Multiply the transpose of a matrix and a vector of arbitrary size.
VARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- m1 I Left-hand matrix to be multiplied. v2 I Right-hand vector to be multiplied. ncol1 I Column dimension of m1 and length of vout. nr1r2 I Row dimension of m1 and length of v2. vout O Product vector m1 transpose * v2.
m1 is a double precision matrix of arbitrary size which forms the left-hand matrix of the multiplication. v2 is a double precision vector on the right of the multiplication. ncol1 is the column dimension of m1 and length of vout. nr1r2 is the row dimension of m1 and length of v2.
vout is the double precision vector which results from the multiplication t vout = (m1) x v2 where the superscript t denotes the transpose of a matrix. vout has length ncol1. vout may overwrite m1 or v2. 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, vout(i) = Summation from k=1 to nr1r2 of ( m1(k,i) * v2(k) )
1) Suppose that | 1 2 | m1 = | 1 3 | | 1 4 | and that | 1 | v2 = | 2 | | 3 | Then calling mxvg_c as shown mtxvg_c ( m1, v2, 2, 3, vout ); will yield the following vector value for vout: vout = | 6 | | 20 |
1) The user is responsible for checking the magnitudes of the elements of m1 and v2 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. Based on SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)
matrix transpose times n-dimensional vector