SRC/ctrttf.f(3)

SRC/ctrttf.f(3) 🌸

Bestie, welcome to the Library Functions Manual page for SRC/ctrttf.f — yes, the LAPACK Fortran page, and it's lowkey iconic. 💅

✨ NAME ✨

SRC/ctrttf.f — that's the file, bestie. This is the manual page vibe for the ctrttf subroutine.

✨ SYNOPSIS ✨

Functions/Subroutines

• 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). Slay. 💖

💖 Function/Subroutine Documentation 💖

subroutine ctrttf

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). That's the whole assignment, and it ate. ✨

Purpose

CTRTTF copies a triangular matrix A from standard full format (TR) to rectangular full packed format (TF). Okay so it's a format glow-up for your triangular matrix. 🦋

Parameters

• TRANSR — is CHARACTER*1: = 'N': ARF in Normal mode is wanted; = 'C': ARF in Conjugate Transpose mode is wanted;
• UPLO — is CHARACTER*1: = 'U': A is upper triangular; = 'L': A is lower triangular.
• N — is INTEGER; the order of the matrix A. N >= 0.
• 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 — is INTEGER; the leading dimension of the matrix A. LDA >= max(1,N).
• 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 — 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 here's the packed-format lore, bestie — diagrams and all. 🫶

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.

Author

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