DEQATN

Bulk Data Entry Specifies one or more equations for use in optimization.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DEQATN EQUID EQN1; EQN2; EQN3;  
  …; … ; EQNn-1; EQNn  

Example 1

DEQATN 3 y(x1, x2) = x1 + x2**-3.0*(2-1)+5.0;  
  z = -y*1.3E-2  

Example 2

DEQATN 104 z(x1, x2) = min(sin(x1), x2);  
  y = max(0.3, -2.0, z) + 4.0  

Definitions

Field Contents SI Unit Example
EQUID Unique equation identification number.

(Integer > 0)

 
EQNi i-th equation.

(Character string)

 

Restrictions

  • Variable names longer than 8 characters are truncated, which may create an error in equation if two names are identical after such truncation.
  • All trigonometric arguments are in radians.
  • Only alphanumeric characters may be used in variable names (that is do not use underscores, monetary symbols, punctuation symbols, mathematical operators, letters from non-English alphabet, and so on).
  • Mathematical function names (such as those listed in Comment 6) should not be used as variable names.
  • The following functions are not accepted:
    DB()
    DBA()
    INVDB()
    INVDBA()

Possible Errors

An informative error message with the DEQATN ID will be displayed if the parsing of the equation fails. However, in certain cases, the following generic message will be provided:
Error 1690
This equation could not be parsed. See the DEQATN entry in the OptiStruct manual.
This error message means that it was not possible to clearly identify the reason for the failure. If this happens, check for the following possible causes, and contact ossupport@altair.com:
  • The length of the equation exceeds the 72 character per line limitation
  • The last character of the equation is an operator
  • There are two adjacent operators in the equation
  • There are non-alphanumeric characters (besides operators) in the equation

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 ( x y )
    atanh2(x,y)
    hyperbolic actangent of quotient
    tanh 1 ( x y )
    dim(x,y)
    positive difference
    x min ( x , y )
    logx(x,y)
    base y logarithm
    lo g y ( x ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGSbGaam4BaiaadEgapaWaaSbaaSqaa8qacaWG5baapaqabaGc daqadaqaa8qacaWG4baapaGaayjkaiaawMcaaaaa@3CEE@
    mod(x,y)
    remainder
    x y × ( I N T ( x y ) )
    Multi-argument functions
    a v g ( x 1 , x , 2 ... x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiaadA hacaWGNbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgbaWcbaGaaGOmaaqabaGccaGGSaGaaiOlaiaac6caca GGUaGaamiEamaaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa @43C6@
    A v e r a g e , 1 n i = 1 n x 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadA hacaWGLbGaamOCaiaadggacaWGNbGaamyzaiaacYcadaWcaaqaaiaa igdaaeaacaWGUbaaamaaqahabaGaamiEamaaBaaaleaacaaIXaaabe aaaeaacaWGPbGaeyypa0JaaGymaaqaaiaad6gaa0GaeyyeIuoaaaa@467F@
    max ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacg gacaGG4bWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42D8@
    maximum of ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyBaiaabg gacaqG4bGaaeyAaiaab2gacaqG1bGaaeyBaiaaykW7caqGVbGaaeOz amaabmaabaGaamiEamaaBaaaleaacaaIXaaabeaakiaacYcacaWG4b WaaSbaaSqaaiaaikdaaeqaaOGaaiilaiablAciljaadIhadaWgaaWc baGaamOBaaqabaaakiaawIcacaGLPaaaaaa@49FD@
    min ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacg gacaGG4bWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42D8@
    minimum of ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyBaiaabg gacaqG4bGaaeyAaiaab2gacaqG1bGaaeyBaiaaykW7caqGVbGaaeOz amaabmaabaGaamiEamaaBaaaleaacaaIXaaabeaakiaacYcacaWG4b WaaSbaaSqaaiaaikdaaeqaaOGaaiilaiablAciljaadIhadaWgaaWc baGaamOBaaqabaaakiaawIcacaGLPaaaaaa@49FD@
    rss( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    Square Root of Sum of Squares, i=1 n x i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabg hacaqG1bGaaeyyaiaabkhacaqGLbGaaeiiaiaabkfacaqGVbGaae4B aiaabshacaqGGaGaae4BaiaabAgacaqGGaGaae4uaiaabwhacaqGTb Gaaeiiaiaab+gacaqGMbGaaeiiaiaabofacaqGXbGaaeyDaiaabgga caqGYbGaaeyzaiaabohacaqGSaGaaGPaVpaakaaabaWaaabCaeaaca WG4bWaa0baaSqaaiaadMgaaeaacaaIYaaaaaqaaiaadMgacqGH9aqp caaIXaaabaGaamOBaaqdcqGHris5aaWcbeaaaaa@5A47@
    s s q ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    Sum of Squares, i=1 n x i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabw hacaqGTbGaaeiiaiaab+gacaqGMbGaaeiiaiaabofacaqGXbGaaeyD aiaabggacaqGYbGaaeyzaiaabohacaqGSaGaaGPaVpaaqahabaGaam iEamaaDaaaleaacaWGPbaabaGaaGOmaaaaaeaacaWGPbGaeyypa0Ja aGymaaqaaiaad6gaa0GaeyyeIuoaaaa@4D35@
    s u m ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    Summation, i=1 n x i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabw hacaqGTbGaaeyBaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaaeil aiaaykW7daaeWbqaaiaadIhadaWgaaWcbaGaamyAaaqabaaabaGaam yAaiabg2da9iaaigdaaeaacaWGUbaaniabggHiLdaaaa@4878@
    m a x a b s ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    maximum of( | x 1 |,| x 2 |,| x n | ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyBaiaabg gacaqG4bGaaeyAaiaab2gacaqG1bGaaeyBaiaabccacaqGVbGaaeOz aiaaykW7daqadaqaamaaemaabaGaamiEamaaBaaaleaacaaIXaaabe aaaOGaay5bSlaawIa7aiaacYcadaabdaqaaiaadIhadaWgaaWcbaGa aGOmaaqabaaakiaawEa7caGLiWoacaGGSaGaeSOjGS0aaqWaaeaaca WG4bWaaSbaaSqaaiaad6gaaeqaaaGccaGLhWUaayjcSdaacaGLOaGa ayzkaaaaaa@5406@
    m i n a b s ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    minimum of( | x 1 |,| x 2 |,| x n | ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyBaiaabM gacaqGUbGaaeyAaiaab2gacaqG1bGaaeyBaiaabccacaqGVbGaaeOz aiaaykW7daqadaqaamaaemaabaGaamiEamaaBaaaleaacaaIXaaabe aaaOGaay5bSlaawIa7aiaacYcadaabdaqaaiaadIhadaWgaaWcbaGa aGOmaaqabaaakiaawEa7caGLiWoacaGGSaGaeSOjGS0aaqWaaeaaca WG4bWaaSbaaSqaaiaad6gaaeqaaaGccaGLhWUaayjcSdaacaGLOaGa ayzkaaaaaa@5404@
    a v g a b s ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    Average 1 n i=1 n | x i | MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiaabA hacaqGLbGaaeOCaiaabggacaqGNbGaaeyzaiaaykW7caaMe8+aaSaa aeaacaaIXaaabaGaamOBaaaadaaeWbqaamaaemaabaGaamiEamaaBa aaleaacaWGPbaabeaaaOGaay5bSlaawIa7aaWcbaGaamyAaiabg2da 9iaaigdaaeaacaWGUbaaniabggHiLdaaaa@4C43@
    s u m a b s ( x 1 , x 2 , x n ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiaado hacaWGZbWaaeWaaeaacaWG4bWaaSbaaSqaaiaaigdaaeqaaOGaaiil aiaadIhadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaeSOjGSKaamiEam aaBaaaleaacaWGUbaabeaaaOGaayjkaiaawMcaaaaa@42EB@
    Summation i=1 n | x i | MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabw hacaqGTbGaaeyBaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaaGPa VpaaqahabaWaaqWaaeaacaWG4bWaaSbaaSqaaiaadMgaaeqaaaGcca GLhWUaayjcSdaaleaacaWGPbGaeyypa0JaaGymaaqaaiaad6gaa0Ga eyyeIuoaaaa@4B00@
  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.