SRC/ctfttr.f(3)

💖 NAME 💖

SRC/ctfttr.f — yep, that's the whole NAME section, bestie. This page lives in the Library Functions Manual, and it's giving very serious linear algebra energy. 💅

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✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

subroutine ctfttr (transr, uplo, n, arf, a, lda, info)
    CTFTTR copies a triangular matrix from the rectangular full packed
    format (TF) to the standard full format (TR).

So CTFTTR is out here copying a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). Lowkey iconic. 🎀

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💅 Function/Subroutine Documentation 💅

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

CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). That's the whole assignment, and it ate. 🔥

🎀 Purpose 🎀

Okay so, CTFTTR copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR). Main character behavior, honestly. 🦋

🍓 Parameters 🍓

🌸 TRANSR 🌸

• TRANSR is CHARACTER*1
• = 'N': ARF is in Normal format;
• = 'C': ARF is in Conjugate-transpose format;

🌸 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.

🌸 ARF 🌸

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

🌸 A 🌸

• A is COMPLEX array, dimension ( LDA, N )
• On exit, 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 array A. LDA >= max(1,N).

🌸 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 🧚

Okay so first up: 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 ctfttr.f.

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🤖 Author 🤖

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