Multiply a matrix and the transpose of a matrix, both of arbitrary size.
VARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m1 I Left-hand matrix to be multiplied. m2 I Right-hand matrix whose transpose is to be multiplied nrow1 I Row dimension of m1 and row dimension of mout. nc1c2 I Column dimension of m1 and column dimension of m2. nrow2 I Row dimension of m2 and column dimension of mout. mout O Product matrix.
m1 may be any double precision matrix of arbitrary size. m2 may be any double precision matrix of arbitrary size. The number of columns in m2 must match the number of columns in m1. nrow1 is the number of rows in both m1 and mout. nc1c2 i the number of columns in m1 and (by necessity) the number of columns of m2. nrow2 is the number of rows in both m2 and the number of columns in mout.
mout is the product matrix given by t mout = (m1) x (m2) where the superscript "t" denotes the transpose matrix. This is a double precision matrix of dimension nrow1 x nrow2. mout may overwrite m1 or m2. Note that this capability does not exist in the Fortran version of SPICELIB; in the Fortran version, the output must not overwrite either input.
The code reflects precisely the following mathematical expression For each value of the subscript i from 1 to nrow1, and j from 1 to nrow2: mout(i,j) = summation from k=1 to nc1c2 of ( m1(i,k) * m2(j,k) ) Notice that the order of the subscripts of m2 are reversed from what they would be if this routine merely multiplied m1 and m2. It is this transposition of subscripts that makes this routine multiply m1 and the TRANPOSE of m2.
1) Let m1 = | 1.0 2.0 3.0 | | | | 3.0 2.0 1.0 | Let m2 = | 1.0 2.0 0.0 | | | | 2.0 1.0 2.0 | | | | 1.0 2.0 0.0 | | | | 2.0 1.0 2.0 | Here nrow1 = 2 nc1c2 = 3 nrow2 = 4 so the call mxmtg_c ( m1, m2, nrow1, nc1c2, nrow2, mout ); produces the matrix mout = | 5.0 10.0 5.0 10.0 | | | | 7.0 10.0 7.0 10.0 |
No error checking is performed to prevent numeric overflow or underflow. No error checking is performed to determine if the input and output matrices have, in fact, been correctly dimensioned. The user is responsible for checking the magnitudes of the elements of m1 and m2 so that a floating point overflow does not occur.
N.J. Bachman (JPL) W.M. Owen (JPL)
-CSPICE Version 1.2.0, 28-AUG-2001 (NJB) Const-qualified input arrays. -CSPICE Version 1.1.0, 08-FEB-1998 (NJB) Corrected a comment describing the local macro INDEX. Made miscellaneous code format corrections. -CSPICE Version 1.0.0, 25-OCT-1997 (NJB) Based on SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)
matrix times matrix_transpose n-dimensional_case