ZPOTRS(3)

💖 ZPOTRS(3) — like, the Cholesky-solve girlie of LAPACK 💖

okay bestie, so this page lives at /home/abui...RC/zpotrs.f(3) in the Library Functions Manual, and it's literally all about one Fortran subroutine that solves your linear system once you've already done the factorization. no cap, it's a whole vibe. 🦋

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✨ SYNOPSIS ✨

Functions/Subroutines — here's the whole cast list:

subroutine ZPOTRS (uplo, n, nrhs, a, lda, b, ldb, info)
          ZPOTRS

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🎀 Function/Subroutine Documentation 🎀

🌸 the actual signature, bestie 🌸

subroutine ZPOTRS (character uplo, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, integer info)

ZPOTRS — yes queen, that's the name, say it with your chest. 👑

Purpose 💫

so basically: ZPOTRS solves a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H * U or A = L * L**H computed by ZPOTRF.

like, ZPOTRF does the hard part (the factorization), and this one comes in and finishes the job. teamwork, fr fr. 🫶

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🌈 Parameters 🌈

time for the ✨parameter era✨ — every single one, no skipping:

• UPLO — is CHARACTER*1. it tells you which triangle of A is stored:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. the order of the matrix A. must be N >= 0. (negative N? not on her watch. 💀)
• NRHS — is INTEGER. the number of right hand sides, i.e., the number of columns of the matrix B. must be NRHS >= 0.
• A — is COMPLEX*16 array, dimension (LDA,N). it holds the triangular factor U or L from the Cholesky factorization A = U**H * U or A = L * L**H, as computed by ZPOTRF. so like, she's not doing the factoring, she's using it. slay.
• LDA — is INTEGER. the leading dimension of the array A. must be LDA >= max(1,N).
• B — is COMPLEX*16 array, dimension (LDB,NRHS). on entry, this is the right hand side matrix B. on exit, it's the solution matrix X. glow-up of the century honestly. ✨
• LDB — is INTEGER. the leading dimension of the array B. must be LDB >= max(1,N).
• INFO — is INTEGER. the receipts:
  • = 0: successful exit 👑
  • < 0: if INFO = -i, the i-th argument had an illegal value 🙈

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🧚 Author 🧚

the legends behind it:

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

Definition at line 109 of file zpotrs.f. 📍

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💅 Author (the meta one) 💅

Generated automatically by Doxygen for LAPACK from the source code. (yes, the docs wrote themselves, main character energy tbh)

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🌸 quick reminder bestie: INFO is how she tells you something went wrong — check it, always. INFO < 0 means an argument was illegal, and INFO = -i points at exactly which one. don't ignore her texts. 💜

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and that's the whole page! 💖 this cutie is from LAPACK, Version 3.12.0, and the footer path vibe was /home/abui...RC/zpotrs.f(3) — periodt. 🎀🔥