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complex.c

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Complex

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

Complex object can be created as literal, andalso 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)

Constants

I: The imaginary unit.

Public Class Methods

polar(abs[, arg]) → complexclick to toggle source

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 VALUEnucomp_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);        return nucomp_s_new_internal(klass, abs, ZERO);      default:        nucomp_real_check(abs);        nucomp_real_check(arg);        break;    }    if (RB_TYPE_P(abs, T_COMPLEX)) {        get_dat1(abs);        abs = dat->real;    }    if (RB_TYPE_P(arg, T_COMPLEX)) {        get_dat1(arg);        arg = dat->real;    }    return f_complex_polar(klass, abs, arg);}

rect(real[, imag]) → complexclick to toggle source

rectangular(real[, imag]) → complex

Returns a complex object which denotes the given rectangular form.

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

                static VALUEnucomp_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]) → complexclick to toggle source

Returns a complex object which denotes the given rectangular form.

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

                static VALUEnucomp_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 → complexclick to toggle source

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)

                VALUErb_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, '*');}

cmp ** numeric → complexclick to toggle source

Performs exponentiation.

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

                VALUErb_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);}

cmp + numeric → complexclick to toggle source

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)

                VALUErb_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 → complexclick to toggle source

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)

                VALUErb_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, '-');}

-cmp → complexclick to toggle source

Returns negation of the value.

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

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

cmp / numeric → complexclick to toggle source

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)

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

cmp<=> object → 0, 1, -1, or nilclick to toggle source

Ifcmp's imaginary part is zero, andobjectis also a real number (or aComplex number wherethe imaginary part is zero), compare the real part ofcmp toobject. Otherwise, return nil.

Complex(2,3)<=>Complex(2,3)#=> nilComplex(2,3)<=>1#=> nilComplex(2)<=>1#=> 1Complex(2)<=>2#=> 0Complex(2)<=>3#=> -1

                static VALUEnucomp_cmp(VALUE self, VALUE other){    if (nucomp_real_p(self) && k_numeric_p(other)) {        if (RB_TYPE_P(other, T_COMPLEX) && nucomp_real_p(other)) {            get_dat2(self, other);            return rb_funcall(adat->real, idCmp, 1, bdat->real);        }        else if (f_real_p(other)) {            get_dat1(self);            return rb_funcall(dat->real, idCmp, 1, other);        }    }    return Qnil;}

cmp == object → true or falseclick to toggle source

Returns true if cmp equals object numerically.

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

                static VALUEnucomp_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 → realclick to toggle source

Returns the absolute part of its polar form.

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

                VALUErb_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 → realclick to toggle source

Returns square of the absolute value.

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

                static VALUEnucomp_abs2(VALUE self){    get_dat1(self);    return f_add(f_mul(dat->real, dat->real),                 f_mul(dat->imag, dat->imag));}

angle → floatclick to toggle source

Returns the angle part of its polar form.

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

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

arg → floatclick to toggle source

Returns the angle part of its polar form.

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

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

conj → complexclick to toggle source

conjugate → complex

Returns the complex conjugate.

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

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

conjugate → complexclick to toggle source

Returns the complex conjugate.

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

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

denominator → integerclick to toggle source

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

See numerator.

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

fdiv(numeric) → complexclick to toggle source

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

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

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

finite? → true or falseclick to toggle source

Returnstrue ifcmp's real and imaginaryparts are both finite numbers, otherwise returnsfalse.

                static VALUErb_complex_finite_p(VALUE self){    get_dat1(self);    if (f_finite_p(dat->real) && f_finite_p(dat->imag)) {        return Qtrue;    }    return Qfalse;}

imag → realclick to toggle source

imaginary → real

Returns the imaginary part.

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

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

imaginary → realclick to toggle source

Returns the imaginary part.

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

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

infinite? → nil or 1click to toggle source

Returns1 ifcmp's real or imaginary part isan infinite number, otherwise returnsnil.

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

                static VALUErb_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;}

inspect → stringclick to toggle source

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 VALUEnucomp_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 → realclick to toggle source

Returns the absolute part of its polar form.

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

                VALUErb_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);}

numerator → numericclick to toggle source

Returns the numerator.

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

See denominator.

                static VALUEnucomp_numerator(VALUE self){    VALUE cd;    get_dat1(self);    cd = nucomp_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 → floatclick to toggle source

Returns the angle part of its polar form.

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

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

polar → arrayclick to toggle source

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

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

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

cmp / numeric → complexclick to toggle source

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)

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

rationalize([eps]) → rationalclick to toggle source

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

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

See to_r.

                static VALUEnucomp_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);}

real → realclick to toggle source

Returns the real part.

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

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

Complex(1).real? → falseclick to toggle source

Complex(1, 2).real? → false

Returns false, even if the complex number has no imaginary part.

                static VALUEnucomp_false(VALUE self){    return Qfalse;}

rect → arrayclick to toggle source

rectangular → array

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

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

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

rect → arrayclick to toggle source

rectangular → array

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

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

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

to_c → selfclick to toggle source

Returns self.

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

                static VALUEnucomp_to_c(VALUE self){    return self;}

to_f → floatclick to toggle source

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

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

                static VALUEnucomp_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 → integerclick to toggle source

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

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

                static VALUEnucomp_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 → rationalclick to toggle source

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

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

See rationalize.

                static VALUEnucomp_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 → stringclick to toggle source

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 VALUEnucomp_to_s(VALUE self){    return f_format(self, rb_String);}

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