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## stftri()

subroutine stftri | ( | character | transr,
|  | character | uplo,
|  | character | diag,
|  | integer | n,
|  | real, dimension( 0: * ) | a,
|  | integer | info )

STFTRI

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

Purpose:

      !>
      !> STFTRI computes the inverse of a triangular matrix A stored in RFP
      !> format.
      !>
      !> This is a Level 3 BLAS version of the algorithm.
      !>

Parameters

  [in]

  TRANSR

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

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  A is upper triangular;
      !>          = 'L':  A is lower triangular.
      !>

  [in]

  DIAG

      !>          DIAG is CHARACTER*1
      !>          = 'N':  A is non-unit triangular;
      !>          = 'U':  A is unit triangular.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix A.  N >= 0.
      !>

  [in,out]

  A

      !>          A is REAL array, dimension (NT);
      !>          NT=N*(N+1)/2. On entry, the triangular factor of a Hermitian
      !>          Positive Definite 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; If UPLO = 'L' the RFP A contains the nt
      !>          elements of lower packed A. 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 N is odd. See the Note below for more details.
      !>
      !>          On exit, the (triangular) inverse of the original matrix, in
      !>          the same storage format.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0: successful exit
      !>          < 0: if INFO = -i, the i-th argument had an illegal value
      !>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
      !>               matrix is singular and its inverse can not be computed.
      !>

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
      !>