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NAME

       ztftri.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine ztftri (characterTRANSR, characterUPLO, characterDIAG, integerN, complex*16,
       dimension( 0: * )A, integerINFO)
       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:
           November 2011

       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 222 of file ztftri.f.

Author

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