Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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 CPFTRF

SYNOPSIS

       SUBROUTINE CPFTRI( TRANSR, UPLO, N, A, INFO )

           CHARACTER      TRANSR, UPLO

           INTEGER        INFO, N

           COMPLEX        A( 0: * )

PURPOSE

       CPFTRI 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 CPFTRF.

ARGUMENTS

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

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        A       (input/output) COMPLEX 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    (output) 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.

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

 LAPACK routine (version 3.3.1)             April 2011                            CPFTRI(3lapack)