SORT03 compares two orthogonal matrices U and V to see if their


 corresponding rows or columns span the same spaces.  The rows are


 checked if RC = 'R', and the columns are checked if RC = 'C'.


 RESULT is the maximum of


    | V*V' - I | / ( MV ulp ), if RC = 'R', or


    | V'*V - I | / ( MV ulp ), if RC = 'C',


 and the maximum over rows (or columns) 1 to K of


    | U(i) - S*V(i) |/ ( N ulp )


 where S is +-1 (chosen to minimize the expression), U(i) is the i-th


 row (column) of U, and V(i) is the i-th row (column) of V.

RC

          RC is CHARACTER*1


          If RC = 'R' the rows of U and V are to be compared.


          If RC = 'C' the columns of U and V are to be compared.

MU

          MU is INTEGER


          The number of rows of U if RC = 'R', and the number of


          columns if RC = 'C'.  If MU = 0 SORT03 does nothing.


          MU must be at least zero.

MV

          MV is INTEGER


          The number of rows of V if RC = 'R', and the number of


          columns if RC = 'C'.  If MV = 0 SORT03 does nothing.


          MV must be at least zero.

N

          N is INTEGER


          If RC = 'R', the number of columns in the matrices U and V,


          and if RC = 'C', the number of rows in U and V.  If N = 0


          SORT03 does nothing.  N must be at least zero.

K

          K is INTEGER


          The number of rows or columns of U and V to compare.


          0 <= K <= max(MU,MV).

U

          U is REAL array, dimension (LDU,N)


          The first matrix to compare.  If RC = 'R', U is MU by N, and


          if RC = 'C', U is N by MU.

LDU

          LDU is INTEGER


          The leading dimension of U.  If RC = 'R', LDU >= max(1,MU),


          and if RC = 'C', LDU >= max(1,N).

V

          V is REAL array, dimension (LDV,N)


          The second matrix to compare.  If RC = 'R', V is MV by N, and


          if RC = 'C', V is N by MV.

LDV

          LDV is INTEGER


          The leading dimension of V.  If RC = 'R', LDV >= max(1,MV),


          and if RC = 'C', LDV >= max(1,N).

WORK

          WORK is REAL array, dimension (LWORK)

LWORK

          LWORK is INTEGER


          The length of the array WORK.  For best performance, LWORK


          should be at least N*N if RC = 'C' or M*M if RC = 'R', but


          the tests will be done even if LWORK is 0.

RESULT

          RESULT is REAL


          The value computed by the test described above.  RESULT is


          limited to 1/ulp to avoid overflow.

INFO

          INFO is INTEGER


          0  indicates a successful exit


          -k indicates the k-th parameter had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.