Loading...
Searching...
No Matches

## dtfsm()

subroutine dtfsm | ( | character | transr,
|  | character | side,
|  | character | uplo,
|  | character | trans,
|  | character | diag,
|  | integer | m,
|  | integer | n,
|  | double precision | alpha,
|  | double precision, dimension( 0: * ) | a,
|  | double precision, dimension( 0: ldb-1, 0: * ) | b,
|  | integer | ldb )

DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).

Download DTFSM + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> Level 3 BLAS like routine for A in RFP Format.
      !>
      !> DTFSM  solves the matrix equation
      !>
      !>    op( A )*X = alpha*B  or  X*op( A ) = alpha*B
      !>
      !> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
      !> non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
      !>
      !>    op( A ) = A   or   op( A ) = A**T.
      !>
      !> A is in Rectangular Full Packed (RFP) Format.
      !>
      !> The matrix X is overwritten on B.
      !>

Parameters

  [in]

  TRANSR

      !>          TRANSR is CHARACTER*1
      !>          = 'N':  The Normal Form of RFP A is stored;
      !>          = 'T':  The Transpose Form of RFP A is stored.
      !>

  [in]

  SIDE

      !>          SIDE is CHARACTER*1
      !>           On entry, SIDE specifies whether op( A ) appears on the left
      !>           or right of X as follows:
      !>
      !>              SIDE = 'L' or 'l'   op( A )*X = alpha*B.
      !>
      !>              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
      !>
      !>           Unchanged on exit.
      !>

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>           On entry, UPLO specifies whether the RFP matrix A came from
      !>           an upper or lower triangular matrix as follows:
      !>           UPLO = 'U' or 'u' RFP A came from an upper triangular matrix
      !>           UPLO = 'L' or 'l' RFP A came from a  lower triangular matrix
      !>
      !>           Unchanged on exit.
      !>

  [in]

  TRANS

      !>          TRANS is CHARACTER*1
      !>           On entry, TRANS  specifies the form of op( A ) to be used
      !>           in the matrix multiplication as follows:
      !>
      !>              TRANS  = 'N' or 'n'   op( A ) = A.
      !>
      !>              TRANS  = 'T' or 't'   op( A ) = A'.
      !>
      !>           Unchanged on exit.
      !>

  [in]

  DIAG

      !>          DIAG is CHARACTER*1
      !>           On entry, DIAG specifies whether or not RFP A is unit
      !>           triangular as follows:
      !>
      !>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
      !>
      !>              DIAG = 'N' or 'n'   A is not assumed to be unit
      !>                                  triangular.
      !>
      !>           Unchanged on exit.
      !>

  [in]

  M

      !>          M is INTEGER
      !>           On entry, M specifies the number of rows of B. M must be at
      !>           least zero.
      !>           Unchanged on exit.
      !>

  [in]

  N

      !>          N is INTEGER
      !>           On entry, N specifies the number of columns of B.  N must be
      !>           at least zero.
      !>           Unchanged on exit.
      !>

  [in]

  ALPHA

      !>          ALPHA is DOUBLE PRECISION
      !>           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
      !>           zero then  A is not referenced and  B need not be set before
      !>           entry.
      !>           Unchanged on exit.
      !>

  [in]

  A

      !>          A is DOUBLE PRECISION array, dimension (NT)
      !>           NT = N*(N+1)/2 if SIDE='R' and NT = M*(M+1)/2 otherwise.
      !>           On entry, the matrix A in RFP Format.
      !>           RFP Format is described by TRANSR, UPLO and N as follows:
      !>           If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
      !>           K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
      !>           TRANSR = 'T' then RFP is the transpose of RFP A as
      !>           defined when TRANSR = 'N'. The contents of RFP A are defined
      !>           by UPLO as follows: If UPLO = 'U' the RFP A contains the NT
      !>           elements of upper packed A either in normal or
      !>           transpose Format. If UPLO = 'L' the RFP A contains
      !>           the NT elements of lower packed A either in normal or
      !>           transpose Format. The LDA of RFP A is (N+1)/2 when
      !>           TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
      !>           even and is N when is odd.
      !>           See the Note below for more details. Unchanged on exit.
      !>

  [in,out]

  B

      !>          B is DOUBLE PRECISION array, dimension (LDB,N)
      !>           Before entry,  the leading  m by n part of the array  B must
      !>           contain  the  right-hand  side  matrix  B,  and  on exit  is
      !>           overwritten by the solution matrix  X.
      !>

  [in]

  LDB

      !>          LDB is INTEGER
      !>           On entry, LDB specifies the first dimension of B as declared
      !>           in  the  calling  (sub)  program.   LDB  must  be  at  least
      !>           max( 1, m ).
      !>           Unchanged on exit.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  We first consider Rectangular Full Packed (RFP) Format when N is
      !>  even. We give an example where N = 6.
      !>
      !>      AP is Upper             AP is Lower
      !>
      !>   00 01 02 03 04 05       00
      !>      11 12 13 14 15       10 11
      !>         22 23 24 25       20 21 22
      !>            33 34 35       30 31 32 33
      !>               44 45       40 41 42 43 44
      !>                  55       50 51 52 53 54 55
      !>
      !>
      !>  Let TRANSR = 'N'. RFP holds AP as follows:
      !>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
      !>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
      !>  the transpose of the first three columns of AP upper.
      !>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
      !>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
      !>  the transpose of the last three columns of AP lower.
      !>  This covers the case N even and TRANSR = 'N'.
      !>
      !>         RFP A                   RFP A
      !>
      !>        03 04 05                33 43 53
      !>        13 14 15                00 44 54
      !>        23 24 25                10 11 55
      !>        33 34 35                20 21 22
      !>        00 44 45                30 31 32
      !>        01 11 55                40 41 42
      !>        02 12 22                50 51 52
      !>
      !>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
      !>  transpose of RFP A above. One therefore gets:
      !>
      !>
      !>           RFP A                   RFP A
      !>
      !>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
      !>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
      !>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
      !>
      !>
      !>  We then consider Rectangular Full Packed (RFP) Format when N is
      !>  odd. We give an example where N = 5.
      !>
      !>     AP is Upper                 AP is Lower
      !>
      !>   00 01 02 03 04              00
      !>      11 12 13 14              10 11
      !>         22 23 24              20 21 22
      !>            33 34              30 31 32 33
      !>               44              40 41 42 43 44
      !>
      !>
      !>  Let TRANSR = 'N'. RFP holds AP as follows:
      !>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
      !>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
      !>  the transpose of the first two columns of AP upper.
      !>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
      !>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
      !>  the transpose of the last two columns of AP lower.
      !>  This covers the case N odd and TRANSR = 'N'.
      !>
      !>         RFP A                   RFP A
      !>
      !>        02 03 04                00 33 43
      !>        12 13 14                10 11 44
      !>        22 23 24                20 21 22
      !>        00 33 34                30 31 32
      !>        01 11 44                40 41 42
      !>
      !>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
      !>  transpose of RFP A above. One therefore gets:
      !>
      !>           RFP A                   RFP A
      !>
      !>     02 12 22 00 01             00 10 20 30 40 50
      !>     03 13 23 33 11             33 11 21 31 41 51
      !>     04 14 24 34 44             43 44 22 32 42 52
      !>