SPPEQU(3)

🌸 NAME 🌸

okay bestie, this is the manual page for SPPEQU(3) from the Library Functions Manual 💅 and the NAME line points at the source file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sppequ.f — the header/footer abbreviate that whole situation as /home/abui...RC/sppequ.f(3) ✨.

✨ SYNOPSIS ✨

🧸 Functions/Subroutines 🧸

subroutine SPPEQU (uplo, n, ap, s, scond, amax, info)
    SPPEQU

💖 Function/Subroutine Documentation 💖

subroutine SPPEQU (character uplo, integer n, real, dimension( * ) ap, real,
    dimension( * ) s, real scond, real amax, integer info)
    SPPEQU

🎀 Purpose 🎀

okay so SPPEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. no cap, that's the whole glow-up ✨.

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1; = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 💅
• N — N is INTEGER; the order of the matrix A. N >= 0. 🎀
• AP — AP is REAL array, dimension (N*(N+1)/2). It's the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 🦋
• S — S is REAL array, dimension (N). If INFO = 0, S contains the scale factors for A. 🌸
• SCOND — SCOND is REAL. If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. yes bestie, the doc really says S there — I'm not fixing it, I'm just reporting it 🙈.
• AMAX — AMAX is REAL. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. 🔥
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, the i-th diagonal element is nonpositive. 💀

👑 Author 👑

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

Definition at line 115 of file sppequ.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. 🪄

okay that's the whole page, bestie 🫶 — LAPACK Version 3.12.0 and the footer tag is /home/abui...RC/sppequ.f(3). mwah 💋✨