SRC/stfttr.f(3)

📦

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✨ NAME ✨

SRC/stfttr.f — that's the file, bestie, and this whole page is about the stfttr subroutine. No cap, it's the glow-up from RFP to full format. 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines:

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

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

💅 Function/Subroutine Documentation 💅

🌟 subroutine stfttr

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

STFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). It's giving conversion era, and honestly it ate. 🫶

🎀 Purpose

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

So yeah, bestie: triangular matrix A, packed format in, full format out. Main character energy for a subroutine, tbh. ✨

💖 Parameters

TRANSR

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

TRANSR — 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.
!>

UPLO — 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.
!>

N — INTEGER
- The order of the matrices ARF and A. N >= 0.

ARF

!>          ARF is REAL 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.
!>

ARF — REAL 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 REAL 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.
!>

A — REAL 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).
!>

LDA — 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
!>

INFO — 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

Definition at line 195 of file stfttr.f.

💜 Author

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That's the whole page, bestie 💋 — LAPACK Version 3.12.0, page SRC/stfttr.f(3). Byeee 🫶

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