SORM22 overwrites the general real M-by-N matrix C with


                  SIDE = 'L'     SIDE = 'R'


  TRANS = 'N':      Q * C          C * Q


  TRANS = 'T':      Q**T * C       C * Q**T


  where Q is a real orthogonal matrix of order NQ, with NQ = M if


  SIDE = 'L' and NQ = N if SIDE = 'R'.


  The orthogonal matrix Q processes a 2-by-2 block structure


         [  Q11  Q12  ]


     Q = [            ]


         [  Q21  Q22  ],


  where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an


  N2-by-N2 upper triangular matrix.

SIDE

          SIDE is CHARACTER*1


          = 'L': apply Q or Q**T from the Left;


          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1


          = 'N':  apply Q (No transpose);


          = 'C':  apply Q**T (Conjugate transpose).

M

          M is INTEGER


          The number of rows of the matrix C. M >= 0.

N

          N is INTEGER


          The number of columns of the matrix C. N >= 0.

N1
N2

          N1 is INTEGER


          N2 is INTEGER


          The dimension of Q12 and Q21, respectively. N1, N2 >= 0.


          The following requirement must be satisfied:


          N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

Q

          Q is REAL array, dimension


                              (LDQ,M) if SIDE = 'L'


                              (LDQ,N) if SIDE = 'R'

LDQ

          LDQ is INTEGER


          The leading dimension of the array Q.


          LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.

C

          C is REAL array, dimension (LDC,N)


          On entry, the M-by-N matrix C.


          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.


          If SIDE = 'L', LWORK >= max(1,N);


          if SIDE = 'R', LWORK >= max(1,M).


          For optimum performance LWORK >= M*N.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal size of the WORK array, returns


          this value as the first entry of the WORK array, and no error


          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

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NAG Ltd.

January 2015