#include <vectmath.h>
CLRV(v) v = 0
i
UNITV(v,j) v = delta
i ij
SETV(v,u) v = u
i i
ADDV(v,u,w) v = u + w
i i i
SUBV(v,u,w) v = u - w
i i i
MULVS(v,u,s) v = u s
i i
DIVVS(v,u,s) v = u / s
i i
DOTVP(s,v,u) s = v u
i i
dotvp(v,u) v u
i i
ABSV(s,v) s = sqrt(v v )
i i
absv(v) sqrt(v v )
i i
DISTV(s,v,u) s = sqrt((v - u ) (v - u ))
i i i i
distv(v,u) sqrt((v - u ) (v - u ))
i i i i
CROSSVP(s,v,u) s = eps v u [only in 2-D]
ij i j
CROSSVP(v,u,w) v = eps u w [only in 3-D]
i ijk j k
CLRM(p) p = 0
ij
SETMI(p) p = delta
ij ij
SETM(p,q) p = q
ij ij
TRANM(p,q) p = q
ij ji
ADDM(p,q,r) p = q + r
ij ij ij
SUBM(p,q,r) p = q - r
ij ij ij
MULM(p,q,r) p = q r
ij ik kj
MULMS(p,q,s) p = q s
ij ij
DIVMS(p,q,s) p = q / s
ij ij
MULMV(v,p,u) v = p u
i ij j
OUTVP(p,v,u) p = v u
ij i j
TRACEM(s,p) s = Tr(p)
tracem(p) Tr(p)
SETVS(v,s) v = s
i
ADDVS(v,u,s) v = u + s
i i
SETMS(p,s) p = s
ij
MULVV(w,v,u) w = v * u
i i i
SADDV(v,u) v = v + u
i i i
SSUBV(v,u) v = v - u
i i i
SMULVS(v,s) v = v * s
i i
SDIVVS(v,s) v = v / s
i i
SMULVV(v,u) v = v * u
i i i
real s;
vector v, u, w;
matrix p, q, r;
To specify how many dimensions vectors have, define ONE of
the following symbols to the C preprocessor:
TWODIM - for 2-D vectors
THREEDIM - for 3-D vectors
NDIM - for N-D vectors
The symbols TWODIM and THREEDIM are flags, and may be defined with any
value whatsoever. NDIM is used as a value, namely (of course) the number
of dimensions. If either TWODIM or THREEDIM are defined, vectmath.h will
define NDIM to be 2 or 3 respectively, incase NDIM is subsequently needed.
If none of these symbols is defined when vectmath.h is included, the default
is THREEDIM. Note that CROSSVP is defined only for TWODIM and THREEDIM. Unless the symbol NOTYPEDEF is defined when vectmath.h is included, vector and matrix will be defined as NDIM and NDIM by NDIM arrays of real numbers, respectively (see stdinc(3NEMO) for a description of real). These may be used to declare vector and matrix objects to be manipulated.
The exact definitions
of these operations correspond to the index language expressions given
above. Some of these definitions imply restrictions on placing the same
object on both sides of the assignment operation. For example,
ADDV(v, v, u);does exactly the right thing, but
CROSSVP(v, v, u);puts garbage into v, instead of the cross-product of v and u.
Most of these
operations are implemented as macros which expand in line. A subtle point
connected with this is that syntactically, a reference to of one of these
macros is a statement, not an expression. This means that, for example,
the code fragment
if (foobar)
ADDV(x, y, z);
else
SUBV(x, y, z);
will not compile, because the terminating semi-colon following the ADDV
is seen as a seperate (null) statement. The best way to solve this problem
is to code the above example as follows: if (foobar) {
ADDV(x, y, z);
} else {
SUBV(x, y, z);
}
The enclosing curly-brackets insure that the code is syntactically correct
both before and after macro expansion.
Those operators which return a scalar
value instead of storing it (currently, dotvp, absv, distv, and tracem)
are implemented by functions which are called from macro expansions. These
functions need to know if their arguments are floating or double arrays;
vectmath.h uses the preprocessor symbol SINGLEPREC to determine the precision
in use. Mixed-precision expressions yield incorrect results; for example,
float x[NDIM]; double y[NDIM]; ... dotvp(x,y); will fail. Consistent use of the abstractions real, vector, and matrix is suggested. Some impure, but useful, vector and matrix operations are also defined. For example, ADDVS sets each element of a vector to a scalar, and MULVV multiplies two vectors with each other, element by element. BugsYou cannot (easily) mix vectors and matrices of different dimensionality within the same source code. History 30-nov-86 (man) Created JEB 22-oct-90 Merged in some starlab macros PJT 27-apr-92 Added SMULVV and documented starlab macros PJT