SRC/stfttp.f(3)

💖 NAME

SRC/stfttp.f — that's the page, bestie, and it's live from the Library Functions Manual. It's all about the stfttp subroutine, which copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). no cap ✨

🎀 SYNOPSIS

🦋 Functions/Subroutines

subroutine stfttp (transr, uplo, n, arf, ap, info)

Okay so <pink>STFTTP</pink> copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). slay 💅

🌸 Function/Subroutine Documentation

🧚 subroutine stfttp

subroutine stfttp (character transr, character uplo, integer n, real, dimension( 0: * ) arf, real, dimension( 0: * ) ap, integer info)

<hotpink>STFTTP</hotpink> copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). iconic behavior, honestly 👑

🔥 Purpose

The source is giving:

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

So yeah, it's taking A from RFP/TF vibes over to standard packed TP vibes. main character energy fr fr 🦋

💖 Parameters

• TRANSR — <purple>CHARACTER*1</purple>; = 'N': ARF is in Normal format; = 'T': ARF is in Transpose format;
• UPLO — <purple>CHARACTER*1</purple>; = 'U': A is upper triangular; = 'L': A is lower triangular.
• N — <cyan>INTEGER</cyan>; the order of the matrix A. N >= 0.
• ARF — <mint>REAL array, dimension ( N*(N+1)/2 ),</mint> on entry, the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.
• AP — <mint>REAL array, dimension ( N*(N+1)/2 ),</mint> on exit, the upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
• INFO — <cyan>INTEGER</cyan>; = 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 bestie, this is the part where the RFP format lore gets real. First up: 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

Next 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 186 of file stfttp.f.

🌟 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💖 — footer vibes: LAPACK Version 3.12.0, page SRC/stfttp.f(3). periodt ✨🎀