/***********************************************************************matrix.h - matrix operationsCopyright (C) 1991 Dean RubineThis program is free software; you can redistribute it and/or modifyit under the terms of the GNU General Public License. See ../COPYING forthe full agreement.**********************************************************************//*  Simple matrix operations Why I am writing this stuff over is beyond me*//*This package provides the Matrix and Vector data typesThe difference between this matrix package and others is that:	Vectors may be accessed as 1d arrays	Matrices may still be accessed like two dimensional arraysThis is accomplished by putting a structure containing the boundsof the matrix before the pointer to the (array of) doubles (in thecase of a Vector) or before the pointer to an (array of) pointersto doubles (in the case of a Matrix).Vectors and matrices are collectively called "arrays" herein.*/#define HEADER(a)	( ((struct array_header *) a) - 1 )#define	NDIMS(a)	(int)(HEADER(a)->ndims)#define NROWS(a)	(int)(HEADER(a)->nrows)#define NCOLS(a)	(int)(HEADER(a)->ncols)#define	ISVECTOR(a)	(NDIMS(a) == 1)#define	ISMATRIX(a)	(NDIMS(a) == 2)/* Note: this structure is prepended at the beginning of a Vector, and causes   the Vector data type to be 32-byte aligned, but not 64-byte aligned.   If this were a problem, filler could be filler[5] (or more) instead.    --Sharon Perl, 12/17/98. */struct array_header {	unsigned char	ndims;	/* 1 = vector, 2 = matrix */	unsigned char	nrows;	unsigned char	ncols;	unsigned char	filler;};typedef double **Matrix;typedef double *Vector;Vector	NewVector();	/* int r; (number of rows) */Matrix	NewMatrix();	/* int r, c; (number of rows, number of columns) */void	FreeVector();	/* Vector v; */void	FreeMatrix();	/* Matrix m; */void	PrintVector();	/* Vector v; char *fmt; any a1,a2,a3,a4,a5,a6,a7,a8 */void	PrintMatrix();	/* Matrix m; char *fmt; any a1,a2,a3,a4,a5,a6,a7,a8 */double	InnerProduct();	/* Vector v1, v2 */void	MatrixMultiply(); /* Matrix m1, m2, prod; */void	VectorTimesMatrix(); /* Vector v; Matrix m; Vector prod; */void	ScalarTimesVector(); /* double s; Vector v; Vector prod; */double	QuadraticForm(); /* Vector v; Matrix m; (computes v'mv) */double	InvertMatrix();	/* Matrix input_matrix, result_matrix (returns det) */Vector	SliceVector();	/* Vector v; BitVector rowmask */Matrix	SliceMatrix();	/* Matrix m; Bitvector rowmask, colmask; */Vector	VectorCopy();	/* Vector v; */Matrix	MatrixCopy();	/* Matrix m; */Vector	InputVector();	/* FILE *f; */Matrix	InputMatrix();	/* FILE *f; */double	InvertSingularMatrix();	/* Matrix input, result (returns det) */Matrix  DeSliceMatrix(); /* Matrix m, double fill, BitVector rowmask, colmask;				Matrix result */void	OutputVector();void	OutputMatrix();void	ZeroVector();void	ZeroMatrix();	/* Matrix m; */void	FillMatrix();	/* Matrix m; double fill; */