ZPBTRS(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME 💅

okay so bestie, this page is zpbtrs.f(3) from the Library Functions Manual 😌 and the star of the show is literally this file path:

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

like… that's the whole NAME section, no cap, that's it. the source file IS the icon 💖

✨ SYNOPSIS ✨

Functions/Subroutines 🫶

  • subroutine ZPBTRS (uplo, n, kd, nrhs, ab, ldab, b, ldb, info) — the one, the only, ZPBTRS 🎀

🌸 Function/Subroutine Documentation 🌸

subroutine ZPBTRS (character uplo, integer n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldb, * ) b, integer ldb, integer info) 💫

ZPBTRS 💅

Purpose: 🌈

!>
!> ZPBTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite band matrix A using the Cholesky factorization
!> A = U**H *U or A = L*L**H computed by ZPBTRF.
!>

so basically: hand it a Hermitian positive definite band matrix A that's already been Cholesky-factored by ZPBTRF, and it'll solve A*X = B for you. iconic behavior honestly 👑

🦋 Parameters 🦋

  • UPLO — UPLO is CHARACTER*1 and it tells us which triangular factor is chilling in AB:
!>          = 'U':  Upper triangular factor stored in AB;
!>          = 'L':  Lower triangular factor stored in AB.
!>
  • N — N is INTEGER, the order of the matrix A. and like, N >= 0, obviously 🙈
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
  • KD — KD is INTEGER, the number of superdiagonals of A when UPLO = 'U', or the number of subdiagonals when UPLO = 'L'. KD >= 0 bestie 💜
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
!>
  • NRHS — NRHS is INTEGER, the number of right hand sides, aka how many columns the matrix B has. NRHS >= 0 fr fr ✨
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
  • AB — AB is COMPLEX*16 array, dimension (LDAB,N). this is where the triangular factor U or L lives, straight outta the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, stored in the first KD+1 rows. the j-th column of U or L sits in the j-th column of AB like this 👇
!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H *U or A = L*L**H of the band matrix A, stored in the
!>          first KD+1 rows of the array.  The j-th column of U or L is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
!>
  • LDAB — LDAB is INTEGER, the leading dimension of the array AB, and it's gotta be LDAB >= KD+1 or we riot 🎀
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>
  • B — B is COMPLEX*16 array, dimension (LDB,NRHS). on entry it's the right hand side matrix B, and on exit it's the solution matrix X. glow-up of the century tbh 💖
!>          B is COMPLEX*16 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), respect the rule 🌟
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>
  • INFO — INFO is INTEGER, the vibe check at the end 🫶
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

so 0 means slay, we're done ✅ and anything < 0 means argument number i was illegal, i.e. it did NOT pass the vibe check 💀

👑 Author 👑

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

Definition at line 120 of file zpbtrs.f. 📍

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. yes the robots wrote the docs, and honestly? they ate 🤖✨

ngl bestie, if you're passing bad arguments here, INFO will absolutely tell on you. no cap 🙈

💖 and that's the whole page! 🎀 LAPACK, Version 3.12.0, and this absolute classic of a file page for /home/abui...RC/zpbtrs.f(3) — mwah, bye bestie, go solve some systems 💅✨🦋

📦 where this page comes from