complex number support

Macros
#define	MAGMA_Z_MAKE(r, i)
#define	MAGMA_Z_REAL(a)
#define	MAGMA_Z_IMAG(a)
#define	MAGMA_Z_ADD(a, b)
#define	MAGMA_Z_SUB(a, b)
#define	MAGMA_Z_MUL(a, b)
#define	MAGMA_Z_DIV(a, b)
#define	MAGMA_Z_ABS(a)
#define	MAGMA_Z_ABS1(a)
#define	MAGMA_Z_CONJ(a)

Functions
__host__ static __device__ double	real (const magmaDoubleComplex &x)
__host__ static __device__ double	imag (const double &x)
__host__ static __device__ double	conj (const double &x)
__host__ static __device__ double	fabs (const magmaDoubleComplex &x)
__host__ static __device__ double	abs1 (const magmaDoubleComplex &x)

Detailed Description

In C++, including magma_operators.h defines the usual unary and binary operators for complex numbers: +, +=, -, -=, *, *=, /, /=, ==, !=.

Additionally, real(), imag(), conj(), fabs(), and abs1() are defined to apply to both complex and real numbers.

In C, there are equivalent macros: MAGMA_Z_{MAKE, REAL, IMAG, ADD, SUB, MUL, DIV, ABS, ABS1, CONJ} for double-complex, MAGMA_C_{...} for float-complex, MAGMA_D_{...} for double, MAGMA_S_{...} for float.

Just the double-complex versions are documented here.

Macro Definition Documentation

MAGMA_Z_MAKE

#define MAGMA_Z_MAKE	(		r,
			i )

Returns

complex number r + i*sqrt(-1).

MAGMA_Z_REAL

#define MAGMA_Z_REAL

(

a

)

Returns

real component of a.

MAGMA_Z_IMAG

#define MAGMA_Z_IMAG

(

a

)

Returns

imaginary component of a.

MAGMA_Z_ADD

#define MAGMA_Z_ADD	(		a,
			b )

Returns

(a + b).

MAGMA_Z_SUB

#define MAGMA_Z_SUB	(		a,
			b )

Returns

(a - b).

MAGMA_Z_MUL

#define MAGMA_Z_MUL	(		a,
			b )

Returns

(a * b).

MAGMA_Z_DIV

#define MAGMA_Z_DIV	(		a,
			b )

Returns

(a / b).

MAGMA_Z_ABS

#define MAGMA_Z_ABS

(

a

)

Returns

absolute value, |a| = sqrt( real(a)^2 + imag(a)^2 ).

MAGMA_Z_ABS1

#define MAGMA_Z_ABS1

(

a

)

Returns

1-norm absolute value, | real(a) | + | imag(a) |.

MAGMA_Z_CONJ

#define MAGMA_Z_CONJ

(

a

)

Returns

conjugate of a.

Function Documentation

real()

__host__ static __device__ double real ( const magmaDoubleComplex & x )

inlinestatic

Returns

real component of complex number x; x for real number.

imag()

__host__ static __device__ double imag ( const double & x )

inlinestatic

Returns

imaginary component of complex number x; 0 for real number.

conj()

__host__ static __device__ double conj ( const double & x )

inlinestatic

Returns

conjugate of complex number x; x for real number.

fabs()

__host__ static __device__ double fabs ( const magmaDoubleComplex & x )

inlinestatic

Returns

2-norm absolute value of complex number x: sqrt( real(x)^2 + imag(x)^2 ). math.h or cmath provide fabs for real numbers.

abs1()

__host__ static __device__ double abs1 ( const magmaDoubleComplex & x )

inlinestatic

Returns

1-norm absolute value of complex nmuber x: | real(x) | + | imag(x) |.