Parallel array formulas

constraint1 : { dimensions: [6], formula: "sqrt((x - dx)^2 + (y - dy)^2) - z", upper: 0 }

This type of array formula is interpreted (evaluated) only once. Every operation is executed in parallel for all components of its array operands. In the above example, x, y, z are scalars, while dx and dy are 1-D arrays containing 6 elements each. The operation (x - dx) is executed for all 6 elements of dx resulting in a 1-D array of 6 elements.

The multi-dimensional result of the formula evaluation is assigned to an array variable with the appropriate dimensions. In the above example, the result is held by the 1-D vertical array constraint1, which has 6 elements. If the formula definition is in the constraints section, one constraint will be generated for each component of the result.

The result of the evaluation is a 1-D horizontal/vertical array, or 2-D array. If a table slice is presented in the formula, it is always considered a vertical array in parallel operations. Currently, the RASON modeling language supports only 2-D arrays. The biggest disadvantage of this array formula type is the prevention of the reverse mode of evaluation which is much faster than the native forward evaluation.