Mathematics

Modules
	1D->1D Polynomial
	2D->1D Polynomial
	2D->2D Polynomial

Macros
#define	max(a, b)   (((a) > (b)) ? (a) : (b))
#define	min(a, b)   (((a) < (b)) ? (a) : (b))
#define	sign(x)   ((x) > 0 ? 1: ((x) == 0 ? 0: (-1)))

Functions
I32	lu_inverse (vcmat *A, vcmat *y, F64 *det)
	Calculate the inverse of a n×n-matrix using the LU decomposition. More...
I32	lu_det (vcmat *A, F64 *det)
	Calculate the determinant of A n×n-matrix using the LU decomposition. More...
I32	vc_QR_solve (vcmat *A, vcvec *y, vcvec *x)
	Solve a system of linear equations using the Householder QR factorization. More...

Detailed Description

Functions in this group provide concepts like matrix, vector, ...

Macro Definition Documentation

max

#define max	(		a,
			b
	)		(((a) > (b)) ? (a) : (b))

Outputs the maximum of a and b.

min

#define min	(		a,
			b
	)		(((a) < (b)) ? (a) : (b))

Outputs the minimum of a and b.

sign

#define sign

(

x

)

((x) > 0 ? 1: ((x) == 0 ? 0: (-1)))

Outputs the sign of x, either 1, 0 or -1.

Function Documentation

lu_inverse()

I32 lu_inverse	(	vcmat *	A,
		vcmat *	y,
		F64 *	det
	)

The function calculates the inverse of the n×n-matrix a and outputs the result in matrix y. The function may be called in-place, i.e. a and y may be the same matrix. The function returns an error if the size of the matrices is not square and not identical. The determinant of the matrix det is output as a F64 value although possibly only calculated as a float value depending ont the type of a.

Parameters

A	source matrix
y	destination matrix
det	determinant of A (output)

lu_det()

I32 lu_det	(	vcmat *	A,
		F64 *	det
	)

The function calculates the determinant of the n×n matrix A. The function returns an error if the size of the matrix is not square. The determinant of the matrix det is output as a F64 value although possibly only calculated as a float value depending ont the type of A.

Parameters

A	source matrix
det	determinant of A (output)

vc_QR_solve()

I32 vc_QR_solve	(	vcmat *	A,
		vcvec *	y,
		vcvec *	x
	)

The QR factorization using the Householder transform is a numerically stable tool for linear least square approximations.

See: Stoer, J "Einfuehrung in die Numerische Mathematik I" pp 164ff, Springer, 1976

The function solves the linear system ||Ax - y|| = min

Parameters

A	source matrix (dimensions m * n)
y	input vector (m)
x	solution vector (n)
det	determinant of a (output)

See also

qr_househ_F64, qr_backs_F64().