DTPRFB applies a real "triangular-pentagonal" block reflector H or its 


 transpose H**T to a real matrix C, which is composed of two 


 blocks A and B, either from the left or right.

SIDE

          SIDE is CHARACTER*1


          = 'L': apply H or H**T from the Left


          = 'R': apply H or H**T from the Right

TRANS

          TRANS is CHARACTER*1


          = 'N': apply H (No transpose)


          = 'T': apply H**T (Transpose)

DIRECT

          DIRECT is CHARACTER*1


          Indicates how H is formed from a product of elementary


          reflectors


          = 'F': H = H(1) H(2) . . . H(k) (Forward)


          = 'B': H = H(k) . . . H(2) H(1) (Backward)

STOREV

          STOREV is CHARACTER*1


          Indicates how the vectors which define the elementary


          reflectors are stored:


          = 'C': Columns


          = 'R': Rows

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 order of the matrix T, i.e. the number of elementary


          reflectors whose product defines the block reflector.  


          K >= 0.

L

          L is INTEGER


          The order of the trapezoidal part of V.  


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

V

          V is DOUBLE PRECISION array, dimension


                                (LDV,K) if STOREV = 'C'


                                (LDV,M) if STOREV = 'R' and SIDE = 'L'


                                (LDV,N) if STOREV = 'R' and SIDE = 'R'


          The pentagonal matrix V, which contains the elementary reflectors


          H(1), H(2), ..., H(K).  See Further Details.

LDV

          LDV is INTEGER


          The leading dimension of the array V.


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


          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);


          if STOREV = 'R', LDV >= K.

T

          T is DOUBLE PRECISION array, dimension (LDT,K)


          The triangular K-by-K matrix T in the representation of the


          block reflector.  

LDT

          LDT is INTEGER


          The leading dimension of the array T. 


          LDT >= K.

A

          A is DOUBLE PRECISION 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 


          H*C or H**T*C or C*H or C*H**T.  See Futher 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 DOUBLE PRECISION array, dimension (LDB,N)


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


          On exit, B is overwritten by the corresponding block of


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

LDB

          LDB is INTEGER


          The leading dimension of the array B. 


          LDB >= max(1,M).

WORK

          WORK is DOUBLE PRECISION array, dimension


          (LDWORK,N) if SIDE = 'L',


          (LDWORK,K) if SIDE = 'R'.

LDWORK

          LDWORK is INTEGER


          The leading dimension of the array WORK.


          If SIDE = 'L', LDWORK >= K; 


          if SIDE = 'R', LDWORK >= M.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

  The matrix C is a composite matrix formed from blocks A and B.


  The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K, 


  and if SIDE = 'L', A is of size K-by-N.


  If SIDE = 'R' and DIRECT = 'F', C = [A B].


  If SIDE = 'L' and DIRECT = 'F', C = [A] 


                                      [B].


  If SIDE = 'R' and DIRECT = 'B', C = [B A].


  If SIDE = 'L' and DIRECT = 'B', C = [B]


                                      [A]. 


  The pentagonal matrix V is composed of a rectangular block V1 and a 


  trapezoidal block V2.  The size of the trapezoidal block is determined by 


  the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;


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


  If DIRECT = 'F' and STOREV = 'C':  V = [V1]


                                         [V2]


     - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)


  If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]


     - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)


  If DIRECT = 'B' and STOREV = 'C':  V = [V2]


                                         [V1]


     - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)


  If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]


    


     - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)


  If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.


  If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.


  If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.


  If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.