses a polar form Box-Muller Transform to generate a pseudorandom number from a gaussian distribution with zero mean and specified standard deviation. Generates two random numbers for each call and stores the unused number for the next call to this function.

void splineInterp	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double	xi,
		double	yi,
		double &	zi,
		int *	xIndices,
		int *	yIndices,
		ColumnVector &	Weights
	)

Uses spline interpolation to determine zi at the point (xi,yi) from the set of data xpts, ypts, and zvals. If zvals is size m x n, xvals is size m x 1 and ypts is size n x 1. The function modifies the the entries in xIndices, yIndices and W. xIndices and yIndices are px1 arrays containing the indices of xpts and ypts used to generate zi. Currently, this function is only implemented if a Matlab engine is running. Otherwise, this function calls nearestInterp().

void splineInterp_mat	(	double *	xpts,
		double *	ypts,
		const Matrix &	zvals,
		double *	xi,
		double *	yi,
		Matrix &	zi,
		Matrix &	var
	)

Interpolates all points in the vectors xi, yi to fill the matrix zi using the data in xpts, ypts and Z. Currently, this function is only implemented if a Matlab engine is running. Otherwise, this function calls nearestInterp_mat().

double unif	(	double	mean,
		double	halfInterval
	)

inline

Generates a pseudorandom number from a uniform distribution with given mean and halfInterval width.

double unif_zeroMean ( const double & halfInterval )

inline

Generates a pseudorandom number from a uniform distribution with zero mean and given halfInterval width.

double unif_zeroOne ( )

inline

Generates a pseudorandom number from a uniform distribution with zero mean and halfInterval width of 1.

Macros

Functions

Detailed Description

Macro Definition Documentation

Function Documentation