DEQATN

Format

Example 1

Example 2

Definitions

Restrictions

Possible Errors

Comments

1. Each equation card is specified in a fixed format, without the limitation of data field boundaries. Equations are located in columns 17-72 on the first card, and in columns 9-72 on each continuation card. There is no limit on the total length of any equation.
2. Large field format is not allowed.
3. Free field format is allowed, but only the same number of characters as in the fixed format (56 on the first line and 64 on the continuation lines) and will be accepted. Characters after the 72nd column will not be accepted. Excess characters are silently disregarded, which may result in DEQATN error or in a valid expression different from that intended. On the continuation card in free format, the comma must be present within the first 8 columns; otherwise, the card will be interpreted in a fixed field format.
4. Blank characters in the equation have no effect, even within a constant, variable or function name. Lower and upper case letters are equivalent.
5. There must be only one variable at the left-hand side of each equation in any equation card. The variable of the first equation must be followed by an argument list in the following format:

   v1(x1,x2,…,xn) = expression(x1,x2,…,xn);
   v2 = expression(x1,x2,…,xn,v1);
   …
   vi  = expression(x1,x2,…,xn,v1,v2,…,vi-1);
   …
   vn = expression(x1,x2,…,xn,v1,v2,…,vn-1);

   Where, vi is the variable of equation i. (x1, x2, …, xn) is the argument list for variable v1. (v1,v2,…,vi-1) is the variable list which corresponds to the result of equation 1 through equation i-1.

   Only the value of the last expression is returned to the Bulk Data card referencing EQUID (DRESP2).

6. Constants can be specified in a format of either integer or floating point. A floating point number can be in a format of either normal decimal-point format (3.90) or scientific notation (-2.0E-3), which means -2×10^-3.
   The list of supported mathematical functions is:

   One-argument functions

   abs(x)

   absolute value

   acos(x)

   arccosine

   acosh(x)

   hyperbolic arccosine

   asin(x)

   arcsine

   asinh(x)

   hyperbolic arcsine

   atan(x)

   arctangent

   atanh(x)

   hyperbolic arctangent

   cos(x)

   cosine

   cosh(x)

   hyperbolic cosine

   exp(x)

   exponential

   log(x)

   natural logarithm

   log10(x)

   common logarithm

   pi(x)

   multiples of π

   sin(x)

   sine

   sinh(x)

   hyperbolic sine

   int (x)

   real to integer conversion

   sqrt(x)

   square root

   Two-argument functions

   atan2(x,y)

   actangent of quotient

   ${\tan }^{-1}\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$y$}\right.\right)$

   atanh2(x,y)

   hyperbolic actangent of quotient

   ${\tanh }^{-1}\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$y$}\right.\right)$

   dim(x,y)

   positive difference

   $x-\min (x,y)$

   logx(x,y)

   base y logarithm

   $lo{g}_y\left(x\right)$

   mod(x,y)

   remainder

   $x-y\times \left(INT\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$y$}\right.\right)\right)$

   Multi-argument functions

   $avg\left(x_1,x{}_2,\mathrm{...}{x}_n\right)$

   $Average,\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_1}$

   $\max \left(x_1,x_2,\dots x_n\right)$

   $\text{maximum}\text{of}\left(x_1,x_2,\dots x_n\right)$

   $\min \left(x_1,x_2,\dots x_n\right)$

   $\text{minimum}\text{of}\left(x_1,x_2,\dots x_n\right)$

   $rss\left(x_1,x_2,\dots x_n\right)$

   $\text{Square Root of Sum of Squares,}\sqrt{{\displaystyle \sum _{i=1}^n{x}_i^2}}$

   $ssq\left(x_1,x_2,\dots x_n\right)$

   $\text{Sum of Squares,}{\displaystyle \sum _{i=1}^n{x}_i^2}$

   $sum\left(x_1,x_2,\dots x_n\right)$

   $\text{Summation,}{\displaystyle \sum _{i=1}^n{x}_i}$

   $maxabs\left(x_1,x_2,\dots x_n\right)$

   $\text{maximum of}\left(\left|x_1\right|,\left|x_2\right|,\dots \left|x_n\right|\right)$

   $minabs\left(x_1,x_2,\dots x_n\right)$

   $\text{minimum of}\left(\left|x_1\right|,\left|x_2\right|,\dots \left|x_n\right|\right)$

   $avgabs\left(x_1,x_2,\dots x_n\right)$

   $\text{Average}\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|x_i\right|}$

   $sumabs\left(x_1,x_2,\dots x_n\right)$

   $\text{Summation}{\displaystyle \sum _{i=1}^n\left|x_i\right|}$

7. The supported operators are:

   Symbol	Meaning	Example
   +	binary +	x + y
   -	binary -	x - y
   *	multiplication,	x * y
   /	division	x / y
   **	power	x**y
   +	unary +	+1.0
   -	unary -	-1.0

8. The precedence of mathematical calculations follows the rules of Fortran language. Parenthesis has a higher priority in the order of precedence than the operators listed above. Two consecutive operators are acceptable only if the second one is unary, plus or minus.
   Examples of operator precedence:

   Expression

   Result

   2**-3

   0.128

   1 / 2 + 3

   3.5

   2*3-4

   2.0

   -2**3**2

   -512.0

   2 + -5

   -3.0

   2 * -5

   -10.0

   2 - -5

   7.0

   2/3/4

   0.16666666…

   2/(3/4)

   2.6666666…

9. Functions can be defined in a layered format, for example, min(sin(x1), x2), with no limit on the number of layers.
10. The DEQATN entry is referenced by DRESP2 and/or DVPREL2 Bulk Data cards.

    DRESP2 card, the variable identified by DVIDi, LABj, NRk, Gr and DPIP correspond to variable arguments listed in the left-hand side of the first equation of a DEQATN card identified by EQUID. The variable arguments x1 through xN (where N = n + m + p + q + s) are assigned in the order DVID1, DVID2, …, DVIDn, LAB1, LAB2, …, LABm, NR1,NR2, …, NRp, G1, …, Gq, DPIP1,…,DPIPS. In a DVPREL2 card, the variables identified by DVIDi and LABj correspond to variable arguments listed in the left-hand side of the first equation of a DEQATN card identified by EQUID. The variable arguments x1 through xN (where N = n + m) are assigned in the order DVID1, DVID2, …, DVIDn, LAB1, LAB2, …, LABm.

    Only the computed value of the last expression (vn) is used by DRESP2 and/or DVPREL2 entry.

11. This card is represented as an optimization function in HyperMesh.