STFTRI(3)

👑 STFTRI(3) — Library Functions Manual 💅

Okay bestie, this is STFTRI(3) from the Library Functions Manual — the page path is /home/abui...RC/stftri.f(3), and yes, the header repeats that same path like a little echo. Periodt.

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here's the function lineup, no cap:

• subroutine STFTRI (transr, uplo, diag, n, a, info) — STFTRI

🫶 Function/Subroutine Documentation 🫶

💖 STFTRI 💖

subroutine STFTRI (character transr, character uplo, character diag, integer
    n, real, dimension( 0: * ) a, integer info)

Yep, it's STFTRI again — main character energy.

💖 Purpose 💖

Bestie, listen: STFTRI computes the inverse of a triangular matrix A stored in RFP format.

It's giving Level 3 BLAS version of the algorithm — that's literally what it is, and we love that for it. ✨

🌈 Parameters 🌈

Parameter by parameter, let's go:

TRANSR

TRANSR is CHARACTER*1.

• = 'N': The Normal TRANSR of RFP A is stored;
• = 'T': The Transpose TRANSR of RFP A is stored.

UPLO

UPLO is CHARACTER*1.

• = 'U': A is upper triangular;
• = 'L': A is lower triangular.

DIAG

DIAG is CHARACTER*1.

• = 'N': A is non-unit triangular;
• = 'U': A is unit triangular.

N

N is INTEGER.

The order of the matrix A. N >= 0.

A

A is REAL array, dimension (NT); NT=N*(N+1)/2.

On entry, it's the triangular factor of a Hermitian Positive Definite matrix A in RFP format. RFP format is described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is the transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the nt elements of upper packed A; If UPLO = 'L' the RFP A contains the nt elements of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N is odd. See the Note below for more details.

On exit, the (triangular) inverse of the original matrix, in the same storage format.

INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.

💀 Danger tea: if INFO = i and A(i,i) is exactly zero, the matrix is singular and its inverse can not be computed. No cap.

🌟 Author 🌟

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🦋 Further Details 🦋

Okay, RFP format time — this is the part where Rectangular Full Packed storage gets its little spotlight. First up: N is even. The example is 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. The example is 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 200 of file stftri.f.

📜 Author 📜

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Mwah 💋 that's the whole page — the footer source/version/date vibe is LAPACK Version 3.12.0 plus /home/abui...RC/stftri.f(3) (no extra calendar date printed in the original, just that source/version/path energy). Bye bestie 🫶