/home/abui...RC/sptsv.f(3)

💅 /home/abui...RC/sptsv.f(3) — Library Functions Manual ✨

okay so bestie, this is a page straight out of the LAPACK 3.12.0 Library Functions Manual, and it's giving very specific Fortran subroutine energy. Buckle in 🎀

The full path of the thing we're talking about is, and I am not making this up:

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

iconic. unhinged. love that for us 💖

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🌸 NAME 🌸

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

like yes ma'am that's the whole name, that's the whole vibe, no notes 🫶

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine SPTSV (n, nrhs, d, e, b, ldb, info) — SPTSV computes the solution to system of linear equations A * X = B for PT matrices

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⭐ Function/Subroutine Documentation ⭐

subroutine SPTSV (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)

SPTSV computes the solution to system of linear equations A * X = B for PT matrices 💫

👑 Purpose:

!>
!> SPTSV computes the solution to a real system of linear equations
!> A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
!> matrix, and X and B are N-by-NRHS matrices.
!>
!> A is factored as A = L*D*L**T, and the factored form of A is then
!> used to solve the system of equations.
!>

so basically: real system, symmetric positive definite tridiagonal matrix, and it factors A as A = L*D*L**T then uses that factored form to actually solve the thing. main character math honestly 😭🔥

🎀 Parameters

• N — N is INTEGER, the order of the matrix A. N >= 0. lowkey the size of everything, no cap.
• NRHS — NRHS is INTEGER, the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. yes it's literally how many B's you got 💅
• D — D is REAL array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T. so it goes in as A's diagonal and comes out as D's diagonal — glow-up arc fr ✨
• E — E is REAL array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A.) like it's serving double duty depending on how you look at it 🦋
• B — B is REAL array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. it literally transforms from problem to answer, we love a character development moment 💀
• LDB — LDB is INTEGER, the leading dimension of the array B. LDB >= max(1,N). do not skimp on this one bestie 🙈
• INFO — INFO is INTEGER
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the leading principal minor of order i is not positive, and the solution has not been computed. The factorization has not been completed unless i = N.

ok so real talk: that > 0 case means your matrix wasn't playing nice — the solution is not computed, and the factorization is left unfinished unless i = N. no silent failing here, she tells you 💀

🌈 Author

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

the whole squad came together for this one 🫶👑

Definition at line 113 of file sptsv.f.

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🧚 Author (again, but doxygen's version)

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing its little docs thing 🤖✨

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and that's the whole page!! generated with love by Doxygen for LAPACK, straight from the source code — LAPACK, Version 3.12.0, and the header/footer said /home/abui...RC/sptsv.f(3) in case you were wondering where we came from 🎀💜 bye bestie, go solve some tridiagonal systems!!