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Operator and Function List Usable in User-defined Field

The usable operators and functions are listed below.

* Both upper-case and lower-case letters can be used for them.

Operator

The calculation order of operators is the same as VB / VBA. In the table below, the operators in the upper rows have the higher priority than the ones in the lower rows.

Operator

Note

Power

Multiplication

Division
* Applicable to vector or tensor operations.

Addition

Subtraction
* Applicable to vector or tensor operations.

Comparison

<> means "NOT equal".
The result will be -1 if it is true.
The result will be 0 if it is false.

And

Bitwise AND

(fractional parts are truncated)

Bitwise OR

(fractional parts are truncated)

Vector/Tensor Operator

Operator	Note
+	Vector + Vector = Vector Tensor + Tensor = Tensor Calculates addition for each component.
-	Vector - Vector = Vector Tensor - Tensor = Tensor Calculates subtraction for each component.
*	Scalar * Vector = Vector Scalar * Tensor = Tensor Vector * Scalar = Vector Tensor * Scalar = Tensor Calculates multiplication for each component of a vector or tensor by a scalar. Vector :* Vector = Scalar Calculates the inner product of two vectors. The same result is given as the function INNER_PRODUCT. The following functions are provided to calculate the multiplication of vectors. Function INNER_PRODUCT_CONJ (Inner product with complex conjugate) Function OUTER_PRODUCT (Outer product) Function OUTER_PRODUCT_CONJ (Outer product with complex conjugate) Tensor * Vector = Vector Calculates multiplication of a tensor and a vector. Vector * Tensor = Vector Calculates multiplication of a transposed tensor and a vector. Tensor * Tensor = Tensor Calculate multiplication of tensors, The following functions are provided to calculate multiplication of tensors. Tensor contraction can be calculated using the inner product function. Function INNER_PRODUCT (Inner product) Function INNER_PRODUCT_CONJ (Inner product with complex conjugate)
/	Vector / Scalar = Vector Tensor / Scalar = Tensor Calculates division of each component of a scalar, vector, or tensor by a scalar. Other combinations are not supported.

Functions (Basic)

Function	Argument	Return value	Note
SIN	Scalar/Vector/Tensor (in radians) Real Number	Argument: Scalar (in radians) -> Scalar Argument: Vector (in radians) -> Vector Argument: Tensor (in radians) -> Tensor Real Number	Returns the sine of the argument. In the case of a vector, returns the sine of each component. In the case of a tensor, returns the tensor obtained by transforming the sine of the principal values back to the original coordinate system.
COS	Scalar/Vector/Tensor (in radians) Real Number	Argument: Scalar (in radians) -> Scalar Argument: Vector (in radians) -> Vector Argument: Tensor (in radians) -> Tensor Real Number	Returns the cosine of the argument. In the case of a vector, returns the cosine of each component. In the case of a tensor, returns the tensor obtained by transforming the cosine of the principal values back to the original coordinate system.
TAN	Scalar/Vector/Tensor (in radians) Real Number	Argument: Scalar (in radians) -> Scalar Argument: Vector (in radians) -> Vector Argument: Tensor (in radians) -> Tensor Real Number	Returns the tangent of the argument. In the case of a vector, returns the tangent of each component. In the case of a tensor, returns the tensor obtained by transforming the tangent of the principal values back to the original coordinate system.
ASIN	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar (in radians) Argument: Vector -> Vector (in radians) Argument: Tensor -> Tensor (in radians) Real Number	Returns the arcsine (in radians) of the argument. In the case of a vector, returns the arcsine of each component. In the case of a tensor, returns the tensor obtained by transforming the arcsine of the principal values back to the original coordinate system.
ACOS	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar (in radians) Argument: Vector -> Vector (in radians) Argument: Tensor -> Tensor (in radians) Real Number	Returns the arccosine (in radians) of the argument. In the case of a vector, returns the arccosine of each component. In the case of a tensor, returns the tensor obtained by transforming the arccosine of the principal values back to the original coordinate system.
ATN	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar (in radians) Argument: Vector -> Vector (in radians) Argument: Tensor -> Tensor (in radians) Real Number	Returns the arctangent (in radians) of the argument. In the case of a vector, returns the arctangent of each component. In the case of a tensor, returns the tensor obtained by transforming the arctangent of the principal values back to the original coordinate system.
LOG	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns the natural logarithm of the argument. In the case of a vector, returns the natural logarithm of each component. In the case of a tensor, returns the tensor obtained by transforming the natural logarithm of the principal values back to the original coordinate system.
LOG10	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns the common logarithm of the argument. In the case of a vector, returns the common logarithm of each component. In the case of a tensor, returns the tensor obtained by transforming the common logarithm of the principal values back to the original coordinate system.
SQR	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns the square root of the argument. In the case of a vector, returns the square root of each component. In the case of a tensor, returns a tensor obtained by transforming the square root of the principal values back to the original coordinate system.
POW	Argument 1: Scalar/Vector/Tensor Real Number Argument 2: Scalar Real Number	Argument 1: Scalar -> Scalar Argument 1: Vector -> Vector Argument 1: Tensor -> Tensor Real Number	Returns the Argument 1 raised to the power of the Argument 2. The delimiter between arguments is a comma. If the Argument 1 is a vector, returns each component raised to the power. If the Argument 1 is a tensor, returns a tensor obtained by transforming the principal values raised to the power back to the original coordinate system. Example: POW(VEC_LENGTH(BERNOULLI_VELOCITY),2) Returns the flow velocity raised to the power of 2.
EXP	Scalar/Vector/Tensor Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns Napier's constant raised to the power of the second argument If Argument 1 is a vector, returns Napier's constant raised to the power of each component. If Argument 1 is a tensor, returns a tensor obtained by transforming Napier's constant raised to the power of the principal value back to the original coordinate system.
F_IF	Argument 1: Scalar Real Number Argument 2, Argument 3: Scalar/Vector/Tensor Complex Number/Real Number	Argument 2. 3: Scalar -> Scalar Argument 2. 3: Vector -> Vector Argument 2. 3: Tensor -> Tensor Argument 2. 3: Complex Number -> Complex Number Argument 2. 3: Real Number -> Real Number	This function changes the return value depending on the conditions. It includes three arguments. If the result from the Argument 1 is not 0.0, returns the Argument 2, and if the result is 0.0, returns the Argument 3. The delimiter between arguments is a comma. Argument 1: Enter the comparisons, logical operations, or mathematical expressions. Argument 2: The value to return if the first argument is not 0.0. Argument 3: The value to return if the first argument is 0.0. Example: F_IF(WATT_TEMPERATURE>50,1,0) If the temperature is higher than 50, returns 1; otherwise, return 0.
ABS	Scalar/Vector/Tensor Complex Number/Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns the absolute value of the complex number. Whether the argument is a complex or real number, returns a real number. If the argument is a vector or tensor, calculates the absolute value of each component and returns a vector or tensor with these absolute values as components.
REAL	Scalar/Vector/Tensor Complex Number/Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns the real part of the complex number. Whether the argument is a complex or real number, returns a real number. If the argument is a vector or tensor, calculates the real part of each component and return a vector or tensor with these real parts as components.
IMAG	Scalar/Vector/Tensor Complex Number/Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Real Number	Returns the imaginary part of the complex number. Whether the argument is a complex or real number, returns a real number. If the argument is a vector or tensor, calculates the imaginary part of each component and return a vector or tensor with these imaginary parts as components.
CONJ	Scalar/Vector/Tensor Complex Number/Real Number	Argument: Scalar -> Scalar Argument: Vector -> Vector Argument: Tensor -> Tensor Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the complex conjugate of the complex number. If the argument is a complex number, returns a complex number; if it is a real number, return a real number. If the argument is a vector or tensor, calculates the complex conjugate of each component and return a vector or tensor with these complex conjugates as components.
PHASE	Argument 1: Scalar (deg) Real Number Argument 2: Scalar/Vector/Tensor Complex Number/Real Number	Argument 2: Scalar -> Scalar Argument 2: Vector -> Vector Argument 2: Tensor -> Tensor Real Number	Returns the magnitude of the complex number (Argument 2) at a particular phase (Argument 1 [deg]). Whether Argument 2 is a complex or real number, returns a real number. If Argument 2 is a vector or tensor, calculates the magnitude of each component at the phase of Argument 1 and return a vector or tensor with these magnitudes as components.
PHASE_VALUE	Scalar/Vector/Tensor Complex Number/Real Number	Argument: Scalar -> Scalar (deg) Argument: Vector -> Vector (deg) Argument: Tensor -> Tensor (deg) Real Number	Returns the phase [deg] of the complex number. Whether Argument 2 is a complex or real number, returns a real number. If the argument is a vector or tensor, calculates the phase of each component and return a vector or tensor with these phases as components.
COORD	No arguments required.	Vector Real Number	Return the coordinates. Represented as "COORD()."
GAS_CONSTANT	No arguments required.	Scalar Real Number	Returns the gas constant, R = 8.314462618 [J/deg/mol].
AMBIENT_PRESSURE	No arguments required.	Scalar Real Number	Returns the ambient pressure defined on the fluid analysis tab.

Functions (Vector/Tensor）

Function	Argument	Return Value	Note
VEC_X	Vector Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the X component of the vector argument.
VEC_Y	Vector Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the Y component of the vector argument.
VEC_Z	Vector Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the Z component of the vector argument.
VEC_LENGTH	Vector Complex Number/Real Number	Scalar Real Number	Returns the magnitude of the vector argument. If the argument is a complex number, returns a real number
TEN_XX	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the XX component of the tensor argument (X-direction normal component).
TEN_YY	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the YY component of the tensor argument (Y-direction normal component).
TEN_ZZ	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the ZZ component of the tensor argument (Z-direction normal component).
TEN_YZ	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the YZ component of the tensor argument (Shear component).
TEN_ZX	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the ZX component of the tensor argument (Shear component).
TEN_XY	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the XY component of the tensor argument (Shear component).
TEN_ZY	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the ZY component of the tensor argument (Shear component).
TEN_XZ	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the XZ component of the tensor argument (Shear component).
TEN_YX	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the YX component of the tensor argument (Shear component).
TEN_P1	Tensor Complex Number/Real Number	Scalar Real Number	Returns the maximum principal value of the tensor argument (if the display type is stress type, maximum principal stress; if it is strain type, maximum principal strain). If the argument is a complex number, returns a real number
TEN_P2	Tensor Real Number	Scalar Real Number	Returns the intermediate principal value of the tensor argument (if the display type is stress type, intermediate principal stress; if it is strain type, intermediate principal strain). If the argument is a complex number, unable to output.
TEN_P3	Tensor Complex Number/Real Number	Scalar Real Number	Returns the minimum principal value of the tensor argument (if the display type is stress type, minimum principal stress; if it is strain type, minimum principal strain). If the argument is a complex number, returns a real number
TEN_XZ_P1	Tensor Complex Number/Real Number	Scalar Real Number	Returns the XZ in-plane maximum principal value of the tensor argument (if the display type is stress type, maximum principal stress; if it is strain type, maximum principal strain). If the argument is a complex number, returns a real number
TEN_XZ_P2	Tensor Real Number	Scalar Real Number	Returns the XZ in-plane minimum principal value of the tensor argument (if the display type is stress type, minimum principal stress; if it is strain type, minimum principal strain). If the argument is a complex number, returns a real number
TEN_XY_P1	Tensor Complex Number/Real Number	Scalar Real Number	Returns the XY in-plane maximum principal value of the tensor argument (if the display type is stress type, maximum principal stress; if it is strain type, maximum principal strain). If the argument is a complex number, returns a real number
TEN_XY_P2	Tensor Real Number	Scalar Real Number	Returns the XY in-plane minimum principal value of the tensor argument (if the display type is stress type, minimum principal stress; if it is strain type, minimum principal strain). If the argument is a complex number, returns a real number
TEN_VOLUME	Tensor Complex Number/Real Number	Scalar Argument: Complex Number -> Complex Number Argument: Real Number -> Real Number	Returns the volumetric value of the tensor argument (if the display type is stress type, hydrostatic pressure; if it is strain type, volume strain).
TEN_EQUIV	Tensor Complex Number/Real Number	Scalar Real Number	Returns the equivalent value of the tensor argument (if the display type is stress type, von Mises equivalent stress; if it is strain type, equivalent strain). If the argument is a complex number, returns a real number
TEN_R	Tensor Complex Number/Real Number	Scalar Real Number	Returns the difference between the maximum and minimum principal values (if the display type is stress type, maximum shear stress; if it is strain type, maximum shear strain). If the argument is a complex number, returns a real number
MAKE_VEC	Arguments 1 to 3: Scalar Complex Number/Real Number	Vector Arguments 1 to 3: Complex Number -> Complex Number Arguments 1 to 3: Real Number -> Real Number	Constructs a vector from three arguments. Example: MAKE_VEC(1,2,3)
MAKE_TEN	Arguments 1 to 9: Scalar Complex Number/Real Number	Tensor Arguments 1 to 3: Complex Number -> Complex Number Arguments 1 to 3: Real Number -> Real Number	Constructs a tensor from nine arguments. Example: MAKE_TEN(1.2, 3.4, 5.6, 1,2,9)
UNIT_TEN	No arguments required.	Tensor Real Number	Creates a unit tensor (diagonal elements are 1, and all other elements are 0).
INNER_PRODUCT	Argument 1, Argument 2: Scalar/Vector/Tensor Complex Number/Real Number	Scalar Complex Number -> Complex Number Real Number -> Real Number	Calculates the inner product of two scalar arguments, vector arguments, and tensor arguments. For a vector or tensor argument, sum the products of their respective components. If the argument is a complex number, returns a real number Example: 0.5*INNER_PRODUCT(GALILEO_STRAIN_E,GALILEO_STRESS) Calculates the strain energy density (static analysis).
INNER_PRODUCT_CONJ	Argument 1: Scalar/Vector/Tensor Complex Number/Real Number Argument 2: Scalar/Vector/Tensor Complex Number/Real Number	Scalar Real Number	Calculates the inner product of two scalar arguments, vector arguments, and tensor arguments. For a vector or tensor argument, sum the products of their respective components. If the arguments are complex numbers, returns a real number calculated using the complex conjugate of the second argument. Example: 0.25*INNER_PRODUCT(GALILEO_STRAIN_E,GALILEO_STRESS) Calculates the strain energy density (average).
CROSS_PRODUCT	Argument 1: Vector Complex Number/Real Number Argument 2: Vector Complex Number/Real Number	Vector Complex Number -> Complex Number Real Number -> Real Number	Calculates the outer product of two vector arguments. Example: 0.5*CROSS_PRODUCT(HERTZ_ELECTRIC_FIELD,HERTZ_MAGNETIC_FIELD) Calculates the poynting vector (vibration).
CROSS_PRODUCT_CONJ	Argument 1: Vector Complex Number/Real Number Argument 2: Vector Complex Number/Real Number	Vector Real Number	Calculates the outer product of two vector arguments. If the arguments are complex numbers, returns a real number calculated using the complex conjugate of the second argument. Example: 0.5*CROSS_PRODUCT(HERTZ_ELECTRIC_FIELD,HERTZ_MAGNETIC_FIELD) Calculates the poynting vector (average).
TRANS	Tensor Complex Number/Real Number	Tensor Complex Number -> Complex Number Real Number -> Real Number	Converts the tensor argument to a transposed matrix.
INVERSE	Tensor Complex Number/Real Number	Tensor Complex Number -> Complex Number Real Number -> Real Number	Converts the tensor argument to an inverse matrix.
DET	Tensor Complex Number/Real Number	Scalar Complex Number -> Complex Number Real Number -> Real Number	Calculates the determinant of the tensor argument.