SRC/strttf.f(3)

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version 3.12.1 · 4 versions
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💖 SRC/strttf.f 💖

Library Functions Manual, bestie — this is the SRC/strttf.f page, and it’s literally all about the strttf routine. ✨

🌸 NAME 🌸

SRC/strttf.f — that’s the page name, periodt.

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • 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). 💅

🎀 Function/Subroutine Documentation 🎀

Here’s the full signature, exactly as it is:

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). No cap. 🫶

🌷 Purpose 🌷

The actual purpose, bestie: 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: 🧚

Real talk: Rectangular Full Packed (RFP) Format has two cases, even and odd. First up, 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 193 of file strttf.f.

👑 Author 👑

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