section L of routines in global.i

home

index

 
             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.  
  

unknown type function, documented at startup/matrix.i   line 252

SEE ALSO:

LUsolve

 
             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.  
  

unknown type function, documented at startup/matrix.i   line 149