numojo.core.complex.complex_simd

ComplexSIMD (numojo.core.complex.complex_simd)

Implement the ComplexSIMD type and its operations.

This module provides a ComplexSIMD type that represents complex numbers using SIMD operations for efficient computation. It supports basic arithmetic operations like addition, subtraction, multiplication, and division, as well as other complex number operations like conjugation and absolute value.

Structs

ComplexSIMD

struct ComplexSIMD[cdtype: ComplexDType = ComplexDType.float64, width: Int = 1]

Memory convention: register_passable_trivial
Implements: AnyType, Copyable, ImplicitlyCopyable, ImplicitlyDestructible, Movable, RegisterPassable, Stringable, TrivialRegisterPassable, Writable

A SIMD-enabled complex number container (SoA layout).

Fields: re: SIMD vector of real parts. im: SIMD vector of imaginary parts.

The parameter cdtype determines the component precision (e.g. cf32, cf64). The parameter width is the SIMD lane count; when width == 1 this acts like a scalar complex number.

Examples:

from numojo.prelude import *
var a = ComplexSIMD[cf32](1.0, 2.0)
var b = ComplexSIMD[cf32](3.0, 4.0)
print(a + b)  # (4.0 + 6.0 j)

# SIMD width=2:
var a2 = ComplexSIMD[cf32, 2](
    SIMD[cf32.dtype, 2](1.0, 1.5),
    SIMD[cf32.dtype, 2](2.0, -0.5)
)
print(a2) # ( [1.0 2.0] + [1.5 -0.5]j )

Convenience factories: ComplexSIMD[cf64].zero() ComplexSIMD[cf64].one() ComplexSIMD[cf64].i() ComplexSIMD[cf64].from_polar(2.0, 0.5)

Parameters:

• cdtype (ComplexDType)
• width (Int)

Fields

• re (SIMD[ComplexSIMD[cdtype, width].dtype, width])
• im (SIMD[ComplexSIMD[cdtype, width].dtype, width])

Aliases

dtype

comptime dtype

Value: cdtype.dtype

Component dtype (underlying real/imag dtype).

__del__is_trivial

comptime __del__is_trivial

Value: True

__move_ctor_is_trivial

comptime __move_ctor_is_trivial

Value: True

__copy_ctor_is_trivial

comptime __copy_ctor_is_trivial

Value: True

Methods

__init__

Overload 1

__init__(other: Self) -> Self

static

Copy constructor for ComplexSIMD.

Initializes a new ComplexSIMD instance by copying the values from another instance.

Args:

• other (Self)

Returns:

• Self

Overload 2

__init__(re: SIMD[ComplexSIMD[cdtype, width].dtype, width], im: SIMD[ComplexSIMD[cdtype, width].dtype, width]) -> Self

static

Constructs a ComplexSIMD from SIMD vectors of real and imaginary parts.

Args:

• re (SIMD): SIMD vector containing the real components.
• im (SIMD): SIMD vector containing the imaginary components.

Returns:

• Self

Overload 3

__init__(val: SIMD[ComplexSIMD[cdtype, width].dtype, width]) -> Self

static

Constructs a ComplexSIMD where both real and imaginary parts are set to the same SIMD value.

Args:

• val (SIMD): SIMD vector to broadcast to both real and imaginary components.

Returns:

• Self

Overload 4

__init__(re: Int, im: Int) -> Self

static

Constructs a ComplexSIMD from scalar integer real and imaginary values, broadcasted to SIMD lanes.

Args:

• re (Int): Integer value for the real component.
• im (Int): Integer value for the imaginary component.

Returns:

• Self

Overload 5

__init__(val: Int) -> Self

static

Constructs a ComplexSIMD where both real and imaginary parts are set to the same integer value broadcasted to SIMD lanes.

Args:

• val (Int): Integer value to broadcast to both real and imaginary components.

Returns:

• Self

__getitem__

__getitem__(self, idx: Int) -> ComplexSIMD[cdtype]

Returns the complex number at the specified lane index.

Example:

from numojo.prelude import *
var c_simd = ComplexSIMD[cf32, 2](SIMD[f32, 2](1, 2), SIMD[f32, 2](3, 4))
var c0 = c_simd[0]  # 1 + 3j
var c1 = c_simd[1]  # 2 + 4j

Args:

• self (Self)
• idx (Int): SIMD lane index (0 to width-1).

Returns:

• ComplexSIMD

Raises

Error if lane index is out of range for the SIMD width.

__setitem__

__setitem__(mut self, idx: Int, value: ComplexSIMD[cdtype])

Sets the complex scalar at the specified lane index.

Example:

from numojo.prelude import *
var c_simd = nm.ComplexSIMD[cf32, 2](SIMD[f32, 2](1, 2), SIMD[f32, 2](3, 4)) # [(1 + 3j), (2 + 4j)]
c_simd[0] = nm.CScalar[cf32](5, 6)
print(c_simd) # [(1 + 3j), (2 + 4j)] becomes [(5 + 6j), (2 + 4j)]

Args:

• self (Self) [mut]
• idx (Int): SIMD lane index (0 to width-1).
• value (ComplexSIMD): ComplexScalar whose values will be assigned.

Raises

Error if lane index is out of range for the SIMD width.

__neg__

__neg__(self) -> Self

Returns the negation of this ComplexSIMD.

Args:

• self (Self)

Returns:

• Self

__pos__

__pos__(self) -> Self

Returns the positive value of this ComplexSIMD (identity operation).

Args:

• self (Self)

Returns:

• Self

__invert__

__invert__(self) -> Self where (cdtype == ComplexDType.bool) if (cdtype == ComplexDType.bool) else cdtype.is_integral()

Element-wise logical NOT operation on this ComplexSIMD instance.

Args:

• self (Self)

Returns:

• Self

__eq__

Overload 1

__eq__(self, other: Self) -> Bool

Checks if two ComplexSIMD instances are exactly equal.

Args:

• self (Self)
• other (Self)

Returns:

• Bool

Overload 2

__eq__(self, other: ImaginaryUnit) -> Bool

Checks if this ComplexSIMD instance is equal to the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z1 = ComplexSIMD[cf64, 1](0.0, 1.0)  # 0 + 1j
var z2 = ComplexSIMD[cf64, 1](1.0, 1.0)  # 1 + 1j
print(z1 == `1j`)  # True
print(z2 == `1j`)  # False

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to compare with this ComplexSIMD instance.

Returns:

• Bool

__ne__

Overload 1

__ne__(self, other: Self) -> Bool

Checks if two ComplexSIMD instances are not equal.

Args:

• self (Self)
• other (Self)

Returns:

• Bool

Overload 2

__ne__(self, other: ImaginaryUnit) -> Bool

Checks if this ComplexSIMD instance is not equal to the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z1 = ComplexSIMD[cf64, 1](0.0, 1.0)  # 0 + 1j
var z2 = ComplexSIMD[cf64, 1](1.0, 1.0)  # 1 + 1j
print(z1 != `1j`)  # False
print(z2 != `1j`)  # True

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to compare with this ComplexSIMD instance.

Returns:

• Bool

__add__

Overload 1

__add__(self, other: Self) -> Self

Returns the element-wise sum of two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

Overload 2

__add__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Returns the sum of this ComplexSIMD instance and a scalar added to the real part.

Args:

• self (Self)
• other (Scalar): Scalar value to add to the real component.

Returns:

• Self

Overload 3

__add__(self, other: SIMD[other.dtype, width]) -> Self

Returns the sum of this ComplexSIMD instance and a SIMD vector added to the real part.

Args:

• self (Self)
• other (SIMD): SIMD vector to add to the real component.

Returns:

• Self

Overload 4

__add__(self, other: ImaginaryUnit) -> Self

Returns the sum of this ComplexSIMD instance and the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = z + `1j`  # 3 + 3j
print(result)  # (3 + 3j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to add to this complex number.

Returns:

• Self

__sub__

Overload 1

__sub__(self, other: Self) -> Self

Returns the element-wise difference of two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

Overload 2

__sub__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Returns the difference of this ComplexSIMD instance and a scalar subtracted from the real part.

Args:

• self (Self)
• other (Scalar): Scalar value to subtract from the real component.

Returns:

• Self

Overload 3

__sub__(self, other: SIMD[other.dtype, width]) -> Self

Returns the difference of this ComplexSIMD instance and a SIMD vector subtracted from the real part.

Args:

• self (Self)
• other (SIMD): SIMD vector to subtract from the real component.

Returns:

• Self

Overload 4

__sub__(self, other: ImaginaryUnit) -> Self

Subtracts the imaginary unit 1j from this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = z - `1j`  # 3 + 1j
print(result)  # (3 + 1j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to subtract from this complex number.

Returns:

• Self

__mul__

Overload 1

__mul__(self, other: Self) -> Self

Returns the element-wise product of two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

Overload 2

__mul__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Returns the product of this ComplexSIMD instance and a scalar.

Args:

• self (Self)
• other (Scalar): Scalar value to multiply with both real and imaginary parts.

Returns:

• Self

Overload 3

__mul__(self, other: SIMD[other.dtype, width]) -> Self

Returns the product of this ComplexSIMD instance and a SIMD vector.

Args:

• self (Self)
• other (SIMD): SIMD vector to multiply with both real and imaginary parts.

Returns:

• Self

Overload 4

__mul__(self, other: ImaginaryUnit) -> Self

Returns the product of this ComplexSIMD instance and the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = z * `1j`  # -2 + 3j
print(result)  # (-2 + 3j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to multiply with this complex number.

Returns:

• Self

__truediv__

Overload 1

__truediv__(self, other: Self) -> Self

Performs element-wise complex division of two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance to divide by.

Returns:

• Self

Overload 2

__truediv__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Performs element-wise division of this ComplexSIMD instance by a scalar.

Args:

• self (Self)
• other (Scalar): Scalar value to divide both real and imaginary parts by.

Returns:

• Self

Overload 3

__truediv__(self, other: SIMD[other.dtype, width]) -> Self

Performs element-wise division of this ComplexSIMD instance by a SIMD vector.

Args:

• self (Self)
• other (SIMD): SIMD vector to divide both real and imaginary parts by.

Returns:

• Self

Overload 4

__truediv__(self, other: ImaginaryUnit) -> Self

Performs division of this ComplexSIMD instance by the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = z / `1j`  # 2 - 3j
print(result)  # (2 - 3j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to divide this complex number by.

Returns:

• Self

__pow__

__pow__(self, n: Int) -> Self

Raises this ComplexSIMD to an integer.

Args:

• self (Self)
• n (Int): Integer exponent.

Returns:

• Self

__and__

__and__(self, other: Self) -> Self where (cdtype == ComplexDType.bool) if (cdtype == ComplexDType.bool) else cdtype.is_integral()

Element-wise logical AND operation between two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

__or__

__or__(self, other: Self) -> Self where (cdtype == ComplexDType.bool) if (cdtype == ComplexDType.bool) else cdtype.is_integral()

Element-wise logical OR operation between two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

__xor__

__xor__(self, other: Self) -> Self where (cdtype == ComplexDType.bool) if (cdtype == ComplexDType.bool) else cdtype.is_integral()

Element-wise logical XOR operation between two ComplexSIMD instances.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

__radd__

Overload 1

__radd__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Returns the sum of a scalar and this ComplexSIMD instance, adding to the real part.

Args:

• self (Self)
• other (Scalar): Scalar value to add to the real component.

Returns:

• Self

Overload 2

__radd__(self, other: SIMD[other.dtype, width]) -> Self

Returns the sum of a SIMD vector and this ComplexSIMD instance, adding to the real part.

Args:

• self (Self)
• other (SIMD): SIMD vector to add to the real component.

Returns:

• Self

Overload 3

__radd__(self, other: ImaginaryUnit) -> Self

Returns the sum of the imaginary unit 1j and this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = `1j` + z  # 3 + 3j
print(result)  # (3 + 3j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to add to this complex number.

Returns:

• Self

__rsub__

Overload 1

__rsub__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Returns the difference of a scalar and this ComplexSIMD instance, subtracting from the real part.

Args:

• self (Self)
• other (Scalar): Scalar value to subtract from the real component.

Returns:

• Self

Overload 2

__rsub__(self, other: SIMD[other.dtype, width]) -> Self

Returns the difference of a SIMD vector and this ComplexSIMD instance, subtracting from the real part.

Args:

• self (Self)
• other (SIMD): SIMD vector to subtract from the real component.

Returns:

• Self

Overload 3

__rsub__(self, other: ImaginaryUnit) -> Self

Returns the difference of the imaginary unit 1j and this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = `1j` - z  # -3 + (-1)j = -3 - 1j
print(result)  # (-3 - 1j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) from which this complex number is subtracted.

Returns:

• Self

__rmul__

Overload 1

__rmul__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Returns the product of a scalar and this ComplexSIMD instance.

Args:

• self (Self)
• other (Scalar): Scalar value to multiply with both real and imaginary parts.

Returns:

• Self

Overload 2

__rmul__(self, other: SIMD[other.dtype, width]) -> Self

Returns the product of a SIMD vector and this ComplexSIMD instance.

Args:

• self (Self)
• other (SIMD): SIMD vector to multiply with both real and imaginary parts.

Returns:

• Self

Overload 3

__rmul__(self, other: ImaginaryUnit) -> Self

Returns the product of the imaginary unit 1j and this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
var result = `1j` * z  # -2 + 3j
print(result)  # (-2 + 3j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to multiply with this complex number.

Returns:

• Self

__rtruediv__

Overload 1

__rtruediv__(self, other: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Performs element-wise division of a scalar by this ComplexSIMD instance.

Args:

• self (Self)
• other (Scalar): Scalar value to be divided by this ComplexSIMD instance.

Returns:

• Self

Overload 2

__rtruediv__(self, other: SIMD[other.dtype, width]) -> Self

Performs element-wise division of a SIMD vector by this ComplexSIMD instance.

Args:

• self (Self)
• other (SIMD): SIMD vector to be divided by this ComplexSIMD instance.

Returns:

• Self

Overload 3

__rtruediv__(self, other: ImaginaryUnit) -> Self

Performs division of the imaginary unit 1j by this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 4.0)  # 3 + 4j
var result = `1j` / z  # 1j / (3 + 4j) = 0.16 - 0.12j
print(result)  # (0.16 - 0.12j)

Args:

• self (Self)
• other (ImaginaryUnit): Imaginary unit (1j) to be divided by this ComplexSIMD instance.

Returns:

• Self

__iadd__

Overload 1

__iadd__(mut self, other: Self)

In-place addition of another ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (Self): Another ComplexSIMD instance.

Overload 2

__iadd__(mut self, other: Scalar[ComplexSIMD[cdtype, width].dtype])

In-place addition of a scalar to the real part of this ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (Scalar): Scalar value to add to the real component.

Overload 3

__iadd__(mut self, other: SIMD[other.dtype, width])

In-place addition of a SIMD vector to the real part of this ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (SIMD): SIMD vector to add to the real component.

Overload 4

__iadd__(mut self, other: ImaginaryUnit)

In-place addition of the imaginary unit 1j to this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
z += `1j`  # Now z = 3 + 3j
print(z)  # (3 + 3j)

Args:

• self (Self) [mut]
• other (ImaginaryUnit): Imaginary unit (1j) to add to this complex number.

__isub__

Overload 1

__isub__(mut self, other: Self)

In-place subtraction of another ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (Self): Another ComplexSIMD instance.

Overload 2

__isub__(mut self, other: Scalar[ComplexSIMD[cdtype, width].dtype])

In-place subtraction of a scalar from the real part of this ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (Scalar): Scalar value to subtract from the real component.

Overload 3

__isub__(mut self, other: SIMD[other.dtype, width])

In-place subtraction of a SIMD vector from the real part of this ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (SIMD): SIMD vector to subtract from the real component.

Overload 4

__isub__(mut self, other: ImaginaryUnit)

In-place subtraction of the imaginary unit 1j from this ComplexSIMD instance.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
z -= `1j`  # Now z = 3 + 1j
print(z)  # (3 + 1j)

Args:

• self (Self) [mut]
• other (ImaginaryUnit): Imaginary unit (1j) to subtract from this complex number.

__imul__

Overload 1

__imul__(mut self, other: Self)

In-place complex multiplication with another ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (Self): Another ComplexSIMD instance.

Overload 2

__imul__(mut self, other: Scalar[ComplexSIMD[cdtype, width].dtype])

In-place multiplication of this ComplexSIMD instance by a scalar.

Args:

• self (Self) [mut]
• other (Scalar): Scalar value to multiply with both real and imaginary parts.

Overload 3

__imul__(mut self, other: SIMD[other.dtype, width])

In-place multiplication of this ComplexSIMD instance by a SIMD vector.

Args:

• self (Self) [mut]
• other (SIMD): SIMD vector to multiply with both real and imaginary parts.

Overload 4

__imul__(mut self, other: ImaginaryUnit)

In-place multiplication of this ComplexSIMD instance by the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
z *= `1j`  # Now z = -2 + 3j
print(z)  # (-2 + 3j)

Args:

• self (Self) [mut]
• other (ImaginaryUnit): Imaginary unit (1j) to multiply with this complex number.

__itruediv__

Overload 1

__itruediv__(mut self, other: Self)

Performs in-place element-wise complex division of self by another ComplexSIMD instance.

Args:

• self (Self) [mut]
• other (Self): Another ComplexSIMD instance to divide by.

Overload 2

__itruediv__(mut self, other: Scalar[ComplexSIMD[cdtype, width].dtype])

Performs in-place element-wise division of this ComplexSIMD instance by a scalar.

Args:

• self (Self) [mut]
• other (Scalar): Scalar value to divide both real and imaginary parts by.

Overload 3

__itruediv__(mut self, other: SIMD[other.dtype, width])

Performs in-place element-wise division of this ComplexSIMD instance by a SIMD vector.

Args:

• self (Self) [mut]
• other (SIMD): SIMD vector to divide both real and imaginary parts by.

Overload 4

__itruediv__(mut self, other: ImaginaryUnit)

Performs in-place division of this ComplexSIMD instance by the imaginary unit 1j.

Examples:

from numojo.prelude import *

var z = ComplexSIMD[cf64, 1](3.0, 2.0)  # 3 + 2j
z /= `1j`  # Now z = 2 - 3j
print(z)  # (2 - 3j)

Args:

• self (Self) [mut]
• other (ImaginaryUnit): Imaginary unit (1j) to divide this complex number by.

zero

zero() -> Self

static

Returns a ComplexSIMD instance with all real and imaginary components set to zero.

Example:

from numojo.prelude import *
var comp = ComplexSIMD[cf64].zero()  # (0 + 0j)

Returns:

• Self

one

one() -> Self

static

Returns a ComplexSIMD instance representing the complex number 1 + 0j.

Example:

from numojo.prelude import *
var comp = ComplexSIMD[cf64].one()  # (1 + 0j)

Returns:

• Self

i

i() -> Self

static

Returns a ComplexSIMD instance representing the imaginary unit 0 + 1j.

Examples:

from numojo.prelude import *

# Create imaginary unit for different types
var i_f64 = ComplexSIMD[cf64].i()  # (0 + 1j)
var i_f32 = ComplexSIMD[cf32].i()  # (0 + 1j)
print(i_f64)  # (0 + 1j)

# Use in complex arithmetic
var z = 3.0 + 4.0 * ComplexSIMD[cf64].i()  # 3 + 4j

Returns:

• Self

from_real_imag

from_real_imag(re: Scalar[ComplexSIMD[cdtype, width].dtype], im: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

static

Constructs a ComplexSIMD instance from scalar real and imaginary values.

Example:

from numojo.prelude import *
var comp = ComplexSIMD[cf64].from_real_imag(2.0, 3.0)  # (2.0 + 3.0j)

Args:

• re (Scalar): Scalar value for the real component.
• im (Scalar): Scalar value for the imaginary component.

Returns:

• Self

from_polar

from_polar(r: Scalar[ComplexSIMD[cdtype, width].dtype], theta: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self where ComplexSIMD[cdtype, width].dtype.is_floating_point()

static

Constructs a ComplexSIMD instance from polar coordinates.

Example:

from numojo.prelude import *
var comp = ComplexSIMD[cf64].from_polar(2.0, 0.5)

Args:

• r (Scalar): Magnitude (radius).
• theta (Scalar): Angle (in radians).

Returns:

• Self

reciprocal

reciprocal(self) -> Self

Returns the element-wise reciprocal (1 / self) of the ComplexSIMD instance.

Args:

• self (Self)

Returns:

• Self

Raises

elem_pow

Overload 1

elem_pow(self, other: Self) -> Self

Raises each component of this ComplexSIMD to the power of the corresponding component in another ComplexSIMD.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance.

Returns:

• Self

Overload 2

elem_pow(self, exponent: Scalar[ComplexSIMD[cdtype, width].dtype]) -> Self

Raises each component of this ComplexSIMD to a scalar exponent.

Args:

• self (Self)
• exponent (Scalar): Scalar exponent to apply to both real and imaginary parts.

Returns:

• Self

allclose

allclose(self, other: Self, *, rtol: Scalar[ComplexSIMD[cdtype, width].dtype] = 1.0000000000000001E-5, atol: Scalar[ComplexSIMD[cdtype, width].dtype] = 1.0E-8) -> Bool

Checks if two ComplexSIMD instances are approximately equal within given tolerances.

For each lane, compares the real and imaginary parts using the formula: abs(a - b) <= atol + rtol * abs(b) where a and b are the corresponding components of self and other.

Note: For SIMD width > 1, all lanes must satisfy the tolerance criteria.

Args:

• self (Self)
• other (Self): Another ComplexSIMD instance to compare against.
• rtol (Scalar): Relative tolerance.
• atol (Scalar): Absolute tolerance.

Returns:

• Bool

__str__

__str__(self) -> String

Args:

• self (Self)

Returns:

• String

write_to

write_to[W: Writer](self, mut writer: W)

Returns a string representation of the ComplexSIMD instance.

For width == 1, the format is: (re + im j). For width > 1, the format is: [(re0 + im0 j), (re1 + im1 j), ...].

Parameters:

• W (Writer)

Args:

• self (Self)
• writer (W) [mut]

__repr__

__repr__(self) -> String

Returns a string representation of the ComplexSIMD instance for debugging. ComplexSIMD[dtype](re=<real SIMD>, im=<imag SIMD>).

Args:

• self (Self)

Returns:

• String

Raises

item

item[name: String](self, idx: Int) -> Scalar[ComplexSIMD[cdtype, width].dtype]

Returns the scalar value for the specified lane index and component.

Example:

from numojo.prelude import *
var c_simd = nm.ComplexSIMD[cf32, 2](SIMD[f32, 2](1, 2), SIMD[f32, 2](3, 4)) # [(1 + 3j), (2 + 4j)]
var re0 = c_simd.item["re"](0)  # 1.0
var im1 = c_simd.item["im"](1)  # 4.0

Parameters:

• name (String): Name of the component ('re' or 'im').

Args:

• self (Self)
• idx (Int): Lane index to retrieve.

Returns:

• Scalar

Raises

• Error if the component name is invalid.

• Error if lane index is out of range for the SIMD width.

itemset

itemset[name: String](mut self, idx: Int, val: Scalar[ComplexSIMD[cdtype, width].dtype])

Sets the scalar value for the specified lane index and component.

Example:

from numojo.prelude import *
var c_simd = nm.ComplexSIMD[cf32, 2](SIMD[f32, 2](1, 2), SIMD[f32, 2](3, 4)) # [(1 + 3j), (2 + 4j)]
c_simd.itemset["re"](0, 5.0)  # Now first complex number is (5 + 3j)
c_simd.itemset["im"](1, 6.0)  # Now second complex number is (2 + 6j)

Parameters:

• name (String): Name of the component ('re' or 'im').

Args:

• self (Self) [mut]
• idx (Int): Lane index to set.
• val (Scalar): Scalar value to assign to the specified component.

Raises

• Error if the component name is invalid.

• Error if lane index is out of range for the SIMD width.

real

real(self) -> SIMD[ComplexSIMD[cdtype, width].dtype, width]

Returns the real part(s) of the complex number(s).

Args:

• self (Self)

Returns:

• SIMD

imag

imag(self) -> SIMD[ComplexSIMD[cdtype, width].dtype, width]

Returns the imaginary part(s) of the complex number(s).

Args:

• self (Self)

Returns:

• SIMD

__abs__

__abs__(self) -> SIMD[ComplexSIMD[cdtype, width].dtype, width]

Returns the magnitude (absolute value) of the complex number(s).

Args:

• self (Self)

Returns:

• SIMD

norm

norm(self) -> SIMD[ComplexSIMD[cdtype, width].dtype, width]

Returns the squared magnitude (norm) of the complex number(s).

Args:

• self (Self)

Returns:

• SIMD

conj

conj(self) -> Self

Returns the complex conjugate of the ComplexSIMD instance.

Args:

• self (Self)

Returns:

• Self

ImaginaryUnit

struct ImaginaryUnit

Memory convention: register_passable_trivial
Implements: AnyType, Boolable, Copyable, ImplicitlyCopyable, ImplicitlyDestructible, Movable, RegisterPassable, Stringable, TrivialRegisterPassable, Writable

Constant representing the imaginary unit complex number 0 + 1j.

The ImaginaryUnit struct provides a convenient way to work with the imaginary unit in complex arithmetic operations. It supports arithmetic operations with SIMD vectors, scalars, and other complex numbers, enabling Python-like syntax for complex number creation.

Examples:

from numojo.prelude import *

# Create complex numbers using the imaginary unit
var z1 = 3 + 4 * `1j`  # 3 + 4j
var z2 = `1j` * 2      # 0 + 2j
var z3 = 5.0 + `1j`    # 5 + 1j

# Powers of the imaginary unit
print(`1j` ** 0)  # 1 + 0j
print(`1j` ** 1)  # 0 + 1j
print(`1j` ** 2)  # -1 + 0j
print(`1j` ** 3)  # 0 - 1j

# SIMD complex vectors
var c4 = SIMD[f32, 4](1.0) + `1j` * SIMD[f32, 4](2.0)  # ComplexSIMD[cf32, 4]
var c5 = SIMD[f64, 2](3.0, 4.0) + `1j`                 # ComplexSIMD[cf64, 2]
var d = SIMD[f32, 2](1) + SIMD[f32, 2](2) * `1j`         # creates [( 1 + 2 j) (1 + 2 j)]

# Mathematical properties
var c6 = `1j` * `1j`                     # -1 (Scalar[f64])
var c7 = `1j` ** 3                       # (0 - 1j) (ComplexScalar[cf64])
var c8 = (1 + `1j`) / `1j`               # (1 - 1j) (ComplexScalar[cf64])

Aliases

__del__is_trivial

comptime __del__is_trivial

Value: True

__move_ctor_is_trivial

comptime __move_ctor_is_trivial

Value: True

__copy_ctor_is_trivial

comptime __copy_ctor_is_trivial

Value: True

Methods

__init__

__init__() -> Self

static

Constructor for ImaginaryUnit.

Creates an instance representing the imaginary unit 1j.

Returns:

• Self

__bool__

__bool__(self) -> Bool

Returns the boolean value of the imaginary unit.

Examples:

from numojo.prelude import *

if `1j`:
    print("Imaginary unit is truthy")  # This will execute

Args:

• self (Self)

Returns:

• Bool

__neg__

__neg__(self) -> ComplexSIMD

Returns the negation of the imaginary unit: -1j.

Examples:

from numojo.prelude import *

var result = -`1j`  # -1j
print(result)  # (0 - 1j)

Args:

• self (Self)

Returns:

• ComplexSIMD

__add__

Overload 1

__add__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Returns the sum of the imaginary unit 1j and a SIMD vector.

Examples:

from numojo.prelude import *

var vec = SIMD[DType.float32, 4](1.0, 2.0, 3.0, 4.0)
var result = `1j` + vec  # [1+1j, 2+1j, 3+1j, 4+1j]

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD): SIMD vector to add to the imaginary unit.

Returns:

• ComplexSIMD

Overload 2

__add__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Returns the sum of the imaginary unit 1j and a scalar.

Examples:

from numojo.prelude import *

var result = `1j` + 3.5  # 3.5 + 1j

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar): Scalar to add to the imaginary unit.

Returns:

• ComplexSIMD

Overload 3

__add__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Returns the sum of the imaginary unit 1j and an integer.

Examples:

from numojo.prelude import *

var result = `1j` + 5  # 5 + 1j

Args:

• self (Self)
• other (Int): Integer to add to the imaginary unit.

Returns:

• ComplexSIMD

Overload 4

__add__(self, other: Self) -> ComplexSIMD

Returns the sum of the imaginary unit with itself: 1j + 1j = 2j.

Examples:

from numojo.prelude import *

var result = `1j` + `1j`  # 2j
print(result)  # (0 + 2j)

Args:

• self (Self)
• other (Self): Another imaginary unit to add.

Returns:

• ComplexSIMD

__sub__

Overload 1

__sub__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Returns the difference of the imaginary unit and a SIMD vector.

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD)

Returns:

• ComplexSIMD

Overload 2

__sub__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Returns the difference of the imaginary unit and a scalar.

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar)

Returns:

• ComplexSIMD

Overload 3

__sub__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Returns the difference of the imaginary unit and an integer.

Args:

• self (Self)
• other (Int)

Returns:

• ComplexSIMD

Overload 4

__sub__(self, other: Self) -> Float64

Returns the difference of the imaginary unit with itself: 1j - 1j = 0.

Examples:

from numojo.prelude import *

var result = `1j` - `1j`  # 0
print(result)  # 0

Args:

• self (Self)
• other (Self): Another imaginary unit to subtract.

Returns:

• Float64

__mul__

Overload 1

__mul__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD)

Returns:

• ComplexSIMD

Overload 2

__mul__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar)

Returns:

• ComplexSIMD

Overload 3

__mul__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Args:

• self (Self)
• other (Int)

Returns:

• ComplexSIMD

Overload 4

__mul__(self, other: Self) -> Float64

Returns the product of the imaginary unit with itself: 1j * 1j = -1.

Examples:

from numojo.prelude import *

var result = `1j` * `1j`  # -1
print(result)  # -1

Args:

• self (Self)
• other (Self): Another imaginary unit to multiply with.

Returns:

• Float64

__truediv__

Overload 1

__truediv__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Returns the division of the imaginary unit by a SIMD vector.

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD)

Returns:

• ComplexSIMD

Overload 2

__truediv__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Returns the division of the imaginary unit by a scalar.

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar)

Returns:

• ComplexSIMD

Overload 3

__truediv__(self, other: Self) -> Float64

Returns the division of the imaginary unit by itself: 1j / 1j = 1.

Examples:

from numojo.prelude import *

var result = `1j` / `1j`  # 1
print(result)  # 1

Args:

• self (Self)
• other (Self): Another imaginary unit to divide by.

Returns:

• Float64

__pow__

__pow__(self, exponent: Int) -> ComplexSIMD

Returns the imaginary unit raised to an integer power.

The powers of 1j cycle with period 4: - 1j^0 = 1 - 1j^1 = 1j - 1j^2 = -1 - 1j^3 = -1j - 1j^4 = 1 (cycle repeats)

Examples:

from numojo.prelude import *

print(`1j` ** 0)  # (1 + 0j)
print(`1j` ** 1)  # (0 + 1j)
print(`1j` ** 2)  # (-1 + 0j)
print(`1j` ** 3)  # (0 - 1j)
print(`1j` ** 4)  # (1 + 0j)

Args:

• self (Self)
• exponent (Int): Integer exponent.

Returns:

• ComplexSIMD

__radd__

Overload 1

__radd__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Returns the sum of a SIMD vector and the imaginary unit.

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD)

Returns:

• ComplexSIMD

Overload 2

__radd__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Returns the sum of a scalar and the imaginary unit.

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar)

Returns:

• ComplexSIMD

Overload 3

__radd__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Returns the sum of an integer and the imaginary unit.

Args:

• self (Self)
• other (Int)

Returns:

• ComplexSIMD

__rsub__

Overload 1

__rsub__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Returns the difference of a SIMD vector and the imaginary unit.

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD)

Returns:

• ComplexSIMD

Overload 2

__rsub__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Returns the difference of a scalar and the imaginary unit.

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar)

Returns:

• ComplexSIMD

Overload 3

__rsub__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Returns the difference of an integer and the imaginary unit.

Args:

• self (Self)
• other (Int)

Returns:

• ComplexSIMD

__rmul__

Overload 1

__rmul__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD)

Returns:

• ComplexSIMD

Overload 2

__rmul__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar)

Returns:

• ComplexSIMD

Overload 3

__rmul__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Args:

• self (Self)
• other (Int)

Returns:

• ComplexSIMD

__rtruediv__

Overload 1

__rtruediv__[dtype: DType, width: Int](self, other: SIMD[dtype, width]) -> ComplexSIMD[ComplexDType(dtype), width]

Returns the division of a SIMD vector by the imaginary unit.

Parameters:

• dtype (DType)
• width (Int)

Args:

• self (Self)
• other (SIMD): SIMD vector to be divided by the imaginary unit.

Returns:

• ComplexSIMD

Overload 2

__rtruediv__[dtype: DType](self, other: Scalar[dtype]) -> ComplexSIMD[ComplexDType(dtype)]

Returns the division of a scalar by the imaginary unit.

Parameters:

• dtype (DType)

Args:

• self (Self)
• other (Scalar): Scalar to be divided by the imaginary unit.

Returns:

• ComplexSIMD

Overload 3

__rtruediv__(self, other: Int) -> ComplexSIMD[ComplexDType.int]

Returns the division of an integer by the imaginary unit.

Args:

• self (Self)
• other (Int): Integer to be divided by the imaginary unit.

Returns:

• ComplexSIMD

conj

conj(self) -> ComplexSIMD

Returns the complex conjugate of the imaginary unit.

Examples:

from numojo.prelude import *

var conj_i = `1j`.conj()  # -1j
print(conj_i)  # (0 - 1j)

Args:

• self (Self)

Returns:

• ComplexSIMD

__str__

__str__(self) -> String

Returns the string representation of the imaginary unit.

Args:

• self (Self)

Returns:

• String

write_to

write_to[W: Writer](self, mut writer: W)

Writes the string representation of the imaginary unit to a writer.

Parameters:

• W (Writer)

Args:

• self (Self)
• writer (W) [mut]: Writer instance to write the string representation to.