SRC/sppequ.f(3)

SRC/sppequ.f

okay bestie, welcome to SRC/sppequ.f(3) from the Library Functions Manual — this is the page for the sppequ routine, and it's lowkey iconic for scaling symmetric positive definite matrices. 💅✨

✨ NAME ✨

SRC/sppequ.f — the manual page for sppequ, no cap.

🌸 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 🎯

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. periodt. 💖

💅 Parameters 💅

• UPLO — the triangle selector, and it's giving choose-your-fighter:
  • UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — the order of the matrix, bestie:
  • N is INTEGER
  • The order of the matrix A. N >= 0.
• AP — the packed matrix storage situation:
  • AP is REAL array, dimension (N*(N+1)/2)
  • 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 — the scale factors live here:
  • S is REAL array, dimension (N)
  • If INFO = 0, S contains the scale factors for A.
• SCOND — the ratio check, highkey important:
  • 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.
• AMAX — the biggest-element vibe check:
  • 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 — the exit-status icon:
  • 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 🎀

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okay that's the whole page, bestie. Signed off by LAPACK, Version 3.12.0, for SRC/sppequ.f(3) — mwah 💋🎀✨