LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ sort03()

subroutine sort03 ( character*( * )  RC,
integer  MU,
integer  MV,
integer  N,
integer  K,
real, dimension( ldu, * )  U,
integer  LDU,
real, dimension( ldv, * )  V,
integer  LDV,
real, dimension( * )  WORK,
integer  LWORK,
real  RESULT,
integer  INFO 
)

SORT03

Purpose:
 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.
Parameters
[in]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.
[in]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.
[in]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.
[in]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.
[in]K
          K is INTEGER
          The number of rows or columns of U and V to compare.
          0 <= K <= max(MU,MV).
[in]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.
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  If RC = 'R', LDU >= max(1,MU),
          and if RC = 'C', LDU >= max(1,N).
[in]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.
[in]LDV
          LDV is INTEGER
          The leading dimension of V.  If RC = 'R', LDV >= max(1,MV),
          and if RC = 'C', LDV >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]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.
[out]RESULT
          RESULT is REAL
          The value computed by the test described above.  RESULT is
          limited to 1/ulp to avoid overflow.
[out]INFO
          INFO is INTEGER
          0  indicates a successful exit
          -k indicates the k-th parameter had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.