DTPMQRT applies a real orthogonal matrix Q obtained from a


 "triangular-pentagonal" real block reflector H to a general


 real matrix C, which consists of two blocks A and B.

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':  No transpose, apply Q;


          = 'T':  Transpose, apply Q**T.

M

          M is INTEGER


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

N

          N is INTEGER


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

K

          K is INTEGER


          The number of elementary reflectors whose product defines


          the matrix Q.

L

          L is INTEGER


          The order of the trapezoidal part of V.


          K >= L >= 0.  See Further Details.

MB

          MB is INTEGER


          The block size used for the storage of T.  K >= MB >= 1.


          This must be the same value of MB used to generate T


          in DTPLQT.

V

          V is REAL array, dimension (LDA,K)


          The i-th row must contain the vector which defines the


          elementary reflector H(i), for i = 1,2,...,k, as returned by


          DTPLQT in B.  See Further Details.

LDV

          LDV is INTEGER


          The leading dimension of the array V.


          If SIDE = 'L', LDV >= max(1,M);


          if SIDE = 'R', LDV >= max(1,N).

T

          T is REAL array, dimension (LDT,K)


          The upper triangular factors of the block reflectors


          as returned by DTPLQT, stored as a MB-by-K matrix.

LDT

          LDT is INTEGER


          The leading dimension of the array T.  LDT >= MB.

A

          A is REAL array, dimension


          (LDA,N) if SIDE = 'L' or


          (LDA,K) if SIDE = 'R'


          On entry, the K-by-N or M-by-K matrix A.


          On exit, A is overwritten by the corresponding block of


          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.

LDA

          LDA is INTEGER


          The leading dimension of the array A.


          If SIDE = 'L', LDC >= max(1,K);


          If SIDE = 'R', LDC >= max(1,M).

B

          B is REAL array, dimension (LDB,N)


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


          On exit, B is overwritten by the corresponding block of


          Q*C or Q**T*C or C*Q or C*Q**T.  See Further Details.

LDB

          LDB is INTEGER


          The leading dimension of the array B.


          LDB >= max(1,M).

WORK

          WORK is REAL array. The dimension of WORK is


           N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.

INFO

          INFO is INTEGER


          = 0:  successful exit


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2017

  The columns of the pentagonal matrix V contain the elementary reflectors


  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a


  trapezoidal block V2:


        V = [V1] [V2].


  The size of the trapezoidal block V2 is determined by the parameter L,


  where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L


  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower triangular;


  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.


  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.


                      [B]


  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.


  The real orthogonal matrix Q is formed from V and T.


  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.


  If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.


  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.


  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.