SRC/dptsv.f(3)

💖 SRC/dptsv.f 💖

okay so bestie, this page is a Library Functions Manual entry and it's genuinely iconic — it's the dptsv subroutine from LAPACK, and it's giving "I solve your tridiagonal systems so you don't have to" energy. no cap, let's get into it. 🦋

---

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

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

---

🌸 Function/Subroutine Documentation 🌸

🫶 subroutine dptsv (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPTSV computes the solution to system of linear equations A * X = B for PT matrices. she's the main character fr fr 💅

⭐ Purpose:

!>
!> DPTSV 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 like — A is an N-by-N symmetric positive definite tridiagonal matrix, X and B are N-by-NRHS matrices. she factors A as A = L*D*L**T and then uses that factored form to solve the whole system. lowkey efficient, highkey slay. 🔥

👑 Parameters

• N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

the order of the matrix A. must be N >= 0. be normal about it. 🙈

• NRHS

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

the number of right hand sides — like, the number of columns of the matrix B. NRHS >= 0. periodt. ✨

• D

!>          D is DOUBLE PRECISION 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.
!>

a DOUBLE PRECISION array, dimension (N). on entry it's the n diagonal elements of the tridiagonal matrix A. on exit it's the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T. she really said "I contain multitudes". 🦋

• E

!>          E is DOUBLE PRECISION 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.)
!>

a DOUBLE PRECISION 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. and bestie, the plot twist: (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A.) dual identity, we love to see it. 💀

• B

!>          B is DOUBLE PRECISION 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.
!>

a DOUBLE PRECISION array, dimension (LDB,NRHS). on entry it's the N-by-NRHS right hand side matrix B. on exit, if INFO = 0, it's the N-by-NRHS solution matrix X. glow-up complete. 💖

• LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

an INTEGER. the leading dimension of the array B. LDB >= max(1,N) — that's the vibe check, don't fail it. 🌈

• 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.
!>

an INTEGER, and she's the emotional support status code:

• = 0: successful exit 🎉 slay
• < 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. 💀 big yikes, read it carefully.

ok real talk bestie — a positive INFO means the solution was not computed, so don't go reading B like it's the answer. that's the dangerous part, keep the meaning fr fr. 🙏

🌟 Author

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

💜 Definition at line 113 of file dptsv.f.

---

and that's the whole page, bestie ✨

this legend was Generated automatically by Doxygen for LAPACK from the source code. — shoutout to the robots. and the page itself is from LAPACK, Version 3.12.0. go solve something cute. 🎀💅🫶