Home Manual Packages Global Index Keywords Quick Reference | # functions in matrix.i - L
LUrcond |
                 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
SEE ALSO: | LUsolve
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.

    interpreted function, defined at i0/matrix.i   line 106
SEE ALSO: | QRsolve, TDsolve, SVsolve, SVdec, LUrcond