Class: Complex

Relationships & Source Files
Namespace Children
Classes: `compatible`
Super Chains via Extension / Inclusion / Inheritance
Class Chain: self, `::Numeric`
Instance Chain: self, `::Numeric`, `::Comparable`
Inherits:	Numeric `::Object` Numeric Complex
Defined in:	complex.c

Overview

A complex number can be represented as a paired real number with imaginary unit; a+bi. Where a is real part, b is imaginary part and i is imaginary unit. Real a equals complex a+0i mathematically.

Complex object can be created as literal, and also by using Kernel.Complex, .rect, .polar or to_c method.

2+1i                 #=> (2+1i)
Complex(1)           #=> (1+0i)
Complex(2, 3)        #=> (2+3i)
Complex.polar(2, 3)  #=> (-1.9799849932008908+0.2822400161197344i)
3.to_c               #=> (3+0i)

You can also create complex object from floating-point numbers or strings.

Complex(0.3)         #=> (0.3+0i)
Complex('0.3-0.5i')  #=> (0.3-0.5i)
Complex('2/3+3/4i')  #=> ((2/3)+(3/4)*i)
Complex('1@2')       #=> (-0.4161468365471424+0.9092974268256817i)

0.3.to_c             #=> (0.3+0i)
'0.3-0.5i'.to_c      #=> (0.3-0.5i)
'2/3+3/4i'.to_c      #=> ((2/3)+(3/4)*i)
'1@2'.to_c           #=> (-0.4161468365471424+0.9092974268256817i)

A complex object is either an exact or an inexact number.

Complex(1, 1) / 2    #=> ((1/2)+(1/2)*i)
Complex(1, 1) / 2.0  #=> (0.5+0.5i)

Constant Summary

I =

The imaginary unit.

# File 'complex.c', line 2327
```
f_complex_new_bang2(rb_cComplex, ZERO, ONE)
```

Class Method Summary

.polar(abs[, arg]) ⇒ Complex

Returns a complex object which denotes the given polar form.
.rect(real[, imag]) ⇒ Complex (also: .rectangular)

Returns a complex object which denotes the given rectangular form.
.rectangular(real[, imag]) ⇒ Complex

Alias for .rect.

Instance Attribute Summary

#finite? ⇒ Boolean readonly

Returns true if cmp‘s real and imaginary parts are both finite numbers, otherwise returns false.
#infinite? ⇒ Boolean readonly

Returns 1 if cmp‘s real or imaginary part is an infinite number, otherwise returns nil.
#real ⇒ Numeric readonly

Returns the real part.
#real? ⇒ Boolean readonly

Returns false.

`::Numeric` - Inherited

#finite?	Returns `true` if `num` is a finite number, otherwise returns `false`.
#infinite?	Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, or `+Infinity`.
#integer?	Returns `true` if `num` is an `::Integer`.
#negative?	Returns `true` if `num` is less than 0.
#nonzero?	Returns `self` if `num` is not zero, `nil` otherwise.
#positive?	Returns `true` if `num` is greater than 0.
#real	Returns self.
#real?	Returns `true` if `num` is a real number (i.e.
#zero?	Returns `true` if `num` has a zero value.

Instance Method Summary

#*(numeric) ⇒ Complex

Performs multiplication.
#**(numeric) ⇒ Complex

Performs exponentiation.
#+(numeric) ⇒ Complex

Performs addition.
#-(numeric) ⇒ Complex

Performs subtraction.
#- ⇒ Complex

Returns negation of the value.
#/(numeric) ⇒ Complex

Performs division.
#==(object) ⇒ Boolean

Returns true if cmp equals object numerically.
#abs ⇒ Numeric (also: #magnitude)

Returns the absolute part of its polar form.
#abs2 ⇒ Numeric

Returns square of the absolute value.
#angle ⇒ Float

Alias for #arg.
#arg ⇒ Float (also: #angle, #phase)

Returns the angle part of its polar form.
#conj ⇒ Complex (also: #conjugate)

Returns the complex conjugate.
#conjugate ⇒ Complex

Alias for #conj.
#denominator ⇒ Integer

Returns the denominator (lcm of both denominator - real and imag).
#fdiv(numeric) ⇒ Complex

Performs division as each part is a float, never returns a float.
#imag ⇒ Numeric (also: #imaginary)

Returns the imaginary part.
#imaginary ⇒ Numeric

Alias for #imag.
#inspect ⇒ String

Returns the value as a string for inspection.
#magnitude ⇒ Numeric

Alias for #abs.
#numerator ⇒ Numeric

Returns the numerator.
#phase ⇒ Float

Alias for #arg.
#polar ⇒ Array

Returns an array; [cmp.abs, cmp.arg].
#quo
#rationalize([eps]) ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).
#rect ⇒ Array (also: #rectangular)

Returns an array; [cmp.real, cmp.imag].
#rectangular ⇒ Array

Alias for #rect.
#to_c ⇒ self

Returns self.
#to_f ⇒ Float

Returns the value as a float if possible (the imaginary part should be exactly zero).
#to_i ⇒ Integer

Returns the value as an integer if possible (the imaginary part should be exactly zero).
#to_r ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).
#to_s ⇒ String

Returns the value as a string.
#coerce(other) Internal use only
#eql?(other) ⇒ Boolean Internal use only
#hash Internal use only
#marshal_dump private Internal use only

`::Numeric` - Inherited

#%	`x.modulo(y)` means `x-y*(x/y).floor`.
#+@	Unary Plus—Returns the receiver.
#-@	Unary Minus—Returns the receiver, negated.
#<=>	Returns zero if `number` equals `other`, otherwise returns `nil`.
#abs	Returns the absolute value of `num`.
#abs2	Returns square of self.
#angle	Alias for Numeric#arg.
#arg	Returns 0 if the value is positive, pi otherwise.
#ceil	Returns the smallest number greater than or equal to `num` with a precision of `ndigits` decimal digits (default: 0).
#clone	Returns the receiver.
#coerce	If `numeric` is the same type as `num`, returns an array `[numeric, num]`.
#conj	Returns self.
#conjugate	Alias for Numeric#conj.
#denominator	Returns the denominator (always positive).
#div	Uses #/ to perform division, then converts the result to an integer.
#divmod	Returns an array containing the quotient and modulus obtained by dividing `num` by `numeric`.
#dup	Returns the receiver.
#eql?	Returns `true` if `num` and `numeric` are the same type and have equal values.
#fdiv	Returns float division.
#floor	Returns the largest number less than or equal to `num` with a precision of `ndigits` decimal digits (default: 0).
#i	Returns the corresponding imaginary number.
#imag	Returns zero.
#imaginary	Alias for Numeric#imag.
#magnitude	Alias for Numeric#abs.
#modulo	Alias for Numeric#%.
#numerator	Returns the numerator.
#phase	Alias for Numeric#arg.
#polar	Returns an array; [num.abs, num.arg].
#quo	Returns the most exact division (rational for integers, float for floats).
#rect	Returns an array; [num, 0].
#rectangular	Alias for Numeric#rect.
#remainder	`x.remainder(y)` means `x-y*(x/y).truncate`.
#round	Returns `num` rounded to the nearest value with a precision of `ndigits` decimal digits (default: 0).
#step	Invokes the given block with the sequence of numbers starting at `num`, incremented by `step` (defaulted to `1`) on each call.
#to_c	Returns the value as a complex.
#to_int	Invokes the child class’s #to_i method to convert `num` to an integer.
#truncate	Returns `num` truncated (toward zero) to a precision of `ndigits` decimal digits (default: 0).
#singleton_method_added	Trap attempts to add methods to `::Numeric` objects.

`::Comparable` - Included

#<	Compares two objects based on the receiver’s `<=>` method, returning true if it returns -1.
#<=	Compares two objects based on the receiver’s `<=>` method, returning true if it returns -1 or 0.
#==	Compares two objects based on the receiver’s `<=>` method, returning true if it returns 0.
#>	Compares two objects based on the receiver’s `<=>` method, returning true if it returns 1.
#>=	Compares two objects based on the receiver’s `<=>` method, returning true if it returns 0 or 1.
#between?	Returns `false` if obj `<=>` min is less than zero or if anObject `<=>` max is greater than zero, `true` otherwise.
#clamp	Returns min if obj `<=>` min is less than zero, max if obj `<=>` max is greater than zero and obj otherwise.

Class Method Details

.polar(abs[, arg]) ⇒ `Complex`

Returns a complex object which denotes the given polar form.

Complex.polar(3, 0)            #=> (3.0+0.0i)
Complex.polar(3, Math::PI/2)   #=> (1.836909530733566e-16+3.0i)
Complex.polar(3, Math::PI)     #=> (-3.0+3.673819061467132e-16i)
Complex.polar(3, -Math::PI/2)  #=> (1.836909530733566e-16-3.0i)

[ GitHub ]

# File 'complex.c', line 614


static VALUE
nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
{
    VALUE abs, arg;

    switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
      case 1:
	nucomp_real_check(abs);
	if (canonicalization) return abs;
	return nucomp_s_new_internal(klass, abs, ZERO);
      default:
	nucomp_real_check(abs);
	nucomp_real_check(arg);
	break;
    }
    return f_complex_polar(klass, abs, arg);
}

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`
Also known as: .rectangular

Returns a complex object which denotes the given rectangular form.

Complex.rectangular(1, 2)  #=> (1+2i)

[ GitHub ]

# File 'complex.c', line 402


static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
    VALUE real, imag;

    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
      case 1:
	nucomp_real_check(real);
	imag = ZERO;
	break;
      default:
	nucomp_real_check(real);
	nucomp_real_check(imag);
	break;
    }

    return nucomp_s_canonicalize_internal(klass, real, imag);
}

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`

Alias for .rect.

Instance Attribute Details

#finite? ⇒ `Boolean` (readonly)

Returns true if cmp‘s real and imaginary parts are both finite numbers, otherwise returns false.

[ GitHub ]

# File 'complex.c', line 1324


static VALUE
rb_complex_finite_p(VALUE self)
{
    get_dat1(self);

    if (f_finite_p(dat->real) && f_finite_p(dat->imag)) {
	return Qtrue;
    }
    return Qfalse;
}

#infinite? ⇒ `Boolean` (readonly)

Returns 1 if cmp‘s real or imaginary part is an infinite number, otherwise returns nil.

For example:

   (1+1i).infinite?                   #=> nil
   (Float::INFINITY + 1i).infinite?   #=> 1

[ GitHub ]

# File 'complex.c', line 1347


static VALUE
rb_complex_infinite_p(VALUE self)
{
    get_dat1(self);

    if (NIL_P(f_infinite_p(dat->real)) && NIL_P(f_infinite_p(dat->imag))) {
	return Qnil;
    }
    return ONE;
}

#real ⇒ Numeric (readonly)

Returns the real part.

Complex(7).real      #=> 7
Complex(9, -4).real  #=> 9

[ GitHub ]

# File 'complex.c', line 641


VALUE
rb_complex_real(VALUE self)
{
    get_dat1(self);
    return dat->real;
}

#real? ⇒ `Boolean` (readonly)

Returns false.

[ GitHub ]

# File 'complex.c', line 1151


static VALUE
nucomp_false(VALUE self)
{
    return Qfalse;
}

Instance Method Details

#*(numeric) ⇒ `Complex`

Performs multiplication.

Complex(2, 3)  * Complex(2, 3)   #=> (-5+12i)
Complex(900)   * Complex(1)      #=> (900+0i)
Complex(-2, 9) * Complex(-9, 2)  #=> (0-85i)
Complex(9, 8)  * 4               #=> (36+32i)
Complex(20, 9) * 9.8             #=> (196.0+88.2i)

[ GitHub ]

# File 'complex.c', line 787


VALUE
rb_complex_mul(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
	VALUE real, imag;
	get_dat2(self, other);

        comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &imag);

	return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	get_dat1(self);

	return f_complex_new2(CLASS_OF(self),
			      f_mul(dat->real, other),
			      f_mul(dat->imag, other));
    }
    return rb_num_coerce_bin(self, other, '*');
}

#**(numeric) ⇒ `Complex`

Performs exponentiation.

Complex('i') ** 2              #=> (-1+0i)
Complex(-8) ** Rational(1, 3)  #=> (1.0000000000000002+1.7320508075688772i)

[ GitHub ]

# File 'complex.c', line 906


VALUE
rb_complex_pow(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && k_exact_zero_p(other))
	return f_complex_new_bang1(CLASS_OF(self), ONE);

    if (RB_TYPE_P(other, T_RATIONAL) && RRATIONAL(other)->den == LONG2FIX(1))
	other = RRATIONAL(other)->num; /* c14n */

    if (RB_TYPE_P(other, T_COMPLEX)) {
	get_dat1(other);

	if (k_exact_zero_p(dat->imag))
	    other = dat->real; /* c14n */
    }

    if (RB_TYPE_P(other, T_COMPLEX)) {
	VALUE r, theta, nr, ntheta;

	get_dat1(other);

	r = f_abs(self);
	theta = f_arg(self);

	nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
			      f_mul(dat->imag, theta)));
	ntheta = f_add(f_mul(theta, dat->real),
		       f_mul(dat->imag, m_log_bang(r)));
	return f_complex_polar(CLASS_OF(self), nr, ntheta);
    }
    if (FIXNUM_P(other)) {
        long n = FIX2LONG(other);
        if (n == 0) {
            return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO);
        }
        if (n < 0) {
            self = f_reciprocal(self);
            other = rb_int_uminus(other);
            n = -n;
        }
        {
            get_dat1(self);
            VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi;

            if (f_zero_p(xi)) {
                zr = rb_num_pow(zr, other);
            }
            else if (f_zero_p(xr)) {
                zi = rb_num_pow(zi, other);
                if (n & 2) zi = f_negate(zi);
                if (!(n & 1)) {
                    VALUE tmp = zr;
                    zr = zi;
                    zi = tmp;
                }
            }
            else {
                while (--n) {
                    long q, r;

                    for (; q = n / 2, r = n % 2, r == 0; n = q) {
                        VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi));
                        xi = f_mul(f_mul(TWO, xr), xi);
                        xr = tmp;
                    }
                    comp_mul(zr, zi, xr, xi, &zr, &zi);
                }
            }
            return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
	}
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	VALUE r, theta;

	if (RB_TYPE_P(other, T_BIGNUM))
	    rb_warn("in a**b, b may be too big");

	r = f_abs(self);
	theta = f_arg(self);

	return f_complex_polar(CLASS_OF(self), f_expt(r, other),
			       f_mul(theta, other));
    }
    return rb_num_coerce_bin(self, other, id_expt);
}

#+(numeric) ⇒ `Complex`

Performs addition.

Complex(2, 3)  + Complex(2, 3)   #=> (4+6i)
Complex(900)   + Complex(1)      #=> (901+0i)
Complex(-2, 9) + Complex(-9, 2)  #=> (-11+11i)
Complex(9, 8)  + 4               #=> (13+8i)
Complex(20, 9) + 9.8             #=> (29.8+9i)

[ GitHub ]

# File 'complex.c', line 693


VALUE
rb_complex_plus(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
	VALUE real, imag;

	get_dat2(self, other);

	real = f_add(adat->real, bdat->real);
	imag = f_add(adat->imag, bdat->imag);

	return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	get_dat1(self);

	return f_complex_new2(CLASS_OF(self),
			      f_add(dat->real, other), dat->imag);
    }
    return rb_num_coerce_bin(self, other, '+');
}

#-(numeric) ⇒ `Complex`

Performs subtraction.

Complex(2, 3)  - Complex(2, 3)   #=> (0+0i)
Complex(900)   - Complex(1)      #=> (899+0i)
Complex(-2, 9) - Complex(-9, 2)  #=> (7+7i)
Complex(9, 8)  - 4               #=> (5+8i)
Complex(20, 9) - 9.8             #=> (10.2+9i)

[ GitHub ]

# File 'complex.c', line 727


VALUE
rb_complex_minus(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
	VALUE real, imag;

	get_dat2(self, other);

	real = f_sub(adat->real, bdat->real);
	imag = f_sub(adat->imag, bdat->imag);

	return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	get_dat1(self);

	return f_complex_new2(CLASS_OF(self),
			      f_sub(dat->real, other), dat->imag);
    }
    return rb_num_coerce_bin(self, other, '-');
}

#- ⇒ `Complex`

Returns negation of the value.

-Complex(1, 2)  #=> (-1-2i)

[ GitHub ]

# File 'complex.c', line 673


VALUE
rb_complex_uminus(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self),
			  f_negate(dat->real), f_negate(dat->imag));
}

#/(numeric) ⇒ `Complex` #quo(numeric) ⇒ `Complex`

Performs division.

Complex(2, 3)  / Complex(2, 3)   #=> ((1/1)+(0/1)*i)
Complex(900)   / Complex(1)      #=> ((900/1)+(0/1)*i)
Complex(-2, 9) / Complex(-9, 2)  #=> ((36/85)-(77/85)*i)
Complex(9, 8)  / 4               #=> ((9/4)+(2/1)*i)
Complex(20, 9) / 9.8             #=> (2.0408163265306123+0.9183673469387754i)

[ GitHub ]

# File 'complex.c', line 869


VALUE
rb_complex_div(VALUE self, VALUE other)
{
    return f_divide(self, other, f_quo, id_quo);
}

#==(object) ⇒ `Boolean`

Returns true if cmp equals object numerically.

Complex(2, 3)  == Complex(2, 3)   #=> true
Complex(5)     == 5               #=> true
Complex(0)     == 0.0             #=> true
Complex('1/3') == 0.33            #=> false
Complex('1/2') == '1/2'           #=> false

[ GitHub ]

# File 'complex.c', line 1004


static VALUE
nucomp_eqeq_p(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
	get_dat2(self, other);

	return f_boolcast(f_eqeq_p(adat->real, bdat->real) &&
			  f_eqeq_p(adat->imag, bdat->imag));
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	get_dat1(self);

	return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
    }
    return f_boolcast(f_eqeq_p(other, self));
}

#abs ⇒ Numeric #magnitude ⇒ Numeric
Also known as: #magnitude

Returns the absolute part of its polar form.

Complex(-1).abs         #=> 1
Complex(3.0, -4.0).abs  #=> 5.0

[ GitHub ]

# File 'complex.c', line 1045


VALUE
rb_complex_abs(VALUE self)
{
    get_dat1(self);

    if (f_zero_p(dat->real)) {
	VALUE a = f_abs(dat->imag);
	if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag))
	    a = f_to_f(a);
	return a;
    }
    if (f_zero_p(dat->imag)) {
	VALUE a = f_abs(dat->real);
	if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag))
	    a = f_to_f(a);
	return a;
    }
    return rb_math_hypot(dat->real, dat->imag);
}

#abs2 ⇒ Numeric

Returns square of the absolute value.

Complex(-1).abs2         #=> 1
Complex(3.0, -4.0).abs2  #=> 25.0

[ GitHub ]

# File 'complex.c', line 1074


static VALUE
nucomp_abs2(VALUE self)
{
    get_dat1(self);
    return f_add(f_mul(dat->real, dat->real),
		 f_mul(dat->imag, dat->imag));
}

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Alias for #arg.

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float
Also known as: #angle, #phase

Returns the angle part of its polar form.

Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966

[ GitHub ]

# File 'complex.c', line 1092


VALUE
rb_complex_arg(VALUE self)
{
    get_dat1(self);
    return rb_math_atan2(dat->imag, dat->real);
}

#coerce(other)

This method is for internal use only.

[ GitHub ]

# File 'complex.c', line 1022


static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && f_real_p(other))
	return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
    if (RB_TYPE_P(other, T_COMPLEX))
	return rb_assoc_new(other, self);

    rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
	     rb_obj_class(other), rb_obj_class(self));
    return Qnil;
}

#conj ⇒ `Complex` #conjugate ⇒ `Complex`
Also known as: #conjugate

Returns the complex conjugate.

Complex(1, 2).conjugate  #=> (1-2i)

[ GitHub ]

# File 'complex.c', line 1138


VALUE
rb_complex_conjugate(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}

#conj ⇒ `Complex` #conjugate ⇒ `Complex`

Alias for #conj.

#denominator ⇒ Integer

Returns the denominator (lcm of both denominator - real and imag).

See numerator.

[ GitHub ]

# File 'complex.c', line 1165


static VALUE
nucomp_denominator(VALUE self)
{
    get_dat1(self);
    return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
}

#eql?(other) ⇒ `Boolean`

This method is for internal use only.

[ GitHub ]

# File 'complex.c', line 1222


static VALUE
nucomp_eql_p(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
	get_dat2(self, other);

	return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
			  (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
			  f_eqeq_p(self, other));

    }
    return Qfalse;
}

#fdiv(numeric) ⇒ `Complex`

Performs division as each part is a float, never returns a float.

Complex(11, 22).fdiv(3)  #=> (3.6666666666666665+7.333333333333333i)

[ GitHub ]

# File 'complex.c', line 885


static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
    return f_divide(self, other, f_fdiv, id_fdiv);
}

#hash

This method is for internal use only.

[ GitHub ]

# File 'complex.c', line 1206


static VALUE
nucomp_hash(VALUE self)
{
    st_index_t v, h[2];
    VALUE n;

    get_dat1(self);
    n = rb_hash(dat->real);
    h[0] = NUM2LONG(n);
    n = rb_hash(dat->imag);
    h[1] = NUM2LONG(n);
    v = rb_memhash(h, sizeof(h));
    return ST2FIX(v);
}

#imag ⇒ Numeric #imaginary ⇒ Numeric
Also known as: #imaginary

Returns the imaginary part.

Complex(7).imaginary      #=> 0
Complex(9, -4).imaginary  #=> -4

[ GitHub ]

# File 'complex.c', line 658


VALUE
rb_complex_imag(VALUE self)
{
    get_dat1(self);
    return dat->imag;
}

#imag ⇒ Numeric #imaginary ⇒ Numeric

Alias for #imag.

#inspect ⇒ String

Returns the value as a string for inspection.

Complex(2).inspect                       #=> "(2+0i)"
Complex('-8/6').inspect                  #=> "((-4/3)+0i)"
Complex('1/2i').inspect                  #=> "(0+(1/2)*i)"
Complex(0, Float::INFINITY).inspect      #=> "(0+Infinity*i)"
Complex(Float::NAN, Float::NAN).inspect  #=> "(NaN+NaN*i)"

[ GitHub ]

# File 'complex.c', line 1303


static VALUE
nucomp_inspect(VALUE self)
{
    VALUE s;

    s = rb_usascii_str_new2("(");
    rb_str_concat(s, f_format(self, rb_inspect));
    rb_str_cat2(s, ")");

    return s;
}

#abs ⇒ Numeric #magnitude ⇒ Numeric

Alias for #abs.

#marshal_dump (private)

This method is for internal use only.

[ GitHub ]

# File 'complex.c', line 1379


static VALUE
nucomp_marshal_dump(VALUE self)
{
    VALUE a;
    get_dat1(self);

    a = rb_assoc_new(dat->real, dat->imag);
    rb_copy_generic_ivar(a, self);
    return a;
}

#numerator ⇒ Numeric

Returns the numerator.

    1   2       3+4i  <-  numerator
    - + -i  ->  ----
    2   3        6    <-  denominator

c = Complex('1/2+2/3i')  #=> ((1/2)+(2/3)*i)
n = c.numerator          #=> (3+4i)
d = c.denominator        #=> 6
n / d                    #=> ((1/2)+(2/3)*i)
Complex(Rational(n.real, d), Rational(n.imag, d))
                         #=> ((1/2)+(2/3)*i)

See denominator.

[ GitHub ]

# File 'complex.c', line 1190


static VALUE
nucomp_numerator(VALUE self)
{
    VALUE cd;

    get_dat1(self);

    cd = f_denominator(self);
    return f_complex_new2(CLASS_OF(self),
			  f_mul(f_numerator(dat->real),
				f_div(cd, f_denominator(dat->real))),
			  f_mul(f_numerator(dat->imag),
				f_div(cd, f_denominator(dat->imag))));
}

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Alias for #arg.

#polar ⇒ Array

Returns an array; [cmp.abs, cmp.arg].

Complex(1, 2).polar  #=> [2.23606797749979, 1.1071487177940904]

[ GitHub ]

# File 'complex.c', line 1123


static VALUE
nucomp_polar(VALUE self)
{
    return rb_assoc_new(f_abs(self), f_arg(self));
}

#quo

[ GitHub ]

#rationalize([eps]) ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).

Complex(1.0/3, 0).rationalize  #=> (1/3)
Complex(1, 0.0).rationalize    # RangeError
Complex(1, 2).rationalize      # RangeError

See to_r.

[ GitHub ]

# File 'complex.c', line 1534


static VALUE
nucomp_rationalize(int argc, VALUE *argv, VALUE self)
{
    get_dat1(self);

    rb_check_arity(argc, 0, 1);

    if (!k_exact_zero_p(dat->imag)) {
       rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
                self);
    }
    return rb_funcallv(dat->real, id_rationalize, argc, argv);
}

#rect ⇒ Array #rectangular ⇒ Array
Also known as: #rectangular

Returns an array; [cmp.real, cmp.imag].

Complex(1, 2).rectangular  #=> [1, 2]

[ GitHub ]

# File 'complex.c', line 1108


static VALUE
nucomp_rect(VALUE self)
{
    get_dat1(self);
    return rb_assoc_new(dat->real, dat->imag);
}

#rect ⇒ Array #rectangular ⇒ Array

Alias for #rect.

#to_c ⇒ `self`

Returns self.

Complex(2).to_c      #=> (2+0i)
Complex(-8, 6).to_c  #=> (-8+6i)

[ GitHub ]

# File 'complex.c', line 1557


static VALUE
nucomp_to_c(VALUE self)
{
    return self;
}

#to_f ⇒ Float

Returns the value as a float if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_f    #=> 1.0
Complex(1, 0.0).to_f  # RangeError
Complex(1, 2).to_f    # RangeError

[ GitHub ]

# File 'complex.c', line 1484


static VALUE
nucomp_to_f(VALUE self)
{
    get_dat1(self);

    if (!k_exact_zero_p(dat->imag)) {
	rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float",
		 self);
    }
    return f_to_f(dat->real);
}

#to_i ⇒ Integer

Returns the value as an integer if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_i    #=> 1
Complex(1, 0.0).to_i  # RangeError
Complex(1, 2).to_i    # RangeError

[ GitHub ]

# File 'complex.c', line 1461


static VALUE
nucomp_to_i(VALUE self)
{
    get_dat1(self);

    if (!k_exact_zero_p(dat->imag)) {
	rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer",
		 self);
    }
    return f_to_i(dat->real);
}

#to_r ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_r    #=> (1/1)
Complex(1, 0.0).to_r  # RangeError
Complex(1, 2).to_r    # RangeError

See rationalize.

[ GitHub ]

# File 'complex.c', line 1509


static VALUE
nucomp_to_r(VALUE self)
{
    get_dat1(self);

    if (!k_exact_zero_p(dat->imag)) {
	rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
		 self);
    }
    return f_to_r(dat->real);
}

#to_s ⇒ String

Returns the value as a string.

Complex(2).to_s                       #=> "2+0i"
Complex('-8/6').to_s                  #=> "-4/3+0i"
Complex('1/2i').to_s                  #=> "0+1/2i"
Complex(0, Float::INFINITY).to_s      #=> "0+Infinity*i"
Complex(Float::NAN, Float::NAN).to_s  #=> "NaN+NaN*i"

[ GitHub ]

# File 'complex.c', line 1285


static VALUE
nucomp_to_s(VALUE self)
{
    return f_format(self, rb_String);
}

Class: Complex

Overview

Constant Summary

Class Method Summary

Instance Attribute Summary

::Numeric - Inherited

Instance Method Summary

::Numeric - Inherited

::Comparable - Included

Class Method Details

.polar(abs[, arg]) ⇒ Complex

.rect(real[, imag]) ⇒ Complex .rectangular(real[, imag]) ⇒ Complex Also known as: .rectangular

.rect(real[, imag]) ⇒ Complex .rectangular(real[, imag]) ⇒ Complex

Instance Attribute Details

#finite? ⇒ Boolean (readonly)

#infinite? ⇒ Boolean (readonly)

#real ⇒ Numeric (readonly)

#real? ⇒ Boolean (readonly)

Instance Method Details

#*(numeric) ⇒ Complex

#**(numeric) ⇒ Complex

#+(numeric) ⇒ Complex

#-(numeric) ⇒ Complex

#- ⇒ Complex

#/(numeric) ⇒ Complex #quo(numeric) ⇒ Complex

#==(object) ⇒ Boolean

#abs ⇒ Numeric #magnitude ⇒ Numeric Also known as: #magnitude

#abs2 ⇒ Numeric

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float Also known as: #angle, #phase

#coerce(other)

#conj ⇒ Complex #conjugate ⇒ Complex Also known as: #conjugate

#conj ⇒ Complex #conjugate ⇒ Complex

#denominator ⇒ Integer

#eql?(other) ⇒ Boolean

#fdiv(numeric) ⇒ Complex

#hash

#imag ⇒ Numeric #imaginary ⇒ Numeric Also known as: #imaginary

#imag ⇒ Numeric #imaginary ⇒ Numeric

#inspect ⇒ String

#abs ⇒ Numeric #magnitude ⇒ Numeric

#marshal_dump (private)

#numerator ⇒ Numeric

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

#polar ⇒ Array

#quo

#rationalize([eps]) ⇒ Rational

#rect ⇒ Array #rectangular ⇒ Array Also known as: #rectangular

#rect ⇒ Array #rectangular ⇒ Array

#to_c ⇒ self

#to_f ⇒ Float

#to_i ⇒ Integer

#to_r ⇒ Rational

#to_s ⇒ String

`::Numeric` - Inherited

`::Numeric` - Inherited

`::Comparable` - Included

.polar(abs[, arg]) ⇒ `Complex`

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`
Also known as: .rectangular

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`

#finite? ⇒ `Boolean` (readonly)

#infinite? ⇒ `Boolean` (readonly)

#real? ⇒ `Boolean` (readonly)

#*(numeric) ⇒ `Complex`

#**(numeric) ⇒ `Complex`

#+(numeric) ⇒ `Complex`

#-(numeric) ⇒ `Complex`

#- ⇒ `Complex`

#/(numeric) ⇒ `Complex` #quo(numeric) ⇒ `Complex`

#==(object) ⇒ `Boolean`

#abs ⇒ Numeric #magnitude ⇒ Numeric
Also known as: #magnitude

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float
Also known as: #angle, #phase

#conj ⇒ `Complex` #conjugate ⇒ `Complex`
Also known as: #conjugate

#conj ⇒ `Complex` #conjugate ⇒ `Complex`

#eql?(other) ⇒ `Boolean`

#fdiv(numeric) ⇒ `Complex`

#imag ⇒ Numeric #imaginary ⇒ Numeric
Also known as: #imaginary

#rect ⇒ Array #rectangular ⇒ Array
Also known as: #rectangular

#to_c ⇒ `self`