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

Definition at line 215 of file ctrttf.f.

  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

Definition at line 193 of file dtrttf.f.

  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

Definition at line 193 of file strttf.f.

  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

Definition at line 215 of file ztrttf.f.

Author

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