Package fi.iki.jmtilli.javafastcomplex

Class ComplexUtils

java.lang.Object
fi.iki.jmtilli.javafastcomplex.ComplexUtils
public class ComplexUtils
extends java.lang.Object
A utility class for complex numbers. This class contains static methods which can be used for objects implementing the ComplexNumber interface.

  • Constructor Details

  • Method Details

    • isNaN

      public static boolean isNaN​(ComplexNumber n)
      Returns whether the complex number is NaN. A comples number is considered NaN if either the real or imaginary part is NaN.
      Parameters:
      n - The complex number
      Returns:
      Whether the complex number is NaN

    • isNaN

      public static boolean isNaN​(ComplexNumberArray n, int i)
      Returns whether the complex number is NaN. A comples number is considered NaN if either the real or imaginary part is NaN.
      Parameters:
      n - The complex number array
      i - The array index
      Returns:
      Whether the complex number is NaN

    • isInfinite

      public static boolean isInfinite​(ComplexNumber n)
      Returns whether the complex number is infinite. A comples number is considered infinite if either the real or imaginary part is infinite and the complex number is not NaN.
      Parameters:
      n - The complex number
      Returns:
      Whether the complex number is infinite

    • isInfinite

      public static boolean isInfinite​(ComplexNumberArray n, int i)
      Returns whether the complex number is infinite. A comples number is considered infinite if either the real or imaginary part is infinite and the complex number is not NaN.
      Parameters:
      n - The complex number array
      i - The array index
      Returns:
      Whether the complex number is infinite

    • abs

      public static double abs​(ComplexNumber num)
      Returns the absolute value of the complex number. If the complex number is NaN, returns NaN. If the complex number is infinite, returns the infinity.
      Parameters:
      num - The complex number
      Returns:
      The absolute value of the complex number.

    • abs

      public static double abs​(ComplexNumberArray num, int i)
      Returns the absolute value of the complex number. If the complex number is NaN, returns NaN. If the complex number is infinite, returns the infinity.
      Parameters:
      num - The complex number array
      i - The array index
      Returns:
      The absolute value of the complex number.

    • arg

      public static double arg​(ComplexNumber num)
      Calculates the argument of this complex number. The argument is the angle between the positive real axis and the point that represents this number in the complex plane.
      Parameters:
      num - The complex number
      Returns:
      -pi≤x≤pi the argument

    • arg

      public static double arg​(ComplexNumberArray num, int i)
      Calculates the argument of this complex number. The argument is the angle between the positive real axis and the point that represents this number in the complex plane.
      Parameters:
      num - The complex number array
      i - The array index
      Returns:
      -pi≤x≤pi the argument

    • newPolar

      public static Complex newPolar​(double abs, double argument)
      Create a complex number from polar coordinates.
      Parameters:
      abs - The absolute value
      argument - The argument
      Returns:
      The new complex number

    • pow

      public static Complex pow​(ComplexNumber a, double b)
      Raise a complex number to a real power
      Parameters:
      a - The complex base
      b - The real power
      Returns:
      The result

    • pow

      public static Complex pow​(ComplexNumberArray a, int i, double b)
      Raise a complex number to a real power
      Parameters:
      a - The complex base array
      i - The array index
      b - The real power
      Returns:
      The result

    • pow

      public static Complex pow​(ComplexNumber a, ComplexNumber b)
      Raise a complex number to a complex power
      Parameters:
      a - The complex base
      b - The complex power
      Returns:
      The result

    • pow

      public static Complex pow​(ComplexNumberArray a, int i, ComplexNumber b)
      Raise a complex number to a complex power
      Parameters:
      a - The complex base array
      i - The array index
      b - The complex power
      Returns:
      The result

    • pow

      public static Complex pow​(ComplexNumberArray a, int i, ComplexNumberArray b, int j)
      Raise a complex number to a complex power
      Parameters:
      a - The complex base array
      i - The array index of first array
      b - The complex power arary
      j - The array index of second array
      Returns:
      The result

    • pow

      public static Complex pow​(ComplexNumber a, ComplexNumberArray b, int j)
      Raise a complex number to a complex power
      Parameters:
      a - The complex base
      b - The complex power array
      j - The array index
      Returns:
      The result

    • toString

      public static java.lang.String toString​(ComplexNumber num)
      Returns a String representation of a complex number.
      Parameters:
      num - The complex number array
      Returns:
      "NaN" if NaN
      re if purely real
      im+"i" if purely imaginary
      (re + " + " + im + "i") if im>0
      (re + " - " + (-im) + "i") if im<0

    • toString

      public static java.lang.String toString​(ComplexNumberArray num, int i)
      Returns a String representation of a complex number.
      Parameters:
      num - The complex number array
      i - The array index
      Returns:
      "NaN" if NaN
      re if purely real
      im+"i" if purely imaginary
      (re + " + " + im + "i") if im>0
      (re + " - " + (-im) + "i") if im<0

    • add

      public static Complex add​(ComplexNumber a, ComplexNumber b)
      Add a complex number to a complex number
      Parameters:
      a - A complex number
      b - A complex number
      Returns:
      The sum

    • add

      public static Complex add​(ComplexNumberArray a, int i, ComplexNumber b)
      Add a complex number to a complex number
      Parameters:
      a - A complex number array
      i - The array index
      b - A complex number
      Returns:
      The sum

    • add

      public static Complex add​(ComplexNumberArray a, int i, ComplexNumberArray b, int j)
      Add a complex number to a complex number
      Parameters:
      a - A complex number array
      i - The array index to first array
      b - A complex number array
      j - The array index to second array
      Returns:
      The sum

    • add

      public static Complex add​(ComplexNumber a, ComplexNumberArray b, int j)
      Add a complex number to a complex number
      Parameters:
      a - A complex number
      b - A complex number array
      j - The array index
      Returns:
      The sum

    • add

      public static Complex add​(ComplexNumber a, double b)
      Add a real number to a complex number
      Parameters:
      a - The complex number
      b - The real number
      Returns:
      The sum

    • add

      public static Complex add​(ComplexNumberArray a, int i, double b)
      Add a real number to a complex number
      Parameters:
      a - The complex number array
      i - The array index
      b - The real number
      Returns:
      The sum

    • add

      public static Complex add​(double a, ComplexNumber b)
      Add a complex number to a real number
      Parameters:
      a - The real number
      b - The complex number
      Returns:
      The sum

    • add

      public static Complex add​(double a, ComplexNumberArray b, int j)
      Add a complex number to a real number
      Parameters:
      a - The real number
      b - The complex number array
      j - The array index
      Returns:
      The sum

    • subtract

      public static Complex subtract​(ComplexNumber a, ComplexNumber b)
      Subtract a complex number from a complex number
      Parameters:
      a - The minuend
      b - The subtrahend
      Returns:
      The difference

    • subtract

      public static Complex subtract​(ComplexNumberArray a, int i, ComplexNumber b)
      Subtract a complex number from a complex number
      Parameters:
      a - The minuend array
      i - The array index
      b - The subtrahend
      Returns:
      The difference

    • subtract

      public static Complex subtract​(ComplexNumberArray a, int i, ComplexNumberArray b, int j)
      Subtract a complex number from a complex number
      Parameters:
      a - The minuend array
      i - The first array index
      b - The subtrahend array
      j - The second array index
      Returns:
      The difference

    • subtract

      public static Complex subtract​(ComplexNumber a, ComplexNumberArray b, int j)
      Subtract a complex number from a complex number
      Parameters:
      a - The minuend
      b - The subtrahend arrary
      j - The array index
      Returns:
      The difference

    • subtract

      public static Complex subtract​(ComplexNumber a, double b)
      Subtract a real number from a complex number
      Parameters:
      a - The complex number
      b - The real number
      Returns:
      The difference

    • subtract

      public static Complex subtract​(ComplexNumberArray a, int i, double b)
      Subtract a real number from a complex number
      Parameters:
      a - The complex number array
      i - The array index
      b - The real number
      Returns:
      The difference

    • subtract

      public static Complex subtract​(double a, ComplexNumber b)
      Subtract a complex number from a real number
      Parameters:
      a - The real number
      b - The complex number
      Returns:
      The difference

    • subtract

      public static Complex subtract​(double a, ComplexNumberArray b, int j)
      Subtract a complex number from a real number
      Parameters:
      a - The real number
      b - The complex number array
      j - The array index
      Returns:
      The difference

    • multiply

      public static Complex multiply​(ComplexNumber a, ComplexNumber b)
      Multiply a complex number by a complex number
      Parameters:
      a - A complex number
      b - A complex number
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(ComplexNumberArray a, int i, ComplexNumber b)
      Multiply a complex number by a complex number
      Parameters:
      a - A complex number array
      i - The array index
      b - A complex number
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(ComplexNumberArray a, int i, ComplexNumberArray b, int j)
      Multiply a complex number by a complex number
      Parameters:
      a - A complex number array
      i - The array index to first array
      b - A complex number array
      j - The array index to second array
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(ComplexNumber a, ComplexNumberArray b, int j)
      Multiply a complex number by a complex number
      Parameters:
      a - A complex number
      b - A complex number arary
      j - The array index
      Returns:
      The result of the multiplication

    • divide

      public static Complex divide​(ComplexNumber a, ComplexNumber b)
      Divide a complex number by a complex number
      Parameters:
      a - The dividend
      b - The divisor
      Returns:
      The result of the division

    • divide

      public static Complex divide​(ComplexNumberArray a, int i, ComplexNumber b)
      Divide a complex number by a complex number
      Parameters:
      a - The dividend array
      i - The array index
      b - The divisor
      Returns:
      The result of the division

    • divide

      public static Complex divide​(ComplexNumberArray a, int i, ComplexNumberArray b, int j)
      Divide a complex number by a complex number
      Parameters:
      a - The dividend array
      i - The array index to first array
      b - The divisor array
      j - The array index to second array
      Returns:
      The result of the division

    • divide

      public static Complex divide​(ComplexNumber a, ComplexNumberArray b, int j)
      Divide a complex number by a complex number
      Parameters:
      a - The dividend
      b - The divisor array
      j - The array index
      Returns:
      The result of the division

    • divide

      public static Complex divide​(ComplexNumber a, double d)
      Divide a complex number by a real number
      Parameters:
      a - The complex number
      d - The real number
      Returns:
      The result of the division

    • divide

      public static Complex divide​(ComplexNumberArray a, int i, double d)
      Divide a complex number by a real number
      Parameters:
      a - The complex number array
      i - The array index
      d - The real number
      Returns:
      The result of the division

    • multiply

      public static Complex multiply​(ComplexNumber a, double d)
      Multiply a complex number by a real number
      Parameters:
      a - The complex number
      d - The real number
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(ComplexNumberArray a, int i, double d)
      Multiply a complex number by a real number
      Parameters:
      a - The complex number array
      i - The array index
      d - The real number
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(double d, ComplexNumber a)
      Multiply a real number by a complex number
      Parameters:
      d - The real number
      a - The complex number
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(double d, ComplexNumberArray a, int i)
      Multiply a real number by a complex number
      Parameters:
      d - The real number
      a - The complex number array
      i - The array index
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(ComplexNumber a, int i)
      Multiply a complex number by an integer
      Parameters:
      a - The complex number
      i - The integer
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(ComplexNumberArray a, int i, int x)
      Multiply a complex number by an integer
      Parameters:
      a - The complex number array
      i - The array index
      x - The integer
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(int i, ComplexNumber a)
      Multiply an integer by a complex number
      Parameters:
      i - The integer
      a - The complex number
      Returns:
      The result of the multiplication

    • multiply

      public static Complex multiply​(int x, ComplexNumberArray a, int i)
      Multiply an integer by a complex number
      Parameters:
      x - The integer
      a - The complex number array
      i - The array index
      Returns:
      The result of the multiplication

    • negate

      public static Complex negate​(ComplexNumber a)
      Calculates the negation of a complex number
      Parameters:
      a - The complex number
      Returns:
      -a

    • negate

      public static Complex negate​(ComplexNumberArray a, int i)
      Calculates the negation of a complex number
      Parameters:
      a - The complex number array
      i - The array index
      Returns:
      -a

    • conjugate

      public static Complex conjugate​(ComplexNumber a)
      Calculates the conjugate of a complex number
      Parameters:
      a - The complex number
      Returns:
      The complex conjugate of a

    • conjugate

      public static Complex conjugate​(ComplexNumberArray a, int i)
      Calculates the conjugate of a complex number
      Parameters:
      a - The complex number array
      i - The array index
      Returns:
      The complex conjugate of a

    • divide

      public static Complex divide​(double d, ComplexNumber c)
      Divide a real number by a complex number
      Parameters:
      d - The real number
      c - The complex number
      Returns:
      The result of the division

    • divide

      public static Complex divide​(double d, ComplexNumberArray c, int i)
      Divide a real number by a complex number
      Parameters:
      d - The real number
      c - The complex number array
      i - The array index
      Returns:
      The result of the division

    • invert

      public static Complex invert​(ComplexNumber c)
      Calculates the inverse of a complex number
      Parameters:
      c - The complex number
      Returns:
      1 divided by c

    • invert

      public static Complex invert​(ComplexNumberArray c, int i)
      Calculates the inverse of a complex number
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      1 divided by c

    • sqrt

      public static Complex sqrt​(ComplexNumber c)
      Calculates the square root of a complex number
      Parameters:
      c - The complex number
      Returns:
      The square root of c

    • sqrt

      public static Complex sqrt​(ComplexNumberArray c, int i)
      Calculates the square root of a complex number
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The square root of c

    • exp

      public static Complex exp​(ComplexNumber c)
      Calculates the exponential of the complex number.
      Parameters:
      c - The complex number
      Returns:
      e raised to the power c

    • exp

      public static Complex exp​(ComplexNumberArray c, int i)
      Calculates the exponential of the complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      e raised to the power c

    • log

      public static Complex log​(ComplexNumber c)
      Calculates the natural logarithm of the complex number.
      Parameters:
      c - The complex number
      Returns:
      The natural logarithm

    • log

      public static Complex log​(ComplexNumberArray c, int i)
      Calculates the natural logarithm of the complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The natural logarithm

    • log1p

      public static Complex log1p​(ComplexNumber c)
      Returns log(c+1). For values of c near 0, calculating log1p(c) is much more accurate than calculating log(1+c).
      Parameters:
      c - The complex number
      Returns:
      The value log(1+x)

    • log1p

      public static Complex log1p​(ComplexNumberArray c, int i)
      Returns log(c+1). For values of c near 0, calculating log1p(c) is much more accurate than calculating log(1+c).
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The value log(1+x)

    • expm1

      public static Complex expm1​(ComplexNumber c)
      Returns exp(c)-1. For values of c near 0, calculating expm1(c) is much more accurate than calculating exp(c)-1.
      Parameters:
      c - The complex number
      Returns:
      The value exp(c)-1

    • expm1

      public static Complex expm1​(ComplexNumberArray c, int i)
      Returns exp(c)-1. For values of c near 0, calculating expm1(c) is much more accurate than calculating exp(c)-1.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The value exp(c)-1

    • acosh

      public static Complex acosh​(ComplexNumber c)
      Calculate the inverse hyperbolic cosine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The inverse hyperbolic cosine of c

    • acosh

      public static Complex acosh​(ComplexNumberArray c, int i)
      Calculate the inverse hyperbolic cosine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The inverse hyperbolic cosine of c

    • asinh

      public static Complex asinh​(ComplexNumber c)
      Calculate the inverse hyperbolic sine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The inverse hyperbolic sine of c

    • asinh

      public static Complex asinh​(ComplexNumberArray c, int i)
      Calculate the inverse hyperbolic sine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The inverse hyperbolic sine of c

    • atanh

      public static Complex atanh​(ComplexNumber c)
      Calculate the inverse hyperbolic tangent of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The inverse hyperbolic tangent of c

    • atanh

      public static Complex atanh​(ComplexNumberArray c, int i)
      Calculate the inverse hyperbolic tangent of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The inverse hyperbolic tangent of c

    • acos

      public static Complex acos​(ComplexNumber c)
      Calculate the inverse cosine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The inverse cosine of c

    • acos

      public static Complex acos​(ComplexNumberArray c, int i)
      Calculate the inverse cosine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The inverse cosine of c

    • asin

      public static Complex asin​(ComplexNumber c)
      Calculate the inverse sine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The inverse sine of c

    • asin

      public static Complex asin​(ComplexNumberArray c, int i)
      Calculate the inverse sine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The inverse sine of c

    • atan

      public static Complex atan​(ComplexNumber c)
      Calculate the inverse tangent of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The inverse tangent of c

    • atan

      public static Complex atan​(ComplexNumberArray c, int i)
      Calculate the inverse tangent of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The inverse tangent of c

    • cos

      public static Complex cos​(ComplexNumber c)
      Calculate the cosine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The cosine of c

    • cos

      public static Complex cos​(ComplexNumberArray c, int i)
      Calculate the cosine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The cosine of c

    • sin

      public static Complex sin​(ComplexNumber c)
      Calculate the sine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The sine of c

    • sin

      public static Complex sin​(ComplexNumberArray c, int i)
      Calculate the sine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The sine of c

    • tan

      public static Complex tan​(ComplexNumber c)
      Calculate the tangent of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The tangent of c

    • tan

      public static Complex tan​(ComplexNumberArray c, int i)
      Calculate the tangent of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The tangent of c

    • cosh

      public static Complex cosh​(ComplexNumber c)
      Calculate the hyperbolic cosine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The hyperbolic cosine of c

    • cosh

      public static Complex cosh​(ComplexNumberArray c, int i)
      Calculate the hyperbolic cosine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The hyperbolic cosine of c

    • sinh

      public static Complex sinh​(ComplexNumber c)
      Calculate the hyperbolic sine of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The hyperbolic sine of c

    • sinh

      public static Complex sinh​(ComplexNumberArray c, int i)
      Calculate the hyperbolic sine of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The hyperbolic sine of c

    • tanh

      public static Complex tanh​(ComplexNumber c)
      Calculate the hyperbolic tangent of a complex number.
      Parameters:
      c - The complex number
      Returns:
      The hyperbolic tangent of c

    • tanh

      public static Complex tanh​(ComplexNumberArray c, int i)
      Calculate the hyperbolic tangent of a complex number.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The hyperbolic tangent of c

    • hashCode

      public static int hashCode​(ComplexNumber c)
      Returns a hash code of the complex number. The hash code is based on the bit representations of the real and imaginary parts. If two complex numbers are considered equal by the equal method, they have the same hash code.
      Parameters:
      c - The complex number
      Returns:
      The hash code

    • hashCode

      public static int hashCode​(ComplexNumberArray c, int i)
      Returns a hash code of the complex number. The hash code is based on the bit representations of the real and imaginary parts. If two complex numbers are considered equal by the equal method, they have the same hash code.
      Parameters:
      c - The complex number array
      i - The array index
      Returns:
      The hash code

    • equal

      public static boolean equal​(ComplexNumber a, ComplexNumber b)
      Compare two complex numbers with all cases of NaN considered equal. Note that this compares the bit representations of the real and imaginary parts. All instances of NaN are considered equal to each other. Thus for example NaN is equal to itself and +0.0+0.0i is not equal to -0.0-0.0i. This definition allows hash tables to work properly.
      Returns:
      true if both complex numbers are NaN
      true if the bit representations of the real and imaginary parts are equal
      false otherwise

    • longBitsEqual

      public static boolean longBitsEqual​(ComplexNumber a, ComplexNumber b)
      Compare the bit representations of real and imaginary parts of two complex numbers. Note that this compares the bit representations of the real and imaginary parts separately. Thus for example +0.0i+0.0i is not equal to -0.0-0.0i. Note that eg. NaN+0i is not equal to 0+NaNi, ie. all instances of NaN are not considered equal to each other.
      Returns:
      true if the bit representations of the real and imaginary parts are equal
      false otherwise

    • equalRealImag

      public static boolean equalRealImag​(ComplexNumber a, ComplexNumber b)
      Compare the real and imaginary parts of two complex numbers. Note that this compares the real and imaginary parts with the "==" operator. Thus for example NaN is not equal to itself, and +0.0+0.0i is considered equal to -0.0-0.0i.
      Returns:
      true if the the real and imaginary parts are equal with the "==" comparison operator
      false otherwise