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

NAME

       LAPACK-3 - computes the inverse of a triangular matrix A stored in RFP format

SYNOPSIS

       SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )

           CHARACTER      TRANSR, UPLO, DIAG

           INTEGER        INFO, N

           DOUBLE         PRECISION A( 0: * )

PURPOSE

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

ARGUMENTS

        TRANSR  (input) CHARACTER*1
                = 'N':  The Normal TRANSR of RFP A is stored;
                = 'T':  The Transpose TRANSR of RFP A is stored.

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

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

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

        A       (input/output) DOUBLE PRECISION  array, dimension (0:nt-1);
                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.

        INFO    (output) 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.

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

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