DTFTTR(3)

💖 NAME 💖

okay so bestie, you're reading DTFTTR(3) from the Library Functions Manual — manual name folded in right here because we're cute like that. The NAME is literally this path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/dtfttr.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

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

✨ Function/Subroutine Documentation ✨

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

DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). That's the whole serve, bestie.

🎀 Purpose 🎀

DTFTTR copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR). Periodt. 💅

💅 Parameters 💅

TRANSR

TRANSR is CHARACTER*1

• = 'N': ARF is in Normal format;
• = 'T': ARF is in 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 matrices ARF and A. N >= 0.

ARF

ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2). On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') matrix A in RFP format. See the below for more details.

A

A is DOUBLE PRECISION 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 🦋

First up, bestie: we consider Rectangular Full Packed (RFP) Format when N is even. 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

Then we consider Rectangular Full Packed (RFP) Format when N is odd. 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 195 of file dtfttr.f.

🌟 Author 🌟

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