DLAHILB.F(3)

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version 3.12.1 · 3 versions
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okay bestie, welcome to TESTING/MATGEN/dlahilb.f(3) from the Library Functions Manual — this is the DLAHILB page, and we are keeping every single technical detail intact while making it make sense. 💅✨

✨ NAME ✨

TESTING/MATGEN/dlahilb.f — the source file for the DLAHILB routine. 💖

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

  • subroutine dlahilb (n, nrhs, a, lda, x, ldx, b, ldb, work, info) — DLAHILB

🦋 Function/Subroutine Documentation 🦋

💫 subroutine dlahilb (...) — DLAHILB 💫

subroutine dlahilb (integer n, integer nrhs, double precision, dimension(lda, n) a, integer lda, double precision, dimension(ldx, nrhs) x, integer ldx, double precision, dimension(ldb, nrhs) b, integer ldb, double precision, dimension(n) work, integer info)

🎯 Purpose 🎯

So DLAHILB generates an N by N scaled Hilbert matrix in A, along with NRHS right-hand sides in B and solutions in X such that A*X=B. iconic behavior, honestly. 👑

The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all entries are integers. The right-hand sides are the first NRHS columns of M * the identity matrix, and the solutions are the first NRHS columns of the inverse Hilbert matrix. no cap, that's the setup. 💖

The condition number of the Hilbert matrix grows exponentially with its size, roughly as O(e ** (3.5*N)) — highkey dramatic. Additionally, the inverse Hilbert matrices beyond a relatively small dimension cannot be generated exactly without extra precision. Precision is exhausted when the largest entry in the inverse Hilbert matrix is greater than 2 to the power of the number of bits in the fraction of the data type used plus one, which is 24 for single precision. that's the precision vibe check, bestie. 😭

In single, the generated solution is exact for N <= 6 and has small componentwise error for 7 <= N <= 11. slay. ✨

🌈 Parameters 🌈

  • N — N is INTEGER. The dimension of the matrix A. 🎀
  • NRHS — NRHS is INTEGER. The requested number of right-hand sides. 💖
  • A — A is DOUBLE PRECISION array, dimension (LDA, N). The generated scaled Hilbert matrix. 🌸
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= N. 🦋
  • X — X is DOUBLE PRECISION array, dimension (LDX, NRHS). The generated exact solutions. Currently, the first NRHS columns of the inverse Hilbert matrix. 💫
  • LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= N. 🌈
  • B — B is DOUBLE PRECISION array, dimension (LDB, NRHS). The generated right-hand sides. Currently, the first NRHS columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. 🔥
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= N. 💜
  • WORK — WORK is DOUBLE PRECISION array, dimension (N). the work array, doing its backstage thing. 🎀
  • INFO — INFO is INTEGER
    • = 0: successful exit
    • = 1: N is too large; the data is still generated but may not be not exact 😭 (yes, the double negative is literally in the page, fr)
    • < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author 👑

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

Definition at line 123 of file dlahilb.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

💖 cute sign-off, bestie: source/version is LAPACK Version 3.12.0, the page is TESTING/MATGEN/dlahilb.f(3), and the date slot is blank on this footer — so no invented date, just the facts. 🫶💖

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