SRC/zlaqsp.f(3)

🎀 NAME 🎀

SRC/zlaqsp.f — bestie, this is the page, and it's chilling in the Library Functions Manual. 💖

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine zlaqsp (uplo, n, ap, s, scond, amax, equed)

The whole point? ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. Slay. 💅

🌸 Function/Subroutine Documentation 🌸

       subroutine zlaqsp (character uplo, integer n, complex*16, dimension( * ) ap,
       double precision, dimension( * ) s, double precision scond, double
       precision amax, character equed)

Okay so this is the same subroutine, fully documented: ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. Iconic behavior, honestly. ✨

💖 Purpose 💖

ZLAQSP equilibrates a symmetric matrix A using the scaling factors in the vector S. That's the main-character job. 👑

🌈 Parameters 🌈

• UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — INTEGER. The order of the matrix A. N >= 0.
• AP — COMPLEX*16 array, dimension (N*(N+1)/2). On entry, 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.

On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A. 💫

• S — DOUBLE PRECISION array, dimension (N). The scale factors for A.
• SCOND — DOUBLE PRECISION. Ratio of the smallest S(i) to the largest S(i).
• AMAX — DOUBLE PRECISION. Absolute value of largest matrix entry.
• EQUED — CHARACTER*1. Specifies whether or not equilibration was done.
  • = 'N': No equilibration.
  • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

🔥 Internal Parameters 🔥

• THRESH — a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done.
• LARGE and SMALL — threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done.

👑 Author 👑

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

📍 Definition at line 125 of file zlaqsp.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Signing off: LAPACK Version 3.12.0 · SRC/zlaqsp.f(3) — periodt, bestie. 💖✨🫶