Single and double precision complex numbers. More...

#include <Complex.h>

Public Member Functions

Bool	isNaN (const Complex &val)
	Complex NaN and Infinity.
void	setNaN (Complex &val)
Bool	isInf (const Complex &val)
void	setInf (Complex &val)
Bool	isFinite (const Complex &val)

Bool	operator>= (const Complex &left, const Complex &right)
	Complex comparisons.
Bool	operator> (const Complex &left, const Complex &right)
Bool	operator<= (const Complex &left, const Complex &right)
Bool	operator< (const Complex &left, const Complex &right)

Bool	isNaN (const DComplex &val)
	DComplex NaN and Infinity.
void	setNaN (DComplex &val)
Bool	isInf (const DComplex &val)
void	setInf (DComplex &val)
Bool	isFinite (const DComplex &val)

Bool	operator>= (const DComplex &left, const DComplex &right)
	DComplex comparisons.
Bool	operator> (const DComplex &left, const DComplex &right)
Bool	operator<= (const DComplex &left, const DComplex &right)
Bool	operator< (const DComplex &left, const DComplex &right)

Double	fabs (const DComplex &val)
	Additional complex mathematical functions.
Float	fabs (const Complex &val)
DComplex	square (const DComplex &val)
Complex	square (const Complex &val)
DComplex	cube (const DComplex &val)
Complex	cube (const Complex &val)
Complex	pow (const Complex &val, Double p)
	The log10 should be in stl.
Complex	operator* (const Complex &val, Double f)
	QMath and scimath need these operators * and /.
Complex	operator* (Double f, const Complex &val)
Complex	operator/ (const Complex &val, Double f)
Complex	operator/ (Double f, const Complex &val)
Complex	operator* (const Complex &val, Int f)
	These operators are useful, otherwise both Float and Double are applicable for Ints.
Complex	operator* (Int f, const Complex &val)
Complex	operator/ (const Complex &val, Int f)
Complex	operator/ (Int f, const Complex &val)
Bool	near (const Complex &val1, const Complex &val2, Double tol=1.0e-5)
	The near functions.
Bool	near (const DComplex &val1, const DComplex &val2, Double tol=1.0e-13)
Bool	nearAbs (const Complex &val1, const Complex &val2, Double tol=1.0e-5)
Bool	nearAbs (const DComplex &val1, const DComplex &val2, Double tol=1.0e-13)
Bool	allNear (const Complex &val1, const Complex &val2, Double tol=1.0e-5)
Bool	allNear (const DComplex &val1, const DComplex &val2, Double tol=1.0e-13)
Bool	allNearAbs (const Complex &val1, const Complex &val2, Double tol=1.0e-5)
Bool	allNearAbs (const DComplex &val1, const DComplex &val2, Double tol=1.0e-13)

Complex	max (const Complex &x, const Complex &y)
	Max and min, floor and ceil functions.
DComplex	max (const DComplex &x, const DComplex &y)
Complex	min (const Complex &x, const Complex &y)
DComplex	min (const DComplex &x, const DComplex &y)
Complex	floor (const Complex &x)
DComplex	floor (const DComplex &x)
Complex	ceil (const Complex &x)
DComplex	ceil (const DComplex &x)

DComplex	fmod (const DComplex &in, const DComplex &f)
	fmod
Complex	fmod (const Complex &in, const Complex &f)

DComplex	atan (const DComplex &in)
	Inverse trigonometry.
Complex	atan (const Complex &in)
DComplex	asin (const DComplex &in)
Complex	asin (const Complex &in)
DComplex	acos (const DComplex &in)
Complex	acos (const Complex &in)
DComplex	atan2 (const DComplex &in, const DComplex &t2)
Complex	atan2 (const Complex &in, const Complex &t2)

DComplex	erf (const DComplex &in)
	Error function.
Complex	erf (const Complex &in)
DComplex	erfc (const DComplex &in)
Complex	erfc (const Complex &in)

Detailed Description

Single and double precision complex numbers.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

<h3>Synopsis</h3>
The class <tt>Complex</tt> is a straight typedef as the 
standard library <tt>complex&lt;float&gt;</tt>.

In a similar way <tt>DComplex</tt> is typedef-ed as
<tt>complex&lt;double&gt;</tt>.

  \link casa::IComplex IComplex \endlink  is defined as a specific class.
It is only used by the <tt>FITS</tt> classes.

<tt>lDComplex</tt> has not been defined: <tt>long double</tt> is not
part of the standard aips++ data suite (yet)

A set of global functions are added for historic reasons (they were present
in the original aips++/gcc complex implementation).

See the standard library documentation for the expected behaviour of 
the <tt>Complex</tt> and <tt>DComplex</tt> classes.

<br><strong>Tip:</strong><em>  In the following all references to <tt>Complex</tt>
can be replaced with <tt>DComplex</tt>; with simultaneous
replacement of <tt>Float</tt> with <tt>Double</tt>; </em><br>

Complex numbers may be constructed and used in the following ways:
<dl>
<dt>Complex x;</dt>
<dd>  Declares an uninitialized Complex. </dd>

<dt>Complex x = 2; Complex y(2.0);</dt>
<dd>  Set x and y to the Complex value (2.0, 0.0); </dd>

<dt>Complex x(2, 3);</dt>
<dd>  Sets x to the Complex value (2, 3); </dd>

<dt>Complex u(x); Complex v = x;</dt>
<dd>  Set u and v to the same value as x. </dd>

<dt>Float real(Complex& x);</dt>
<dd>  returns the real part of x. </dd>

<dt>Float imag(Complex& x);</dt>
<dd>  returns the imaginary part of x. </dd>

<dt>Float abs(Complex& x);</dt>
<dd>  returns the magnitude of x. </dd>

<dt>Float norm(Complex& x);</dt>
<dd>  returns the square of the magnitude of x. </dd>

<dt>Float arg(Complex& x);</dt>
<dd>  returns the argument (amplitude) of x. </dd>

<dt>Complex polar(Float r, Float t = 0.0);</dt>
<dd>  returns a Complex with abs of r and arg of t. </dd>

<dt>Complex conj(Complex& x);</dt>
<dd>  returns the complex conjugate of x </dd>

<dt>Complex cos(Complex& x);</dt>
<dd>  returns the complex cosine of x. </dd>

<dt>Complex sin(Complex& x);</dt>
<dd>  returns the complex sine of x. </dd>

<dt>Complex cosh(Complex& x);</dt>
<dd>  returns the complex hyperbolic cosine of x. </dd>

<dt>Complex sinh(Complex& x);</dt>
<dd>  returns the complex hyperbolic sine of x. </dd>

<dt>Complex exp(Complex& x);</dt>
<dd>  returns the exponential of x. </dd>

<dt>Complex log(Complex& x);</dt>
<dd>  returns the natural log of x. </dd>

<dt>Complex pow(Complex& x, long p);</dt>
<dd>  returns x raised to the p power. </dd>

<dt>Complex pow(Complex& x, Complex& p);</dt>
<dd>  returns x raised to the p power. </dd>

<dt>Complex sqrt(Complex& x);</dt>
<dd>  returns the square root of x. </dd>

<dt> Complex min(Complex x,Complex y);
<dd> Returns the minumum of x,y (using operator<=, i.e. the norm).

<dt> Complex max(Complex x,Complex y);
<dd> Returns the maximum of x,y (using operator>=, i.e. the norm).

<dt>Bool near(Complex val1, Complex val2, Double tol = 1.0e-5);</dt>
<dd>  returns whether val1 is relatively near val2 (see Math.h).
    (Note the Double tolerance) </dd>

<dt>Bool nearAbs(Complex val1, Complex val2, Double tol = 1.0e-5);</dt>
<dd>  returns whether val1 is absolutely near val2 (see Math.h).
    (Note the Double tolerance) </dd>

<dt>ostream << x;</dt>
<dd>  prints x in the form (re, im). </dd>

<dt>istream >> x;</dt>
 <dd> reads x in the form (re, im), or just (re) or re in which case the
     imaginary part is set to zero. </dd>
</dl>

Definition at line 158 of file Complex.h.

Member Function Documentation

DComplex casa::Complex_global_functions_Complex_desc::acos ( const DComplex & in )

Complex casa::Complex_global_functions_Complex_desc::acos ( const Complex & in )

Bool casa::Complex_global_functions_Complex_desc::allNear	(	const Complex &	val1,
		const Complex &	val2,
		Double	tol = `1.0e-5`
	)		`[inline]`

Definition at line 264 of file Complex.h.

References casa::near().

Bool casa::Complex_global_functions_Complex_desc::allNear	(	const DComplex &	val1,
		const DComplex &	val2,
		Double	tol = `1.0e-13`
	)		`[inline]`

Definition at line 267 of file Complex.h.

References casa::near().

Bool casa::Complex_global_functions_Complex_desc::allNearAbs	(	const Complex &	val1,
		const Complex &	val2,
		Double	tol = `1.0e-5`
	)		`[inline]`

Definition at line 270 of file Complex.h.

References casa::nearAbs().

Bool casa::Complex_global_functions_Complex_desc::allNearAbs	(	const DComplex &	val1,
		const DComplex &	val2,
		Double	tol = `1.0e-13`
	)		`[inline]`

Definition at line 273 of file Complex.h.

References casa::nearAbs().

DComplex casa::Complex_global_functions_Complex_desc::asin ( const DComplex & in )

Complex casa::Complex_global_functions_Complex_desc::asin ( const Complex & in )

DComplex casa::Complex_global_functions_Complex_desc::atan ( const DComplex & in )

Inverse trigonometry.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

atan not valid for z == -1

Complex casa::Complex_global_functions_Complex_desc::atan ( const Complex & in )

DComplex casa::Complex_global_functions_Complex_desc::atan2	(	const DComplex &	in,
		const DComplex &	t2
	)

Complex casa::Complex_global_functions_Complex_desc::atan2	(	const Complex &	in,
		const Complex &	t2
	)

Complex casa::Complex_global_functions_Complex_desc::ceil ( const Complex & x ) [inline]

Definition at line 296 of file Complex.h.

References casa::ceil().

DComplex casa::Complex_global_functions_Complex_desc::ceil ( const DComplex & x ) [inline]

Definition at line 298 of file Complex.h.

References casa::ceil().

DComplex casa::Complex_global_functions_Complex_desc::cube ( const DComplex & val ) [inline]

Definition at line 224 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::cube ( const Complex & val ) [inline]

Definition at line 225 of file Complex.h.

DComplex casa::Complex_global_functions_Complex_desc::erf ( const DComplex & in )

Error function.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Preliminary to get Functionals working. erf(z) will return erf(real(z)) only for now.

Complex casa::Complex_global_functions_Complex_desc::erf ( const Complex & in )

DComplex casa::Complex_global_functions_Complex_desc::erfc ( const DComplex & in )

Complex casa::Complex_global_functions_Complex_desc::erfc ( const Complex & in )

Double casa::Complex_global_functions_Complex_desc::fabs ( const DComplex & val ) [inline]

Additional complex mathematical functions.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Definition at line 219 of file Complex.h.

References casa::abs().

Float casa::Complex_global_functions_Complex_desc::fabs ( const Complex & val ) [inline]

Definition at line 220 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::floor ( const Complex & x ) [inline]

Definition at line 291 of file Complex.h.

References casa::floor().

DComplex casa::Complex_global_functions_Complex_desc::floor ( const DComplex & x ) [inline]

Definition at line 293 of file Complex.h.

References casa::floor().

DComplex casa::Complex_global_functions_Complex_desc::fmod	(	const DComplex &	in,
		const DComplex &	f
	)

fmod

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Complex casa::Complex_global_functions_Complex_desc::fmod	(	const Complex &	in,
		const Complex &	f
	)

Bool casa::Complex_global_functions_Complex_desc::isFinite ( const Complex & val )

Bool casa::Complex_global_functions_Complex_desc::isFinite ( const DComplex & val )

Bool casa::Complex_global_functions_Complex_desc::isInf ( const Complex & val )

Bool casa::Complex_global_functions_Complex_desc::isInf ( const DComplex & val )

Bool casa::Complex_global_functions_Complex_desc::isNaN ( const Complex & val )

Complex NaN and Infinity.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Bool casa::Complex_global_functions_Complex_desc::isNaN ( const DComplex & val )

DComplex NaN and Infinity.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Complex casa::Complex_global_functions_Complex_desc::max	(	const Complex &	x,
		const Complex &	y
	)		`[inline]`

Max and min, floor and ceil functions.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Definition at line 282 of file Complex.h.

DComplex casa::Complex_global_functions_Complex_desc::max	(	const DComplex &	x,
		const DComplex &	y
	)		`[inline]`

Definition at line 284 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::min	(	const Complex &	x,
		const Complex &	y
	)		`[inline]`

Definition at line 286 of file Complex.h.

DComplex casa::Complex_global_functions_Complex_desc::min	(	const DComplex &	x,
		const DComplex &	y
	)		`[inline]`

Definition at line 288 of file Complex.h.

Bool casa::Complex_global_functions_Complex_desc::near	(	const Complex &	val1,
		const Complex &	val2,
		Double	tol = `1.0e-5`
	)

The near functions.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Bool casa::Complex_global_functions_Complex_desc::near	(	const DComplex &	val1,
		const DComplex &	val2,
		Double	tol = `1.0e-13`
	)

Bool casa::Complex_global_functions_Complex_desc::nearAbs	(	const Complex &	val1,
		const Complex &	val2,
		Double	tol = `1.0e-5`
	)

Bool casa::Complex_global_functions_Complex_desc::nearAbs	(	const DComplex &	val1,
		const DComplex &	val2,
		Double	tol = `1.0e-13`
	)

Complex casa::Complex_global_functions_Complex_desc::operator*	(	const Complex &	val,
		Double	f
	)		`[inline]`

QMath and scimath need these operators * and /.

Definition at line 240 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator*	(	Double	f,
		const Complex &	val
	)		`[inline]`

Definition at line 241 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator*	(	const Complex &	val,
		Int	f
	)		`[inline]`

These operators are useful, otherwise both Float and Double are applicable for Ints.

Definition at line 248 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator*	(	Int	f,
		const Complex &	val
	)		`[inline]`

Definition at line 249 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator/	(	const Complex &	val,
		Double	f
	)		`[inline]`

Definition at line 242 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator/	(	Double	f,
		const Complex &	val
	)		`[inline]`

Definition at line 243 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator/	(	const Complex &	val,
		Int	f
	)		`[inline]`

Definition at line 250 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::operator/	(	Int	f,
		const Complex &	val
	)		`[inline]`

Definition at line 251 of file Complex.h.

Bool casa::Complex_global_functions_Complex_desc::operator<	(	const Complex &	left,
		const Complex &	right
	)		`[inline]`

Definition at line 182 of file Complex.h.

References casa::False, and casa::norm().

Bool casa::Complex_global_functions_Complex_desc::operator<	(	const DComplex &	left,
		const DComplex &	right
	)		`[inline]`

Definition at line 209 of file Complex.h.

References casa::norm().

Bool casa::Complex_global_functions_Complex_desc::operator<=	(	const Complex &	left,
		const Complex &	right
	)		`[inline]`

Definition at line 180 of file Complex.h.

References casa::norm(), and casa::True.

Bool casa::Complex_global_functions_Complex_desc::operator<=	(	const DComplex &	left,
		const DComplex &	right
	)		`[inline]`

Definition at line 207 of file Complex.h.

References casa::norm().

Bool casa::Complex_global_functions_Complex_desc::operator>	(	const Complex &	left,
		const Complex &	right
	)		`[inline]`

Definition at line 178 of file Complex.h.

References casa::False, and casa::norm().

Bool casa::Complex_global_functions_Complex_desc::operator>	(	const DComplex &	left,
		const DComplex &	right
	)		`[inline]`

Definition at line 205 of file Complex.h.

References casa::norm().

Bool casa::Complex_global_functions_Complex_desc::operator>=	(	const Complex &	left,
		const Complex &	right
	)		`[inline]`

Complex comparisons.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Definition at line 176 of file Complex.h.

References casa::norm(), and casa::True.

Bool casa::Complex_global_functions_Complex_desc::operator>=	(	const DComplex &	left,
		const DComplex &	right
	)		`[inline]`

DComplex comparisons.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25

Definition at line 203 of file Complex.h.

References casa::norm().

Complex casa::Complex_global_functions_Complex_desc::pow	(	const Complex &	val,
		Double	p
	)		`[inline]`

The log10 should be in stl.

ArrayMath::pow needs this pow function (on SGI).

Definition at line 236 of file Complex.h.

References casa::pow().

void casa::Complex_global_functions_Complex_desc::setInf ( Complex & val )

void casa::Complex_global_functions_Complex_desc::setInf ( DComplex & val )

void casa::Complex_global_functions_Complex_desc::setNaN ( Complex & val )

void casa::Complex_global_functions_Complex_desc::setNaN ( DComplex & val )

DComplex casa::Complex_global_functions_Complex_desc::square ( const DComplex & val ) [inline]

Definition at line 221 of file Complex.h.

Complex casa::Complex_global_functions_Complex_desc::square ( const Complex & val ) [inline]

Definition at line 222 of file Complex.h.

The documentation for this struct was generated from the following file:

casacore/casa/BasicSL/Complex.h

Public Member Functions

Detailed Description

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