ztftri.f(3)

NAME
ztftri.f

SYNOPSIS

  Functions/Subroutines
subroutine ztftri (TRANSR, UPLO, DIAG, N, A, INFO)
ZTFTRI

Function/Subroutine Documentation

  subroutine ztftri (character TRANSR, character UPLO, character DIAG, integer N, complex*16, dimension( 0: * ) A, integer INFO)

ZTFTRI

Purpose:

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

Parameters:
    TRANSR

              TRANSR is CHARACTER*1
              = 'N':  The Normal TRANSR of RFP A is stored;
              = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.

    UPLO

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

    DIAG

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

    N

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

    A

              A is COMPLEX*16 array, dimension ( N*(N+1)/2 );
              On entry, the triangular 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 = 'C' then RFP is
              the Conjugate-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 = 'C'. 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.

    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.

Date:
    December 2016

Further Details:

      We first consider Standard Packed 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
      conjugate-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
      conjugate-transpose of the last three columns of AP lower.
      To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
      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 next  consider Standard Packed 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
      conjugate-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
      conjugate-transpose of the last two   columns of AP lower.
      To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
      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

Definition at line 223 of file ztftri.f.

Author

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