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Martin Diehl
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@ -32,6 +32,7 @@
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief general quaternion math, not limited to unit quaternions
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!> @details w is the real part, (x, y, z) are the imaginary parts.
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!> @details https://users.aalto.fi/~ssarkka/pub/quat.pdf
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!---------------------------------------------------------------------------------------------------
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module quaternions
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use prec
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@ -118,6 +119,14 @@ module quaternions
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module procedure log__
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end interface log
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interface real
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module procedure real__
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end interface real
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interface aimag
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module procedure aimag__
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end interface aimag
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private :: &
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unitTest
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@ -125,18 +134,18 @@ contains
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!--------------------------------------------------------------------------------------------------
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!> @brief doing self test
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!> @brief do self test
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!--------------------------------------------------------------------------------------------------
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subroutine quaternions_init
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write(6,'(/,a)') ' <<<+- quaternions init -+>>>'
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write(6,'(/,a)') ' <<<+- quaternions init -+>>>'; flush(6)
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call unitTest
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end subroutine quaternions_init
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!---------------------------------------------------------------------------------------------------
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!> constructor for a quaternion from a 4-vector
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!> construct a quaternion from a 4-vector
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!---------------------------------------------------------------------------------------------------
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type(quaternion) pure function init__(array)
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@ -151,7 +160,7 @@ end function init__
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!---------------------------------------------------------------------------------------------------
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!> assigning a quaternion
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!> assign a quaternion
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!---------------------------------------------------------------------------------------------------
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elemental pure subroutine assign_quat__(self,other)
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@ -164,7 +173,7 @@ end subroutine assign_quat__
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!---------------------------------------------------------------------------------------------------
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!> assigning a 4-vector
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!> assign a 4-vector
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!---------------------------------------------------------------------------------------------------
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pure subroutine assign_vec__(self,other)
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@ -180,7 +189,7 @@ end subroutine assign_vec__
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!---------------------------------------------------------------------------------------------------
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!> addition of two quaternions
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!> add a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function add__(self,other)
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@ -192,7 +201,7 @@ end function add__
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!---------------------------------------------------------------------------------------------------
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!> unary positive operator
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!> return (unary positive operator)
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function pos__(self)
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@ -204,7 +213,7 @@ end function pos__
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!---------------------------------------------------------------------------------------------------
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!> subtraction of two quaternions
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!> subtract a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function sub__(self,other)
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@ -216,7 +225,7 @@ end function sub__
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!---------------------------------------------------------------------------------------------------
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!> unary negative operator
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!> negate (unary negative operator)
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function neg__(self)
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@ -228,7 +237,7 @@ end function neg__
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!---------------------------------------------------------------------------------------------------
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!> multiplication of two quaternions
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!> multiply with a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function mul_quat__(self,other)
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@ -243,7 +252,7 @@ end function mul_quat__
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!---------------------------------------------------------------------------------------------------
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!> multiplication of quaternion with scalar
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!> multiply with a scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function mul_scal__(self,scal)
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@ -256,7 +265,7 @@ end function mul_scal__
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!---------------------------------------------------------------------------------------------------
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!> division of two quaternions
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!> divide by a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function div_quat__(self,other)
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@ -268,7 +277,7 @@ end function div_quat__
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!---------------------------------------------------------------------------------------------------
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!> divisiont of quaternions by scalar
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!> divide by a scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function div_scal__(self,scal)
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@ -281,7 +290,7 @@ end function div_scal__
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!---------------------------------------------------------------------------------------------------
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!> equality of two quaternions
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!> test equality
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!---------------------------------------------------------------------------------------------------
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logical elemental pure function eq__(self,other)
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@ -294,7 +303,7 @@ end function eq__
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!---------------------------------------------------------------------------------------------------
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!> inequality of two quaternions
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!> test inequality
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!---------------------------------------------------------------------------------------------------
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logical elemental pure function neq__(self,other)
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@ -306,20 +315,7 @@ end function neq__
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!---------------------------------------------------------------------------------------------------
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!> quaternion to the power of a scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function pow_scal__(self,expon)
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class(quaternion), intent(in) :: self
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real(pReal), intent(in) :: expon
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pow_scal__ = exp(log(self)*expon)
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end function pow_scal__
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!---------------------------------------------------------------------------------------------------
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!> quaternion to the power of a quaternion
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!> raise to the power of a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function pow_quat__(self,expon)
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@ -332,7 +328,20 @@ end function pow_quat__
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!---------------------------------------------------------------------------------------------------
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!> exponential of a quaternion
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!> raise to the power of a scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function pow_scal__(self,expon)
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class(quaternion), intent(in) :: self
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real(pReal), intent(in) :: expon
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pow_scal__ = exp(log(self)*expon)
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end function pow_scal__
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!---------------------------------------------------------------------------------------------------
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!> take exponential
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!> ToDo: Lacks any check for invalid operations
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function exp__(self)
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@ -340,7 +349,7 @@ type(quaternion) elemental pure function exp__(self)
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class(quaternion), intent(in) :: self
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real(pReal) :: absImag
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absImag = norm2([self%x, self%y, self%z])
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absImag = norm2(aimag(self))
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exp__ = exp(self%w) * [ cos(absImag), &
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self%x/absImag * sin(absImag), &
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@ -351,7 +360,7 @@ end function exp__
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!---------------------------------------------------------------------------------------------------
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!> logarithm of a quaternion
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!> take logarithm
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!> ToDo: Lacks any check for invalid operations
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function log__(self)
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@ -359,7 +368,7 @@ type(quaternion) elemental pure function log__(self)
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class(quaternion), intent(in) :: self
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real(pReal) :: absImag
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absImag = norm2([self%x, self%y, self%z])
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absImag = norm2(aimag(self))
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log__ = [log(abs(self)), &
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self%x/absImag * acos(self%w/abs(self)), &
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@ -370,7 +379,7 @@ end function log__
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!---------------------------------------------------------------------------------------------------
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!> norm of a quaternion
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!> return norm
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!---------------------------------------------------------------------------------------------------
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real(pReal) elemental pure function abs__(a)
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@ -382,7 +391,7 @@ end function abs__
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!---------------------------------------------------------------------------------------------------
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!> dot product of two quaternions
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!> calculate dot product
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!---------------------------------------------------------------------------------------------------
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real(pReal) elemental pure function dot_product__(a,b)
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@ -394,7 +403,7 @@ end function dot_product__
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!---------------------------------------------------------------------------------------------------
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!> conjugate complex of a quaternion
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!> take conjugate complex
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function conjg__(a)
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@ -406,7 +415,7 @@ end function conjg__
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!---------------------------------------------------------------------------------------------------
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!> homomorphed quaternion of a quaternion
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!> homomorph
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function quat_homomorphed(self)
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@ -418,7 +427,7 @@ end function quat_homomorphed
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!---------------------------------------------------------------------------------------------------
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!> quaternion as plain array
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!> return as plain array
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!---------------------------------------------------------------------------------------------------
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pure function asArray(self)
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@ -432,7 +441,7 @@ end function asArray
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!---------------------------------------------------------------------------------------------------
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!> real part of a quaternion
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!> real part (scalar)
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!---------------------------------------------------------------------------------------------------
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pure function real__(self)
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@ -445,7 +454,7 @@ end function real__
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!---------------------------------------------------------------------------------------------------
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!> imaginary part of a quaternion
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!> imaginary part (3-vector)
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!---------------------------------------------------------------------------------------------------
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pure function aimag__(self)
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@ -463,7 +472,6 @@ end function aimag__
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subroutine unitTest
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real(pReal), dimension(4) :: qu
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type(quaternion) :: q, q_2
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call random_number(qu)
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