Struct nalgebra::Complex[][src]

#[repr(C)]
pub struct Complex<T> { pub re: T, pub im: T, }
Expand description

A complex number in Cartesian form.

Representation and Foreign Function Interface Compatibility

Complex<T> is memory layout compatible with an array [T; 2].

Note that Complex<F> where F is a floating point type is only memory layout compatible with C’s complex types, not necessarily calling convention compatible. This means that for FFI you can only pass Complex<F> behind a pointer, not as a value.

Examples

Example of extern function declaration.

use num_complex::Complex;
use std::os::raw::c_int;

extern "C" {
    fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,
              x: *const Complex<f64>, incx: *const c_int,
              y: *mut Complex<f64>, incy: *const c_int);
}

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Implementations

Create a new Complex

Returns imaginary unit

Returns the square of the norm (since T doesn’t necessarily have a sqrt function), i.e. re^2 + im^2.

Multiplies self by the scalar t.

Divides self by the scalar t.

Raises self to an unsigned integer power.

Returns the complex conjugate. i.e. re - i im

Returns 1/self

Raises self to a signed integer power.

Returns the L1 norm |re| + |im| – the Manhattan distance from the origin.

Checks if the given complex number is NaN

Checks if the given complex number is infinite

Checks if the given complex number is finite

Checks if the given complex number is normal

Trait Implementations

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

Performs the += operation. Read more

Performs the += operation. Read more

Performs the += operation. Read more

Performs the += operation. Read more

Convert a value to another, using the as operator.

Formats the value using the given formatter.

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Formats the value using the given formatter. Read more

Returns the “default value” for a type. Read more

Deserialize this value from the given Serde deserializer. Read more

Formats the value using the given formatter. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

Performs the conversion.

Performs the conversion.

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

The associated error which can be returned from parsing.

Feeds this value into the given Hasher. Read more

Feeds a slice of this type into the given Hasher. Read more

The result after applying the operator.

Returns the multiplicative inverse of self. Read more

The result after applying the operator.

Returns the multiplicative inverse of self. Read more

Formats the value using the given formatter.

Formats the value using the given formatter.

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the * operator.

Performs the * operation. Read more

The resulting type after applying the fused multiply-add.

Performs the fused multiply-add operation.

The resulting type after applying the fused multiply-add.

Performs the fused multiply-add operation.

Performs the fused multiply-add operation.

Performs the fused multiply-add operation.

Performs the *= operation. Read more

Performs the *= operation. Read more

Performs the *= operation. Read more

Performs the *= operation. Read more

The resulting type after applying the - operator.

Performs the unary - operation. Read more

The resulting type after applying the - operator.

Performs the unary - operation. Read more

The type of the norm.

Computes the norm.

Computes the squared norm.

Multiply self by n.

Divides self by n.

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned. Read more

Formats the value using the given formatter.

Returns the multiplicative identity element of Self, 1. Read more

Returns true if self is equal to the multiplicative identity. Read more

Sets self to the multiplicative identity element of Self, 1.

This method tests for self and other values to be equal, and is used by ==. Read more

This method tests for !=.

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

The result after applying the operator.

Returns self to the power rhs. Read more

Method which takes an iterator and generates Self from the elements by multiplying the items. Read more

Method which takes an iterator and generates Self from the elements by multiplying the items. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

The resulting type after applying the % operator.

Performs the % operation. Read more

Performs the %= operation. Read more

Performs the %= operation. Read more

Performs the %= operation. Read more

Performs the %= operation. Read more

Serialize this value into the given Serde serializer. Read more

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Computes e^(self), where e is the base of the natural logarithm.

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

Raises self to a floating point power.

Returns the logarithm of self with respect to an arbitrary base.

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

Type of the coefficients of a complex number.

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The argument of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

The type of the elements of each lane of this SIMD value.

Type of the result of comparing two SIMD values like self.

The number of lanes of this SIMD value.

Initializes an SIMD value with each lanes set to val.

Extracts the i-th lane of self. Read more

Extracts the i-th lane of self without bound-checking.

Replaces the i-th lane of self by val. Read more

Replaces the i-th lane of self by val without bound-checking.

Merges self and other depending on the lanes of cond. Read more

Applies a function to each lane of self. Read more

Applies a function to each lane of self paired with the corresponding lane of b. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

The resulting type after applying the - operator.

Performs the - operation. Read more

Performs the -= operation. Read more

Performs the -= operation. Read more

Performs the -= operation. Read more

Performs the -= operation. Read more

The inclusion map: converts self to the equivalent element of its superset.

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

Checks if element is actually part of the subset Self (and can be converted to it).

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

Method which takes an iterator and generates Self from the elements by “summing up” the items. Read more

Method which takes an iterator and generates Self from the elements by “summing up” the items. Read more

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned. Read more

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned. Read more

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned. Read more

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned. Read more

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned. Read more

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned. Read more

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned. Read more

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned. Read more

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned. Read more

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned. Read more

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned. Read more

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned. Read more

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32. Read more

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64. Read more

Formats the value using the given formatter.

Formats the value using the given formatter.

Returns the additive identity element of Self, 0. Read more

Returns true if self is equal to the additive identity.

Sets self to the additive identity element of Self, 0.

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more

Immutably borrows from an owned value. Read more

Mutably borrows from an owned value. Read more

Performs the conversion.

Performs the conversion.

Should always be Self

Type of the coefficients of a complex number.

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The argument of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

The absolute value of this complex number: self / self.signum(). Read more

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

Cardinal sine

Cardinal cos

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

Checks if self is actually part of its subset T (and can be converted to it).

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

The inclusion map: converts self to the equivalent element of its superset.

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

Converts the given value to a String. Read more

The type returned in the event of a conversion error.

Performs the conversion.

The type returned in the event of a conversion error.

Performs the conversion.