tftri(3)

NAME
tftri - tftri: triangular inverse, RFP

SYNOPSIS

  Functions

subroutine ctftri (transr, uplo, diag, n, a, info)
CTFTRI
subroutine dtftri (transr, uplo, diag, n, a, info)
DTFTRI
subroutine stftri (transr, uplo, diag, n, a, info)
STFTRI
subroutine ztftri (transr, uplo, diag, n, a, info)
ZTFTRI

Detailed Description

Function Documentation

  subroutine ctftri (character transr, character uplo, character diag, integer n, complex, dimension( 0: * ) a, integer info)

CTFTRI

Purpose:

    !>
    !> CTFTRI 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 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.

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
    !>

  subroutine dtftri (character transr, character uplo, character diag, integer n, double precision, dimension( 0: * ) a, integer info)

DTFTRI

Purpose:

    !>
    !> DTFTRI 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;
    !>          = 'T':  The 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 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

    !>          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.

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
    !>

  subroutine stftri (character transr, character uplo, character diag, integer n, real, dimension( 0: * ) a, integer info)

STFTRI

Purpose:

    !>
    !> STFTRI 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;
    !>          = 'T':  The 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 REAL array, dimension (NT);
    !>          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

    !>          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.

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
    !>

  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.

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
    !>

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