DLAHILB(3)

💖 DLAHILB(3) — dlahilb.f 💖

okay so this is a Library Functions Manual page, and the star of the show is dlahilb.f. No cap, it's a LAPACK test-matrix generator and it's lowkey iconic.

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/dlahilb.f

That's the whole NAME, bestie — it's literally the file path.

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

DLAHILB slay

💅 Function/Subroutine Documentation 💅

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)

DLAHILB — main character energy, fr fr.

✨ Purpose ✨

Okay so here's the tea: 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. 💖

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. It's giving exact-solution realness ✨

The condition number of the Hilbert matrix grows exponentially with its size, roughly as O(e ** (3.5*N)). 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. Numbers don't lie 🔥

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

🌸 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). 🧚
• INFO — INFO is INTEGER. Here's the vibe check:
  • = 0: successful exit 🎉
  • = 1: N is too large; the data is still generated but may not be not exact. (yes, that's literally the wording — keep it in your heart 😭)
  • < 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.

Academic royalty, honestly. 👑

Definition at line 123 of file dlahilb.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off time, bestie: this page is from LAPACK Version 3.12.0, and the footer path is /home/abui...N/dlahilb.f(3). No date in the footer, just pure manual-page energy. Mwah 💋✨