SRC/zppequ.f(3)

okay bestie, you found SRC/zppequ.f(3) from the Library Functions Manual — and no cap, this one is a little packed-storage baddie that scales Hermitian positive definite matrices so their condition numbers stop being dramatic. 💅✨

🌸 NAME 🌸

SRC/zppequ.f

📚 SYNOPSIS 📚

Functions/Subroutines

• subroutine zppequ (uplo, n, ap, s, scond, amax, info) — ZPPEQU

💻 Function/Subroutine Documentation 💻

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

ZPPEQU is literally the subroutine we're talking about, main character energy only. 👑

🎯 Purpose 🎯

ZPPEQU 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. Gorgeous. 🌈

🧾 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*16 array, dimension (N*(N+1)/2). It holds 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.

Packed columnwise? It's giving organized. 🎀

S

S is DOUBLE PRECISION array, dimension (N). If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is DOUBLE PRECISION. 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

AMAX is DOUBLE PRECISION. 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 zppequ.f.

👑 Author (auto-generated) 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

mwah 💋 this page is from LAPACK Version 3.12.0, source SRC/zppequ.f(3) — bye bestie, go scale something pretty! 🫶💖