!>
!> ZPFTRI computes the inverse of a complex Hermitian positive definite
!> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
!> computed by ZPFTRF.
!> 

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':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!> 

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 Hermitian 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 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 Hermitian 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, the (i,i) element of the factor U or L is
!>                zero, and the inverse could not be computed.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  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
!>