SPFTRS(3)

✨ NAME ✨

Okay bestie, SPFTRS(3) is from the Library Functions Manual, and this is the file it's serving:

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

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💅 SYNOPSIS 💅

🫶 Functions/Subroutines 🫶

• subroutine SPFTRS (transr, uplo, n, nrhs, a, b, ldb, info) — SPFTRS

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🦋 Function/Subroutine Documentation 🦋

subroutine SPFTRS (character transr, character uplo, integer n, integer nrhs, real, dimension( 0: * ) a, real, dimension( ldb, * ) b, integer ldb, integer info)

SPFTRS

🎯 Purpose: 🎯

SPFTRS solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPFTRF.

🧸 Parameters 🧸

🔥 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': Upper triangle of RFP A is stored;
• = 'L': Lower triangle of RFP A is stored.

🌸 N

N is INTEGER

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

🍓 NRHS

NRHS is INTEGER

The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

🌈 A

A is REAL array, dimension ( N*(N+1)/2 )

The triangular factor U or L from the Cholesky factorization of RFP A = U**H*U or RFP A = L*L**T, as computed by SPFTRF. See note below for more details about RFP A.

🦋 B

B is REAL array, dimension (LDB,NRHS)

On entry, the right hand side matrix B. On exit, the solution matrix X.

🎀 LDB

LDB is INTEGER

The leading dimension of the array B. LDB >= 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, the Rectangular Full Packed (RFP) Format when 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 like this:

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. 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 198 of file spftrs.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Signed off with LAPACK, Version 3.12.0 and /home/abui...RC/spftrs.f(3) — no date in the footer, but the vibes are timeless 💅