7.5.3
Complex Number Calculation Class Library
The header file for the complex number calculation class library is as follows:
Defines the float_complex and double_complex classes.
These classes have no derivation.
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Type
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value_type
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float type
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Variable
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_re
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Defines the real part of float precision.
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_im
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Defines the imaginary part of float precision.
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Function
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float_complex(float re = 0.0f, float im = 0.0f)
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Constructor.
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float_complex(const double_complex& rhs)
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float real() const
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Acquires the real part (_re).
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float imag() const
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Acquires the imaginary part (_im).
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float_complex& operator=(float rhs)
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Copies rhs to the real part..
0.0f is assigned to the imaginary part.
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float_complex& operator+=(float rhs)
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Adds rhs to the real part and stores the sum in *this.
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float_complex& operator-=(float rhs)
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Subtracts rhs from the real part and stores the difference in *this.
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float_complex& operator*=(float rhs)
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Multiplies *this by rhs and stores the product in *this.
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float_complex& operator/=(float rhs)
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Divides *this by rhs and stores the quotient in *this.
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float_complex& operator=(
const float_complex& rhs)
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Copies rhs.
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float_complex& operator+=(
const float_complex& rhs)
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Adds rhs to *this and stores the sum in *this.
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float_complex& operator-=(
const float_complex& rhs)
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Subtracts rhs from *this and stores the difference in *this.
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float_complex& operator*=(
const float_complex& rhs)
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Multiplies *this by rhs and stores the product in *this.
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float_complex& operator/=(
const float_complex& rhs)
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Divides *this by rhs and stores the quotient in *this.
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float_complex::float_complex(float re = 0.0f, float im = 0.0f)
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Constructor of class float_complex.
The initial settings are as follows:
_re = re;
_im = im;
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float_ complex::float_complex(const double_complex& rhs)
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Constructor of class float_complex.
The initial settings are as follows:
_re = (float)rhs.real();
_im = (float)rhs.imag();
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float float_complex::real() const
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Acquires the real part.
Return value: this->_re
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float float_complex::imag() const
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Acquires the imaginary part.
Return value: this->_im
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float_complex& float_complex::operator=(float rhs)
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Copies rhs to the real part (_re).
0.0f is assigned to the imaginary part (_im).
Return value: *this
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float_complex& float_complex::operator+=(float rhs)
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Adds rhs to the real part (_re) and stores the result in the real part (_re).
The value of the imaginary part (_im) does not change.
Return value: *this
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float_complex& float_complex::operator-=(float rhs)
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Subtracts rhs from the real part (_re) and stores the result in the real part (_re).
The value of the imaginary part (_im) does not change.
Return value: *this
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float_complex& float_complex::operator*=(float rhs)
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Multiplies *this by rhs and stores the result in *this.
(_re=_re*rhs, _im=_im*rhs)
Return value: *this
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float_complex& float_complex::operator/=(float rhs)
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Divides *this by rhs and stores the result in *this.
(_re=_re/rhs, _im=_im/rhs)
Return value: *this
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float_complex& float_complex::operator=(const float_complex& rhs)
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Copies rhs to *this.
Return value: *this
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float_complex& float_complex::operator+=(const float_complex& rhs)
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Adds rhs to *this and stores the result in *this
Return value: *this
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float_complex& float_complex::operator-=(const float_complex& rhs)
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Subtracts rhs from *this and stores the result in *this.
Return value: *this
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float_complex& float_complex::operator*=(const float_complex& rhs)
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Multiplies *this by rhs and stores the result in *this.
Return value: *this
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float_complex& float_complex::operator/=(const float_complex& rhs)
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Divides *this by rhs and stores the result in *this.
Return value: *this
(b) | float_complex Non-Member Function |
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Function
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float_complex operator+(
const float_complex& lhs)
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Performs unary + operation of lhs.
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float_complex operator+(
const float_complex& lhs,
const float_complex& rhs)
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Returns the result of adding lhs to rhs.
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float_complex operator+(
const float_complex& lhs,
const float& rhs)
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float_complex operator+(
const float& lhs,
const float_complex& rhs)
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float_complex operator-(
const float_complex& lhs)
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Performs unary - operation of lhs.
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float_complex operator-(
const float_complex& lhs,
const float_complex& rhs)
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Returns the result of subtracting rhs from lhs.
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float_complex operator-(
const float_complex& lhs,
const float& rhs)
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float_complex operator-(
const float& lhs,
const float_complex& rhs)
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Function
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float_complex operator*(
const float_complex& lhs,
const float_complex& rhs)
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Returns the result of multiplying lhs by rhs.
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float_complex operator*(
const float_complex& lhs,
const float& rhs)
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float_complex operator*(
const float& lhs,
const float_complex& rhs)
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float_complex operator/(
const float_complex& lhs,
const float_complex& rhs)
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Returns the result of dividing lhs by rhs.
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float_complex operator/(
const float_complex& lhs,
const float& rhs)
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float_complex operator/(
const float& lhs,
const float_complex& rhs)
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Divides lhs by rhs and stores the quotient in lhs.
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bool operator==(
const float_complex& lhs,
const float_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
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bool operator==(
const float_complex& lhs,
const float& rhs)
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bool operator== (
const float& lhs,
const float_complex& rhs)
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bool operator!=(
const float_complex& lhs,
const float_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
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bool operator!=(
const float_complex& lhs,
const float& rhs)
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bool operator!=(
const float& lhs,
const float_complex& rhs)
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istream& operator>>(
istream& is,
float_complex& x)
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Inputs x in a format of u, (u), or (u,v) (u: real part, v: imaginary part).
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ostream& operator<<(
ostream& os,
const float_complex& x)
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Outputs x in a format of u, (u), or (u,v) (u: real part, v: imaginary part).
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float real(const float_complex& x)
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Acquires the real part.
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float imag(const float_complex& x)
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Acquires the imaginary part.
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float abs(const float_complex& x)
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Calculates the absolute value.
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float arg(const float_complex& x)
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Calculates the phase angle.
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float norm(const float_complex& x)
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Calculates the absolute value of the square.
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Function
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float_complex conj(const float_complex& x)
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Calculates the conjugate complex number.
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float_complex polar(
const float& rho,
const float& theta)
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Calculates the float_complex value for a complex number with size rho and phase angle theta.
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float_complex cos(const float_complex& x)
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Calculates the complex cosine.
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float_complex cosh(const float_complex& x)
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Calculates the complex hyperbolic cosine.
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float_complex exp(const float_complex& x)
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Calculates the exponent function.
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float_complex log(const float_complex& x)
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Calculates the natural logarithm.
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float_complex log10(const float_complex& x)
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Calculates the common logarithm.
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float_complex pow(
const float_complex& x,
int y)
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Calculates x to the yth power.
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float_complex pow(
const float_complex& x,
const float& y)
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float_complex pow(
const float_complex& x,
const float_complex& y)
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float_complex pow(
const float& x,
const float_complex& y)
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float_complex sin(const float_complex& x)
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Calculates the complex sine.
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float_complex sinh(const float_complex& x)
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Calculates the complex hyperbolic sine.
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float_complex sqrt(const float_complex& x)
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Calculates the square root within the right half space.
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float_complex tan(const float_complex& x)
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Calculates the complex tangent.
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float_complex tanh(const float_complex& x)
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Calculates the complex hyperbolic tangent.
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float_complex operator+(const float_complex& lhs)
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Performs unary + operation of lhs.
Return value: lhs
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float_complex operator+(const float_complex& lhs, const float_complex& rhs)
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Returns the result of adding lhs to rhs.
Return value: float_complex(lhs)+=rhs
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float_complex operator+(const float_complex& lhs, const float& rhs)
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Returns the result of adding lhs to rhs.
Return value: float_complex(lhs)+=rhs
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float_complex operator+(const float& lhs, const float_complex& rhs)
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Returns the result of adding lhs to rhs.
Return value: float_complex(lhs)+=rhs
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float_complex operator-(const float_complex& lhs)
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Performs unary - operation of lhs.
Return value: float_complex(-lhs.real(), -lhs.imag())
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float_complex operator-(const float_complex& lhs, const float_complex& rhs)
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Returns the result of subtracting rhs from lhs.
Return value: float_complex(lhs)-=rhs
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float_complex operator-(const float_complex& lhs, const float& rhs)
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Returns the result of subtracting rhs from lhs.
Return value: float_complex(lhs)-=rhs
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float_complex operator-(const float& lhs, const float_complex& rhs)
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Returns the result of subtracting rhs from lhs.
Return value: float_complex(lhs)-=rhs
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float_complex operator*(const float_complex& lhs, const float_complex& rhs)
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Returns the result of multiplying lhs by rhs.
Return value: float_complex(lhs)*=rhs
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float_complex operator*(const float_complex& lhs, const float& rhs)
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Returns the result of multiplying lhs by rhs.
Return value: float_complex(lhs)*=rhs
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float_complex operator*(const float& lhs, const float_complex& rhs)
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Returns the result of multiplying lhs by rhs.
Return value: float_complex(lhs)*=rhs
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float_complex operator/(const float_complex& lhs, const float_complex& rhs)
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Returns the result of dividing lhs by rhs.
Return value: float_complex(lhs)/=rhs
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float_complex operator/(const float_complex& lhs, const float& rhs)
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Returns the result of dividing lhs by rhs.
Return value: float_complex(lhs)/=rhs
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float_complex operator/(const float& lhs, const float_complex& rhs)
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Returns the result of dividing lhs by rhs.
Return value: float_complex(lhs)/=rhs
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bool operator==(const float_complex& lhs, const float_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a float type parameter, the imaginary part is assumed to be 0.0f.
Return value: lhs.real()==rhs.real() && lhs.imag()==rhs.imag()
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bool operator==(const float_complex& lhs, const float& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a float type parameter, the imaginary part is assumed to be 0.0f.
Return value: lhs.real()==rhs.real() && lhs.imag()==rhs.imag()
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bool operator==(const float& lhs, const float_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a float type parameter, the imaginary part is assumed to be 0.0f.
Return value: lhs.real()==rhs.real() && lhs.imag()==rhs.imag()
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bool operator!=(const float_complex& lhs, const float_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a float type parameter, the imaginary part is assumed to be 0.0f.
Return value: lhs.real()!=rhs.real() || lhs.imag()!=rhs.imag()
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bool operator!=(const float_complex& lhs, const float& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a float type parameter, the imaginary part is assumed to be 0.0f.
Return value: lhs.real()!=rhs.real() || lhs.imag()!=rhs.imag()
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bool operator!=(const float& lhs, const float_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a float type parameter, the imaginary part is assumed to be 0.0f.
Return value: lhs.real()!=rhs.real() || lhs.imag()!=rhs.imag()
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istream& operator>>(istream& is, float_complex& x)
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Inputs x in a format of u, (u), or (u,v) (u: real part, v: imaginary part).
The input value is converted to float_complex.
If x is input in a format other than the u, (u), or (u,v) format, is.setstate(ios_base::failbit) is called.
Return value: is
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ostream& operator<<(ostream& os, const float_complex& x)
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Outputs x to os.
The output format is u, (u), or (u,v) (u: real part, v: imaginary part).
Return value: os
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float real(const float_complex& x)
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Acquires the real part.
Return value: x.real()
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float imag(const float_complex& x)
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Acquires the imaginary part.
Return value: x.imag()
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float abs(const float_complex& x)
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Calculates the absolute value.
Return value: (|x.real()|2 + |x.imag()|2)1/2
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float arg(const float_complex& x)
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Calculates the phase angle.
Return value: atan2f(x.imag(), x.real())
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float norm(const float_complex& x)
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Calculates the absolute value of the square.
Return value: |x.real()|2 + |x.imag()|2
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float_complex conj(const float_complex& x)
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Calculates the conjugate complex number.
Return value: float_complex(x.real(), (-1)*x.imag())
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float_complex polar(const float& rho, const float& theta)
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Calculates the float_complex value for a complex number with size rho and phase angle (argument) theta.
Return value: float_complex(rho*cosf(theta), rho*sinf(theta))
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float_complex cos(const float_complex& x)
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Calculates the complex cosine.
Return value: float_complex(cosf(x.real())*coshf(x.imag()),
(-1)*sinf(x.real())*sinhf(x.imag()))
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float_complex cosh(const float_complex& x)
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Calculates the complex hyperbolic cosine.
Return value: cos(float_complex((-1)*x.imag(), x.real()))
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float_complex& float_complex::operator-=(const float_complex& rhs)
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Calculates the exponent function.
Return value: expf(x.real())*cosf(x.imag()),expf(x.real())*sinf(x.imag())
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float_complex log(const float_complex& x)
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Calculates the natural logarithm (base e).
Return value: float_complex(logf(abs(x)), arg(x))
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float_complex log10(const float_complex& x)
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Calculates the common logarithm (base 10).
Return value: float_complex(log10f(abs(x)), arg(x)/logf(10))
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float_complex pow(const float_complex& x, int y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: If float_complex pow(const float_complex& x, const float_complex& y): exp(y*logf(x))
Otherwise: exp(y*log(x))
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float_complex pow(const float_complex& x, const float& y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: If float_complex pow(const float_complex& x, const float_complex& y): exp(y*logf(x))
Otherwise: exp(y*log(x))
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float_complex pow(const float_complex& x, const float_complex& y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: If float_complex pow(const float_complex& x, const float_complex& y): exp(y*logf(x))
Otherwise: exp(y*log(x))
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float_complex pow(const float& x, const float_complex& y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: If float_complex pow(const float_complex& x, const float_complex& y): exp(y*logf(x))
Otherwise: exp(y*log(x))
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float_complex sin(const float_complex& x)
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Calculates the complex sine.
Return value: float_complex(sinf(x.real())*coshf(x.imag()), cosf(x.real())*sinhf(x.imag()))
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float_complex sinh(const float_complex& x)
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Calculates the complex hyperbolic sine.
Return value: float_complex(0,-1)*sin(float_complex((-1)*x.imag(),x.real()))
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float_complex sqrt(const float_complex& x)
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Calculates the square root within the right half space.
Return value: float_complex(sqrtf(abs(x))*cosf(arg(x)/2), sqrtf(abs(x))*sinf(arg(x)/2))
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float_complex tan(const float_complex& x)
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Calculates the complex tangent.
Return value: sin(x)/cos(x)
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float_complex tanh(const float_complex& x)
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Calculates the complex hyperbolic tangent.
Return value: sinh(x)/cosh(x)
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Type
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value_type
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double type.
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Variable
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_re
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Defines the real part of double precision.
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_im
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Defines the imaginary part of double precision.
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Function
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double_complex(
double re = 0.0,
double im = 0.0)
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Constructor.
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double_complex(const float_complex&)
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double real() const
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Acquires the real part.
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double imag() const
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Acquires the imaginary part.
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double_complex& operator=(double rhs)
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Copies rhs to the real part.
0.0 is assigned to the imaginary part.
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double_complex& operator+=(double rhs)
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Adds rhs to the real part of *this and stores the sum in *this.
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double_complex& operator-=(double rhs)
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Subtracts rhs from the real part of *this and stores the difference in *this.
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double_complex& operator*=(double rhs)
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Multiplies *this by rhs and stores the product in *this.
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double_complex& operator/=(double rhs)
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Divides *this by rhs and stores the quotient in *this.
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double_complex& operator=(
const double_complex& rhs)
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Copies rhs.
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double_complex& operator+=(
const double_complex& rhs)
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Adds rhs to *this and stores the sum in *this.
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double_complex& operator-=(
const double_complex& rhs)
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Subtracts rhs from *this and stores the difference in *this.
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double_complex& operator*=(
const double_complex& rhs)
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Multiplies *this by rhs and stores the product in *this.
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double_complex& operator/=(
const double_complex& rhs)
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Divides *this by rhs and stores the quotient in *this.
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double_complex::double_complex(double re = 0.0, double im = 0.0)
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Constructor of class double_complex.
The initial settings are as follows:
_re = re;
_im = im;
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double_complex::double_complex(const float_complex&)
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Constructor of class double_complex.
The initial settings are as follows:
_re = (double)rhs.real();
_im = (double)rhs.imag();
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double double_complex::real() const
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Acquires the real part.
Return value: this->_re
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double double_complex::imag() const
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Acquires the imaginary part.
Return value: this->_im
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double_complex& double_complex::operator=(double rhs)
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Copies rhs to the real part (_re).
0.0 is assigned to the imaginary part (_im).
Return value: *this
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double_complex& double_complex::operator+=(double rhs)
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Adds rhs to the real part (_re) and stores the result in the real part (_re).
The value of the imaginary part (_im) does not change.
Return value: *this
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double_complex& double_complex::operator-= (double rhs)
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Subtracts rhs from the real part (_re) and stores the result in the real part (_re).
The value of the imaginary part (_im) does not change.
Return value: *this
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double_complex& double_complex::operator*=(double rhs)
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Multiplies *this by rhs and stores the result in *this.
(_re=_re*rhs, _im=_im*rhs)
Return value: *this
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double_complex& double_complex::operator/=(double rhs)
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Divides *this by rhs and stores the result in *this.
(_re=_re/rhs, _im=_im/rhs)
Return value: *this
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double_complex& double_complex::operator=(const double_complex& rhs)
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Copies rhs to *this.
Return value: *this
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double_complex& double_complex::operator+=(const double_complex& rhs)
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Adds rhs to *this and stores the result in *this.
Return value: *this
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double_complex& double_complex::operator-=(const double_complex& rhs)
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Subtracts rhs from *this and stores the result in *this.
Return value: *this
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double_complex& double_complex::operator*=(const double_complex& rhs)
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Multiplies *this by rhs and stores the result in *this.
Return value: *this
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double_complex& double_complex::operator/=(const double_complex& rhs)
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Divides *this by rhs and stores the result in *this.
Return value: *this
(d) | double_complex Non-Member Function |
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Function
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double_complex operator+(
const double_complex& lhs)
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Performs unary + operation of lhs.
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double_complex operator+(
const double_complex& lhs,
const double_complex& rhs)
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Returns the result of adding rhs to lhs.
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double_complex operator+(
const double_complex& lhs,
const double& rhs)
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double_complex operator+(
const double& lhs,
const double_complex& rhs)
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double_complex operator-(
const double_complex& lhs)
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Performs unary - operation of lhs.
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double_complex operator-(
const double_complex& lhs,
const double_complex& rhs)
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Returns the result of subtracting rhs from lhs.
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double_complex operator-(
const double_complex& lhs,
const double& rhs)
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double_complex operator-(
const double& lhs,
const double_complex& rhs)
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Function
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double_complex operator*(
const double_complex& lhs,
const double_complex& rhs)
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Returns the result of multiplying lhs by rhs.
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double_complex operator*(
const double_complex& lhs,
const double& rhs)
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double_complex operator*(
const double& lhs,
const double_complex& rhs)
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double_complex operator/(
const double_complex& lhs,
const double_complex& rhs)
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Returns the result of dividing lhs by rhs.
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double_complex operator/(
const double_complex& lhs,
const double& rhs)
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double_complex operator/(
const double& lhs,
const double_complex& rhs)
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bool operator==(
const double_complex& lhs,
const double_complex& rhs)
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Compares the real part of lhs and rhs, and the imaginary parts of lhs and rhs.
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bool operator==(
const double_complex& lhs,
const double& rhs)
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bool operator==(
const double& lhs,
const double_complex& rhs)
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bool operator!=(
const double_complex& lhs,
const double_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
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bool operator!=(
const double_complex& lhs,
const double& rhs)
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bool operator!=(
const double& lhs,
const double_complex& rhs)
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istream& operator>>(
istream& is,
double_complex& x)
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Inputs x in a format of u, (u), or (u,v) (u: real part, v: imaginary part).
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ostream& operator<<(
ostream& os,
const double_complex& x)
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Outputs x in a format of u, (u), or (u,v) (u: real part, v: imaginary part).
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double real(const double_complex& x)
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Acquires the real part.
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double imag(const double_complex& x)
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Acquires the imaginary part.
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double abs(const double_complex& x)
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Calculates the absolute value.
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double arg(const double_complex& x)
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Calculates the phase angle.
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double norm(const double_complex& x)
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Calculates the absolute value of the square.
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Function
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double_complex conj(
const double_complex& x)
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Calculates the conjugate complex number.
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double_complex polar(
const double& rho,
const double& theta)
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Calculates the double_complex value for a complex number with size rho and phase angle theta.
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double_complex cos(
const double_complex& x)
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Calculates the complex cosine.
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double_complex cosh(
const double_complex& x)
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Calculates the complex hyperbolic cosine.
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double_complex exp(
const double_complex& x)
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Calculates the exponent function.
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double_complex log(
const double_complex& x)
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Calculates the natural logarithm.
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double_complex log10(
const double_complex& x)
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Calculates the common logarithm.
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double_complex pow(
const double_complex& x,
int y)
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Calculates x to the yth power.
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double_complex pow(
const double_complex& x,
const double& y)
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double_complex pow(
const double_complex& x,
const double_complex& y)
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double_complex pow(
const double& x,
const double_complex& y)
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double_complex sin(
const double_complex& x)
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Calculates the complex sine.
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double_complex sinh(
const double_complex& x)
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Calculates the complex hyperbolic sine.
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double_complex sqrt(
const double_complex& x)
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Calculates the square root within the right half space.
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double_complex tan(
const double_complex& x)
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Calculates the complex tangent.
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double_complex tanh(
const double_complex& x)
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Calculates the complex hyperbolic tangent.
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double_complex operator+(const double_complex& lhs)
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Performs unary + operation of lhs.
Return value: lhs
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double_complex operator+(const double_complex& lhs, const double_complex& rhs)
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Returns the result of adding lhs to rhs.
Return value: double_complex(lhs)+=rhs
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double_complex operator+(const double_complex& lhs, const double& rhs)
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Returns the result of adding lhs to rhs.
Return value: double_complex(lhs)+=rhs
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double_complex operator+(const double& lhs, const double_complex& rhs)
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Returns the result of adding lhs to rhs.
Return value: double_complex(lhs)+=rhs
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double_complex operator-(const double_complex& lhs)
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Performs unary - operation of lhs.
Return value: double_complex(-lhs.real(), -lhs.imag())
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double_complex operator-(const double_complex& lhs, const double_complex& rhs)
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Returns the result of subtracting rhs from lhs.
Return value: double_complex(lhs)-=rhs
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double_complex operator-(const double_complex& lhs, const double& rhs)
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Returns the result of subtracting rhs from lhs.
Return value: double_complex(lhs)-=rhs
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double_complex operator-(const double& lhs, const double_complex& rhs)
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Returns the result of subtracting rhs from lhs.
Return value: double_complex(lhs)-=rhs
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double_complex operator*(const double_complex& lhs, const double_complex& rhs)
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Returns the result of multiplying lhs by rhs.
Return value: double_complex(lhs)*=rhs
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double_complex operator*(const double_complex& lhs, const double& rhs)
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Returns the result of multiplying lhs by rhs.
Return value: double_complex(lhs)*=rhs
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double_complex operator*(const double& lhs, const double_complex& rhs)
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Returns the result of multiplying lhs by rhs.
Return value: double_complex(lhs)*=rhs
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double_complex operator/(const double_complex& lhs, const double_complex& rhs)
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Returns the result of dividing lhs by rhs.
Return value: double_complex(lhs)/=rhs
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double_complex operator/(const double_complex& lhs, const double& rhs)
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Returns the result of dividing lhs by rhs.
Return value: double_complex(lhs)/=rhs
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double_complex operator/(const double& lhs, const double_complex& rhs)
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Returns the result of dividing lhs by rhs.
Return value: double_complex(lhs)/=rhs
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bool operator==(const double_complex& lhs, const double_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a double type parameter, the imaginary part is assumed to be 0.0.
Return value: lhs.real()==rhs.real() && lhs.imag()==rhs.imag()
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bool operator==(const double_complex& lhs, const double& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a double type parameter, the imaginary part is assumed to be 0.0.
Return value: lhs.real()==rhs.real() && lhs.imag()==rhs.imag()
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bool operator==(const double& lhs, const double_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a double type parameter, the imaginary part is assumed to be 0.0.
Return value: lhs.real()==rhs.real() && lhs.imag()==rhs.imag()
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bool operator!=(const double_complex& lhs, const double_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a double type parameter, the imaginary part is assumed to be 0.0.
Return value: lhs.real()!=rhs.real() || lhs.imag()!=rhs.imag()
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bool operator!=(const double_complex& lhs, const double& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a double type parameter, the imaginary part is assumed to be 0.0.
Return value: lhs.real()!=rhs.real() || lhs.imag()!=rhs.imag()
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bool operator!=(const double& lhs, const double_complex& rhs)
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Compares the real parts of lhs and rhs, and the imaginary parts of lhs and rhs.
For a double type parameter, the imaginary part is assumed to be 0.0.
Return value: lhs.real()!=rhs.real() || lhs.imag()!=rhs.imag()
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istream& operator>>(istream& is, double_complex& x)
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Inputs complex number x in a format of u, (u), or (u,v) (u: real part, v: imaginary part).
The input value is converted to double_complex.
If x is input in a format other than the u, (u), or (u,v) format, is.setstate(ios_base::failbit) is called.
Return value: is
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ostream& operator<<(ostream& os, const double_complex& x)
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Outputs x to os.
The output format is u, (u), or (u,v) (u: real part, v: imaginary part).
Return value: os
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double real(const double_complex& x)
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Acquires the real part.
Return value: x.real()
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double imag(const double_complex& x)
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Acquires the imaginary part.
Return value: x.imag()
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double abs(const double_complex& x)
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Calculates the absolute value.
Return value: (|x.real()|2 + |x.imag()|2)1/2
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double arg(const double_complex& x)
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Calculates the phase angle.
Return value: atan2(x.imag(), x.real())
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double norm(const double_complex& x)
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Calculates the absolute value of the square.
Return value: |x.real()|2 + |x.imag()|2
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double_complex conj(const double_complex& x)
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Calculates the conjugate complex number.
Return value: double_complex(x.real(), (-1)*x.imag())
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double_complex polar(const double& rho, const double& theta)
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Calculates the double_complex value for a complex number with size rho and phase angle (argument) theta.
Return value: double_complex(rho*cos(theta), rho*sin(theta))
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double_complex cos(const double_complex& x)
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Calculates the complex cosine.
Return value: double_complex(cos(x.real())*cosh(x.imag()),
(-1)*sin(x.real())*sinh(x.imag()))
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double_complex cosh(const double_complex& x)
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Calculates the complex hyperbolic cosine.
Return value: cos(double_complex((-1)*x.imag(), x.real()))
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double_complex exp(const double_complex& x)
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Calculates the exponent function.
Return value: exp(x.real())*cos(x.imag()),exp(x.real())*sin(x.imag())
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double_complex log(const double_complex& x)
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Calculates the natural logarithm (base e).
Return value: double_complex(log(abs(x)), arg(x))
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double_complex log10(const double_complex& x)
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Calculates the common logarithm (base 10).
Return value: double_complex(log10(abs(x)), arg(x)/log(10))
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double_complex pow(const double_complex& x, int y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: exp(y*log(x))
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double_complex pow(const double_complex& x, const double& y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: exp(y*log(x))
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double_complex pow(const double_complex& x, const double_complex& y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: exp(y*log(x))
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double_complex pow(const double& x, const double_complex& y)
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Calculates x to the yth power.
If pow(0,0), a domain error will occur.
Return value: exp(y*log(x))
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double_complex sin(const double_complex& x)
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Calculates the complex sine
Return value: double_complex(sin(x.real())*cosh(x.imag()), cos(x.real())*sinh(x.imag()))
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double_complex sinh(const double_complex& x)
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Calculates the complex hyperbolic sine
Return value: double_complex(0,-1)*sin(double_complex((-1)*x.imag(),x.real()))
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double_complex sqrt(const double_complex& x)
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Calculates the square root within the right half space
Return value: double_complex(sqrt(abs(x))*cos(arg(x)/2), sqrt(abs(x))*sin(arg(x)/2))
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double_complex tan(const double_complex& x)
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Calculates the complex tangent.
Return value: sin(x)/cos(x)
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double_complex tanh(const double_complex& x)
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Calculates the complex hyperbolic tangent.
Return value: sinh(x)/cosh(x)