gonum.org/v1/gonum@v0.14.0/num/quat/exp.go (about)

     1  // Copyright ©2018 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  // Copyright 2017 The Go Authors. All rights reserved.
     6  // Use of this source code is governed by a BSD-style
     7  // license that can be found in the LICENSE file.
     8  
     9  package quat
    10  
    11  import "math"
    12  
    13  // Exp returns e**q, the base-e exponential of q.
    14  func Exp(q Number) Number {
    15  	w, uv := split(q)
    16  	if uv == zero {
    17  		return lift(math.Exp(w))
    18  	}
    19  	v := Abs(uv)
    20  	e := math.Exp(w)
    21  	s, c := math.Sincos(v)
    22  	return join(e*c, Scale(e*s/v, uv))
    23  }
    24  
    25  // Log returns the natural logarithm of q.
    26  func Log(q Number) Number {
    27  	w, uv := split(q)
    28  	if uv == zero {
    29  		return lift(math.Log(w))
    30  	}
    31  	v := Abs(uv)
    32  	return join(math.Log(Abs(q)), Scale(math.Atan2(v, w)/v, uv))
    33  }
    34  
    35  // Pow return q**r, the base-q exponential of r.
    36  // For generalized compatibility with math.Pow:
    37  //
    38  //	Pow(0, ±0) returns 1+0i+0j+0k
    39  //	Pow(0, c) for real(c)<0 returns Inf+0i+0j+0k if imag(c), jmag(c), kmag(c) are zero,
    40  //	    otherwise Inf+Inf i+Inf j+Inf k.
    41  func Pow(q, r Number) Number {
    42  	if q == zero {
    43  		w, uv := split(r)
    44  		switch {
    45  		case w == 0:
    46  			return Number{Real: 1}
    47  		case w < 0:
    48  			if uv == zero {
    49  				return Number{Real: math.Inf(1)}
    50  			}
    51  			return Inf()
    52  		case w > 0:
    53  			return zero
    54  		}
    55  	}
    56  	return Exp(Mul(Log(q), r))
    57  }
    58  
    59  // PowReal return q**r, the base-q exponential of r.
    60  // For generalized compatibility with math.Pow:
    61  //
    62  //	PowReal(0, ±0) returns 1+0i+0j+0k
    63  //	PowReal(0, c) for c<0 returns Inf+0i+0j+0k.
    64  func PowReal(q Number, r float64) Number {
    65  	if q == zero {
    66  		switch {
    67  		case r == 0:
    68  			return Number{Real: 1}
    69  		case r < 0:
    70  			return Inf()
    71  		case r > 0:
    72  			return zero
    73  		}
    74  	}
    75  	return Exp(Scale(r, Log(q)))
    76  }
    77  
    78  // Sqrt returns the square root of q.
    79  func Sqrt(q Number) Number {
    80  	if q == zero {
    81  		return zero
    82  	}
    83  	return PowReal(q, 0.5)
    84  }