trttf(3)

NAME
trttf - trttf: triangular matrix, full (tr) to RFP (tf)

SYNOPSIS

  Functions

subroutine ctrttf (transr, uplo, n, a, lda, arf, info)
CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
subroutine dtrttf (transr, uplo, n, a, lda, arf, info)
DTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
subroutine strttf (transr, uplo, n, a, lda, arf, info)
STRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
subroutine ztrttf (transr, uplo, n, a, lda, arf, info)
ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).

Detailed Description

Function Documentation

  subroutine ctrttf (character transr, character uplo, integer n, complex, dimension( 0: lda-1, 0: * ) a, integer lda, complex, dimension( 0: * ) arf, integer info)

CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).

Purpose:

    !>
    !> CTRTTF copies a triangular matrix A from standard full format (TR)
    !> to rectangular full packed format (TF) .
    !>

Parameters
    TRANSR

    !>          TRANSR is CHARACTER*1
    !>          = 'N':  ARF in Normal mode is wanted;
    !>          = 'C':  ARF in Conjugate Transpose mode is wanted;
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension ( LDA, N )
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the matrix A.  LDA >= max(1,N).
    !>

    ARF

    !>          ARF is COMPLEX array, dimension ( N*(N+1)/2 ),
    !>          On exit, the upper or lower triangular matrix A stored in
    !>          RFP format. For a further discussion see Notes below.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

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 dtrttf (character transr, character uplo, integer n, double precision, dimension( 0: lda-1, 0: * ) a, integer lda, double precision, dimension( 0: * ) arf, integer info)

DTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).

Purpose:

    !>
    !> DTRTTF copies a triangular matrix A from standard full format (TR)
    !> to rectangular full packed format (TF) .
    !>

Parameters
    TRANSR

    !>          TRANSR is CHARACTER*1
    !>          = 'N':  ARF in Normal form is wanted;
    !>          = 'T':  ARF in Transpose form is wanted.
    !>

    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 DOUBLE PRECISION array, dimension (LDA,N).
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the matrix A. LDA >= max(1,N).
    !>

    ARF

    !>          ARF is DOUBLE PRECISION array, dimension (NT).
    !>          NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

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 strttf (character transr, character uplo, integer n, real, dimension( 0: lda-1, 0: * ) a, integer lda, real, dimension( 0: * ) arf, integer info)

STRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).

Purpose:

    !>
    !> STRTTF copies a triangular matrix A from standard full format (TR)
    !> to rectangular full packed format (TF) .
    !>

Parameters
    TRANSR

    !>          TRANSR is CHARACTER*1
    !>          = 'N':  ARF in Normal form is wanted;
    !>          = 'T':  ARF in Transpose form is wanted.
    !>

    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 REAL array, dimension (LDA,N).
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the matrix A. LDA >= max(1,N).
    !>

    ARF

    !>          ARF is REAL array, dimension (NT).
    !>          NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

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 ztrttf (character transr, character uplo, integer n, complex*16, dimension( 0: lda-1, 0: * ) a, integer lda, complex*16, dimension( 0: * ) arf, integer info)

ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).

Purpose:

    !>
    !> ZTRTTF copies a triangular matrix A from standard full format (TR)
    !> to rectangular full packed format (TF) .
    !>

Parameters
    TRANSR

    !>          TRANSR is CHARACTER*1
    !>          = 'N':  ARF in Normal mode is wanted;
    !>          = 'C':  ARF in Conjugate Transpose mode is wanted;
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension ( LDA, N )
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the matrix A.  LDA >= max(1,N).
    !>

    ARF

    !>          ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
    !>          On exit, the upper or lower triangular matrix A stored in
    !>          RFP format. For a further discussion see Notes below.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

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
    !>

Author

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