class Complex
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, Complex::rect, Complex::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)
Constants
- I
The imaginary unit.
Public Class Methods
json_create(object)
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polar(abs[, arg]) → complex
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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)
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
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rectangular(real[, imag]) → complex
Returns a complex object which denotes the given rectangular form.
Complex.rectangular(1, 2) #=> (1+2i)
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);
}
rectangular(real[, imag]) → complex
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Returns a complex object which denotes the given rectangular form.
Complex.rectangular(1, 2) #=> (1+2i)
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);
}
Public Instance Methods
cmp * numeric → complex
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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)
VALUE
rb_complex_mul(VALUE self, VALUE other)
{
if (RB_TYPE_P(other, T_COMPLEX)) {
VALUE real, imag;
VALUE areal, aimag, breal, bimag;
int arzero, aizero, brzero, bizero;
get_dat2(self, other);
arzero = f_zero_p(areal = adat->real);
aizero = f_zero_p(aimag = adat->imag);
brzero = f_zero_p(breal = bdat->real);
bizero = f_zero_p(bimag = bdat->imag);
real = f_sub(safe_mul(areal, breal, arzero, brzero),
safe_mul(aimag, bimag, aizero, bizero));
imag = f_add(safe_mul(areal, bimag, arzero, bizero),
safe_mul(aimag, breal, aizero, brzero));
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, '*');
}
cmp ** numeric → complex
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Performs exponentiation.
Complex('i') ** 2 #=> (-1+0i) Complex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i)
static VALUE
nucomp_expt(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)) {
if (f_gt_p(other, ZERO)) {
VALUE x, z;
long n;
x = self;
z = x;
n = FIX2LONG(other) - 1;
while (n) {
long q, r;
while (1) {
get_dat1(x);
q = n / 2;
r = n % 2;
if (r)
break;
x = nucomp_s_new_internal(CLASS_OF(self),
f_sub(f_mul(dat->real, dat->real),
f_mul(dat->imag, dat->imag)),
f_mul(f_mul(TWO, dat->real), dat->imag));
n = q;
}
z = f_mul(z, x);
n--;
}
return z;
}
return f_expt(f_reciprocal(self), rb_int_uminus(other));
}
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);
}
cmp + numeric → complex
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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)
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, '+');
}
cmp - numeric → complex
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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)
static VALUE
nucomp_sub(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, '-');
}
-cmp → complex
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Returns negation of the value.
-Complex(1, 2) #=> (-1-2i)
static VALUE
nucomp_negate(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self),
f_negate(dat->real), f_negate(dat->imag));
}
cmp / numeric → complex
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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)
static VALUE
nucomp_div(VALUE self, VALUE other)
{
return f_divide(self, other, f_quo, id_quo);
}
cmp == object → true or false
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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
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 → real
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Returns the absolute part of its polar form.
Complex(-1).abs #=> 1 Complex(3.0, -4.0).abs #=> 5.0
static VALUE
nucomp_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 → real
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Returns square of the absolute value.
Complex(-1).abs2 #=> 1 Complex(3.0, -4.0).abs2 #=> 25.0
static VALUE
nucomp_abs2(VALUE self)
{
get_dat1(self);
return f_add(f_mul(dat->real, dat->real),
f_mul(dat->imag, dat->imag));
}
angle → float
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Returns the angle part of its polar form.
Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
static VALUE
nucomp_arg(VALUE self)
{
get_dat1(self);
return rb_math_atan2(dat->imag, dat->real);
}
arg → float
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Returns the angle part of its polar form.
Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
static VALUE
nucomp_arg(VALUE self)
{
get_dat1(self);
return rb_math_atan2(dat->imag, dat->real);
}
as_json(*)
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Returns a hash, that will be turned into a JSON object and represent this object.
# File ext/json/lib/json/add/complex.rb, line 17 def as_json(*) { JSON.create_id => self.class.name, 'r' => real, 'i' => imag, } end
conj → complex
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conjugate → complex
Returns the complex conjugate.
Complex(1, 2).conjugate #=> (1-2i)
static VALUE
nucomp_conj(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}
conjugate → complex
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Returns the complex conjugate.
Complex(1, 2).conjugate #=> (1-2i)
static VALUE
nucomp_conj(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}
denominator → integer
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Returns the denominator (lcm of both denominator - real and imag).
See numerator.
static VALUE
nucomp_denominator(VALUE self)
{
get_dat1(self);
return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
}
fdiv(numeric) → complex
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Performs division as each part is a float, never returns a float.
Complex(11, 22).fdiv(3) #=> (3.6666666666666665+7.333333333333333i)
static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
return f_divide(self, other, f_fdiv, id_fdiv);
}
finite? → true or false
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Returns true if cmp's magnitude is finite number, oterwise returns false.
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;
}
imag → real
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imaginary → real
Returns the imaginary part.
Complex(7).imaginary #=> 0 Complex(9, -4).imaginary #=> -4
static VALUE
nucomp_imag(VALUE self)
{
get_dat1(self);
return dat->imag;
}
imaginary → real
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Returns the imaginary part.
Complex(7).imaginary #=> 0 Complex(9, -4).imaginary #=> -4
static VALUE
nucomp_imag(VALUE self)
{
get_dat1(self);
return dat->imag;
}
infinite? → nil or 1 or -1
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Returns values corresponding to the value of cmp's magnitude:
finite-
nil - +
Infinity -
+
1
For example: (1+1i).infinite? #=> nil (Float::INFINITY + 1i).infinite? #=> 1
static VALUE
rb_complex_infinite_p(VALUE self)
{
VALUE magnitude = nucomp_abs(self);
if (FINITE_TYPE_P(magnitude)) {
return Qnil;
}
if (RB_FLOAT_TYPE_P(magnitude)) {
const double f = RFLOAT_VALUE(magnitude);
if (isinf(f)) {
return INT2FIX(f < 0 ? -1 : 1);
}
return Qnil;
}
else {
return rb_funcall(magnitude, id_infinite_p, 0);
}
}
inspect → string
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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)"
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;
}
magnitude → real
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Returns the absolute part of its polar form.
Complex(-1).abs #=> 1 Complex(3.0, -4.0).abs #=> 5.0
static VALUE
nucomp_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);
}
numerator → numeric
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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.
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))));
}
phase → float
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Returns the angle part of its polar form.
Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966
static VALUE
nucomp_arg(VALUE self)
{
get_dat1(self);
return rb_math_atan2(dat->imag, dat->real);
}
polar → array
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Returns an array; [cmp.abs, cmp.arg].
Complex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904]
static VALUE
nucomp_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
cmp / numeric → complex
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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)
static VALUE
nucomp_div(VALUE self, VALUE other)
{
return f_divide(self, other, f_quo, id_quo);
}
rationalize([eps]) → rational
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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.
static VALUE
nucomp_rationalize(int argc, VALUE *argv, VALUE self)
{
get_dat1(self);
rb_scan_args(argc, argv, "01", NULL);
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);
}
real → real
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Returns the real part.
Complex(7).real #=> 7 Complex(9, -4).real #=> 9
static VALUE
nucomp_real(VALUE self)
{
get_dat1(self);
return dat->real;
}
real? → false
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Returns false.
static VALUE
nucomp_false(VALUE self)
{
return Qfalse;
}
rect → array
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rectangular → array
Returns an array; [cmp.real, cmp.imag].
Complex(1, 2).rectangular #=> [1, 2]
static VALUE
nucomp_rect(VALUE self)
{
get_dat1(self);
return rb_assoc_new(dat->real, dat->imag);
}
rect → array
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rectangular → array
Returns an array; [cmp.real, cmp.imag].
Complex(1, 2).rectangular #=> [1, 2]
static VALUE
nucomp_rect(VALUE self)
{
get_dat1(self);
return rb_assoc_new(dat->real, dat->imag);
}
to_c → self
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Returns self.
Complex(2).to_c #=> (2+0i) Complex(-8, 6).to_c #=> (-8+6i)
static VALUE
nucomp_to_c(VALUE self)
{
return self;
}
to_f → float
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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
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
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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
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_json(*)
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to_r → rational
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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.
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
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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"
static VALUE
nucomp_to_s(VALUE self)
{
return f_format(self, rb_String);
}
conj → complex
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conjugate → complex
Returns the complex conjugate.
Complex(1, 2).conjugate #=> (1-2i)
static VALUE
nucomp_conj(VALUE self)
{
get_dat1(self);
return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}