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mathjs/src/function/arithmetic/cbrt.js at develop · webdeb/mathjs · GitHub
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cbrt.js
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import
{
factory
}
from
'../../utils/factory.js'
import
{
isBigNumber
,
isComplex
,
isFraction
}
from
'../../utils/is.js'
import
{
cbrtNumber
}
from
'../../plain/number/index.js'
const
name
=
'cbrt'
const
dependencies
=
[
'config'
,
'typed'
,
'isNegative'
,
'unaryMinus'
,
'matrix'
,
'Complex'
,
'BigNumber'
,
'Fraction'
]
export
const
createCbrt
=
/* #__PURE__ */
factory
(
name
,
dependencies
,
(
{
config
,
typed
,
isNegative
,
unaryMinus
,
matrix
,
Complex
,
BigNumber
,
Fraction
}
)
=>
{
/**
* Calculate the cubic root of a value.
*
* To avoid confusion with the matrix cube root, this function does not
* apply to matrices. For a matrix, to take the cube root elementwise,
* see the examples.
*
* Syntax:
*
* math.cbrt(x)
* math.cbrt(x, allRoots)
*
* Examples:
*
* math.cbrt(27) // returns 3
* math.cube(3) // returns 27
* math.cbrt(-64) // returns -4
* math.cbrt(math.unit('27 m^3')) // returns Unit 3 m
* math.map([27, 64, 125], x => math.cbrt(x)) // returns [3, 4, 5]
*
* const x = math.complex('8i')
* math.cbrt(x) // returns Complex 1.7320508075689 + i
* math.cbrt(x, true) // returns Matrix [
* // 1.7320508075689 + i
* // -1.7320508075689 + i
* // -2i
* // ]
*
* See also:
*
* square, sqrt, cube
*
*
@param
{
number | BigNumber | Complex | Unit
} x
* Value for which to calculate the cubic root.
*
@param
{
boolean
} [allRoots] Optional, false by default. Only applicable
* when `x` is a number or complex number. If true, all complex
* roots are returned, if false (default) the principal root is
* returned.
*
@return
{
number | BigNumber | Complex | Unit
}
* Returns the cubic root of `x`
*/
return
typed
(
name
,
{
number
:
cbrtNumber
,
// note: signature 'number, boolean' is also supported,
// created by typed as it knows how to convert number to Complex
Complex
:
_cbrtComplex
,
'Complex, boolean'
:
_cbrtComplex
,
BigNumber
:
function
(
x
)
{
return
x
.
cbrt
(
)
}
,
Unit
:
_cbrtUnit
}
)
/**
* Calculate the cubic root for a complex number
*
@param
{
Complex
} x
*
@param
{
boolean
} [allRoots] If true, the function will return an array
* with all three roots. If false or undefined,
* the principal root is returned.
*
@returns
{
Complex | Array.<Complex> | Matrix.<Complex>
} Returns the cubic root(s) of x
*
@private
*/
function
_cbrtComplex
(
x
,
allRoots
)
{
// https://www.wikiwand.com/en/Cube_root#/Complex_numbers
const
arg3
=
x
.
arg
(
)
/
3
const
abs
=
x
.
abs
(
)
// principal root:
const
principal
=
new
Complex
(
cbrtNumber
(
abs
)
,
0
)
.
mul
(
new
Complex
(
0
,
arg3
)
.
exp
(
)
)
if
(
allRoots
)
{
const
all
=
[
principal
,
new
Complex
(
cbrtNumber
(
abs
)
,
0
)
.
mul
(
new
Complex
(
0
,
arg3
+
Math
.
PI
*
2
/
3
)
.
exp
(
)
)
,
new
Complex
(
cbrtNumber
(
abs
)
,
0
)
.
mul
(
new
Complex
(
0
,
arg3
-
Math
.
PI
*
2
/
3
)
.
exp
(
)
)
]
return
(
config
.
matrix
===
'Array'
)
?
all
:
matrix
(
all
)
}
else
{
return
principal
}
}
/**
* Calculate the cubic root for a Unit
*
@param
{
Unit
} x
*
@return
{
Unit
} Returns the cubic root of x
*
@private
*/
function
_cbrtUnit
(
x
)
{
if
(
x
.
value
&&
isComplex
(
x
.
value
)
)
{
let
result
=
x
.
clone
(
)
result
.
value
=
1.0
result
=
result
.
pow
(
1.0
/
3
)
// Compute the units
result
.
value
=
_cbrtComplex
(
x
.
value
)
// Compute the value
return
result
}
else
{
const
negate
=
isNegative
(
x
.
value
)
if
(
negate
)
{
x
.
value
=
unaryMinus
(
x
.
value
)
}
// TODO: create a helper function for this
let
third
if
(
isBigNumber
(
x
.
value
)
)
{
third
=
new
BigNumber
(
1
)
.
div
(
3
)
}
else
if
(
isFraction
(
x
.
value
)
)
{
third
=
new
Fraction
(
1
,
3
)
}
else
{
third
=
1
/
3
}
const
result
=
x
.
pow
(
third
)
if
(
negate
)
{
result
.
value
=
unaryMinus
(
result
.
value
)
}
return
result
}
}
}
)
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