functions in matrix.i - L

    LUrcond(a)  
 or LUrcond(a, one_norm=1)  


returns the reciprocal condition number of the N-by-N matrix A.  
If the ONE_NORM argument is non-nil and non-zero, the 1-norm  
condition number is returned, otherwise the infinity-norm condition  
number is returned.  
The condition number is the ratio of the largest to the smallest  
singular value, max(singular_values)*max(1/singular_values) (or  
sum(abs(singular_values)*sum(abs(1/singular_values)) if ONE_NORM  
is selected?).  If the reciprocal condition number is near zero  
then A is numerically singular; specifically, if  
     1.0+LUrcond(a) == 1.0  
then A is numerically singular.  
Interpreted function, defined at i0/matrix.i   line 225  

    LUsolve(a, b)  
 or LUsolve(a, b, which=which)  
 or a_inverse= LUsolve(a)  


returns the solution x of the matrix equation:  
   A(,+)*x(+) = B  
If A is an n-by-n matrix then B must have length n, and the returned  
x will also have length n.  
B may have additional dimensions, in which case the returned x  
will have the same additional dimensions.  The WHICH dimension of B,  
and of the returned x is the one of length n which participates  
in the matrix solve.  By default, WHICH=1, so that the equations  
being solved are:  
   A(,+)*x(+,..) = B  
Non-positive WHICH counts from the final dimension (as for the  
sort and transpose functions), so that WHICH=0 solves:  
   x(..,+)*A(,+) = B  
Other examples:  
   A_ij X_jklm = B_iklm   (WHICH=1)  
   A_ij X_kjlm = B_kilm   (WHICH=2)  
   A_ij X_klmj = B_klmi   (WHICH=4 or WHICH=0)  
If the B argument is omitted, the inverse of A is returned:  
A(,+)*x(+,) and A(,+)*x(,+) will be unit matrices.  
LUsolve works by LU decomposition using Gaussian elimination with  
pivoting.  It is the fastest way to solve square matrices.  QRsolve  
handles non-square matrices, as does SVsolve.  SVsolve is slowest,  
but can deal with highly singular matrices sensibly.  
Interpreted function, defined at i0/matrix.i   line 106