Multiply the transpose of a matrix with another matrix, both of arbitrary size. (The dimensions of the matrices must be compatible with this multiplication.)
VARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m1 I nr1r2 X ncol1 double precision matrix. m2 I nr1r2 X ncol2 double precision matrix. ncol1 I Column dimension of m1 and row dimension of mout. nr1r2 I Row dimension of m1 and m2. ncol2 I Column dimension of m2 (and also mout). mout O Transpose of m1 times m2.
m1 is any double precision matrix of arbitrary size. m2 is any double precision matrix of arbitrary size. The number of rows in m2 must match the number of rows in m1. ncol1 is the number of columns in m1 and the number of rows of mout. nr1r2 is the number of rows in both m1 and (by necessity) m2. ncol2 is the number of columns in both m2 and mout.
mout mout is the product matrix defined as the transpose of m1 times m2, that is t mout = (m1) x (m2) where the superscript t denotes the transpose of m1. mout is a double precision matrix of dimension ncol1 x ncol2. 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 ncol1, and j from 1 to ncol2: mout(i,j) = Summation from k=1 to nr1r2 of m1(k,i) * m2(k,j)
1) Suppose that m1 = | 1 2 3 0 | | 1 1 1 1 | and that m2 = | 1 2 3 | | 0 0 0 | Then calling mtxmg_c as shown mtxmg_c ( m1, m2, 4, 2, 3, mout ) will yield the following value for mout: | 1 2 3 | mout = | 2 4 6 | | 3 6 9 | | 0 0 0 |
1) No error checking is performed to prevent numeric overflow or underflow. 2) No error checking performed to determine if the input and output matrices have, in fact, been correctly dimensioned.
1) If dynamic allocation of memory fails, the error SPICE(MEMALLOCFAILED) is signalled.
N.J. Bachman (JPL) W.M. Owen (JPL)
-CSPICE Version 1.2.0, 28-AUG-2001 (NJB) Const-qualified input arrays. -CSPICE Version 1.0.0, 16-APR-1999 (NJB)
matrix transpose times matrix n-dimensional_case