SRC/dpftrs.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 💖

okay so this page is literally SRC/dpftrs.f(3) from the Library Functions Manual, bestie 🫶. The name is SRC/dpftrs.f, and yes it’s giving very “LAPACK source file walked so your linear algebra could run” energy 💅✨.

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine dpftrs (transr, uplo, n, nrhs, a, b, ldb, info)
    DPFTRS

🎀 Function/Subroutine Documentation 🎀

subroutine dpftrs (character transr, character uplo, integer n, integer
    nrhs, double precision, dimension( 0: * ) a, double precision,
    dimension( ldb, * ) b, integer ldb, integer info)
    DPFTRS

🦋 Purpose 🦋

DPFTRS 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 DPFTRF. no cap, that’s the whole main-character job 💖.

🍓 Parameters 🍓

  • TRANSR — it’s CHARACTER*1, and here’s the vibe check: = 'N': The Normal TRANSR of RFP A is stored; and = 'T': The Transpose TRANSR of RFP A is stored. 👑
  • UPLO — also CHARACTER*1: = 'U': Upper triangle of RFP A is stored; and = 'L': Lower triangle of RFP A is stored. ✨
  • N — INTEGER, the order of the matrix A. N >= 0. periodt.
  • NRHS — INTEGER, the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 🫶
  • A — DOUBLE PRECISION array, dimension ( N*(N+1)/2 ). It’s the triangular factor U or L from the Cholesky factorization of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF. See note below for more details about RFP A 👀.
  • B — DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. slay 💅.
  • LDB — INTEGER, the leading dimension of the array B. LDB >= max(1,N). 🎀
  • INFO — INTEGER: = 0: successful exit and < 0: if INFO = -i, the i-th argument had an illegal value. very “we been knew” energy 😭.

👑 Author 👑

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

🌈 Further Details 🌈

First up: Rectangular Full Packed (RFP) Format when N is even. Example where N = 6, bestie 🧚:

      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'. iconic ✨.

         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, and the vibe is still impeccable 🌸:

     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'. highkey obsessed with this indexing lore 🔥.

         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 dpftrs.f. iykyk 💜.

💜 Author 💜

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