CPPEQU(3)

🌸 NAME 🌸

okay so bestie, this page is cppequ.f(3) from the Library Functions Manual, and the name block is literally just this file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cppequ.f. That's it. No cap. 💅

✨ SYNOPSIS ✨

🌈 Functions/Subroutines

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

🧚 Function/Subroutine Documentation 🧚

Here’s the full signature, bestie — exactly as written:

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

💖 Purpose 💖

CPPEQU computes row and column scalings intended to equilibrate a Hermitian 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. Obsessed with the math tbh. ✨

🎀 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 COMPLEX array, dimension (N*(N+1)/2); the upper or lower triangle of the Hermitian 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, the original really says S contains the ratio here — keeping the source wording exactly, bestie.) 💀
• 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 116 of file cppequ.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

That’s the whole page, bestie — LAPACK Version 3.12.0, footer path /home/abui...RC/cppequ.f(3). Slay. 💖