Complex
Complex类
Parent:Numeric
一个复数可以用虚数单位表示为一个配对实数; a+bi。a是实部，b是虚部，i是虚部。在数学上等于实现一个复数a + 0i。
复杂对象可以创建为文字，也可以使用Kernel＃Complex，:: rect，:: polar或#to_c方法。
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)
您也可以使用浮点数字或字符串创建复杂的对象。
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)
一个复杂的对象是一个确切的或不精确的数字。
Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i)
Complex(1, 1) / 2.0 #=> (0.5+0.5i)
常量
I
虚构的单位。
公共类方法
json_create(object)
通过将实数值r，虚数值i转换为复杂对象来反序列化JSON字符串。
# File ext/json/lib/json/add/complex.rb, line 11
def self.json_create(object)
Complex(object['r'], object['i'])
end
polar(abs, arg) → complex 显示源文件
返回表示给定极坐标形式的复杂对象。
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 显示源文件
rectangular(real, imag) → complex
返回表示给定矩形形式的复杂对象。
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 显示源文件
返回表示给定矩形形式的复杂对象。
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
}
公共实例方法
cmp * numeric → complex 显示源文件
执行乘法。
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 显示源文件
执行取幂。
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 显示源文件
执行添加。
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 显示源文件
执行减法。
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 显示源文件
返回值的否定。
-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 显示源文件
quo(numeric) → complex
执行划分。
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 显示源文件
如果cmp等于数字对象，则返回true。
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 显示源文件
返回其极坐标的绝对部分。
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 显示源文件
返回绝对值的平方。
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 显示源文件
返回其极坐标的角度部分。
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 显示源文件
返回其极坐标的角度部分。
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(*) 显示源文件
返回一个散列，它将变成一个JSON对象并表示这个对象。
# 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 显示源文件
conjugate → complex
返回复共轭。
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 显示源文件
返回复共轭。
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 显示源文件
返回分母（两个分母 - 真实和成像的lcm）。
见分子。
static VALUE
nucomp_denominator(VALUE self)
{
get_dat1(self
return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag)
}
fdiv(numeric) → complex 显示源文件
由于每个部分都是一个浮点数，所以不会返回浮点数。
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 显示源文件
返回true如果cmp的幅度是有限的数量，oterwise回报false。
static VALUE
rb_complex_finite_p(VALUE self)
{
VALUE magnitude = nucomp_abs(self
if (FINITE_TYPE_P(magnitude)) {
return Qtrue;
}
else if (RB_FLOAT_TYPE_P(magnitude)) {
const double f = RFLOAT_VALUE(magnitude
return isinf(f) ? Qfalse : Qtrue;
}
else {
return rb_funcall(magnitude, id_finite_p, 0
}
}
imag → real 显示源文件
imaginary → real
返回虚部。
Complex(7).imaginary #=> 0
Complex(9, -4).imaginary #=> -4
static VALUE
nucomp_imag(VALUE self)
{
get_dat1(self
return dat->imag;
}
imaginary → real Show source
返回虚部。
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 Show source
返回对应于cmp幅度值的值：
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 Show source
将该值作为字符串返回以进行检查。
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 Show source
返回其极坐标的绝对部分。
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 Show source
返回分子。
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)
请参阅分母。
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 Show source
返回其极坐标的角度部分。
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 Show source
返回一个数组; 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 Show source
quo(numeric) → complex
执行划分。
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 Show source
如果可能，将值作为有理数返回（虚数部分应该完全为零）。
Complex(1.0/3, 0).rationalize #=> (1/3)
Complex(1, 0.0).rationalize # RangeError
Complex(1, 2).rationalize # RangeError
请参阅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 Show source
返回实部。
Complex(7).real #=> 7
Complex(9, -4).real #=> 9
static VALUE
nucomp_real(VALUE self)
{
get_dat1(self
return dat->real;
}
real? → false Show source
返回false。
static VALUE
nucomp_false(VALUE self)
{
return Qfalse;
}
rect → array Show source
rectangular → array
返回一个数组; 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 Show source
rectangular → array
返回一个数组; 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 Show source
返回自身。
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 Show source
如果可能，以浮点形式返回值（虚部应该完全为零）。
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 Show source
如果可能，以整数形式返回值（虚部应完全为零）。
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(*) Show source
以JSON字符串形式存储类名称（Complex）以及实际值r和虚数值i
# File ext/json/lib/json/add/complex.rb, line 26
def to_json(*)
as_json.to_json
end
to_r → rational Show source
如果可能，将值作为有理数返回（虚数部分应该完全为零）。
Complex(1, 0).to_r #=> (1/1)
Complex(1, 0.0).to_r # RangeError
Complex(1, 2).to_r # RangeError
参阅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 Show source
以字符串形式返回值。
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 Show source
conjugate → complex
返回复共轭。
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)
}
