12.7 Vector operations

The following simple vector operations are possible:

• Copying or appending a vector to another vector. For instance S=R copies a vector R to a vector S. S(3)=R copies R to S(3), S(4), .... S(#S+1)=R appends vector R to vector S. It is also possible to access a range of subsequent elements in a vector: S=R(2:4) copies elements 2 to 4 of R to S(1), S(2), S(3). Note that R(2:) denotes elements R(2) to R(#R), but R(2) denotes a single element of R.

• Vector-scalar operations: R=R*2 multiplies each element of R by 2. Instead of the number 2, also scalar (one dimensional) variables or expressions can be used, e.g., R=R*ANG converts all elements of R from Ångstrøm to bohr, or Z=R*COS(THETA) creates a vector Z with elements Z(i) = R(i)*COS(THETA). All other algebraic operators can be used instead of ``*''.

• Vector-vector operations: If A and B are vectors of the same length, then A $\times$ B is also a vector of this length. Here $\times$ stands for any algebraic operator, and the operation is done for each pair of corresponding elements. For instance, A + B adds the vectors A and B, and A * B multiplies their elements. Note that the latter case is not a scalar product. If an attempt is made to connect two vectors of different lengths by an algebraic operator, an error occurs.

• Intrinsic functions: Assume THETA=[100,110,120,-130] to be a vector of angles (in degrees). In this case X=2*COS(THETA) is also a vector containing the cosines of each element of THETA multiplied by two, i.e., X(i) = 2*COS(THETA(i)). MAX(THETA) or MIN(THETA) return the maximum and minimum values, respectively, in array THETA. Vector operations can also be nested, e.g., MAX(ABS(THETA)) returns the maximum value in array ABS(THETA).

At present, vector operations are not supported with string variables.