SRC/zpoequb.f(3)

🦋 SRC/zpoequb.f(3) — Library Functions Manual 🦋

okay bestie, this is the page for SRC/zpoequb.f(3) from the LAPACK Library Functions Manual, and we're about to get into ZPOEQUB. No cap, she's a whole vibe. 💅✨

---

💖 NAME 💖

SRC/zpoequb.f — literally the name, periodt. 🎀

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

   Functions/Subroutines
       subroutine zpoequb (n, a, lda, s, scond, amax, info)
           ZPOEQUB

🫶 Function/Subroutine Documentation 🫶

   subroutine zpoequb (integer n, complex*16, dimension( lda, * ) a, integer
       lda, double precision, dimension( * ) s, double precision scond, double
       precision amax, integer info)
       ZPOEQUB

🌸 Purpose 🌸

okay so ZPOEQUB computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A 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.

This routine differs from ZPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). 🧚✨

🎀 Parameters 🎀

• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). The N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 118 of file zpoequb.f.

Generated automatically by Doxygen for LAPACK from the source code. 💻✨

---

mwah 💋 — this page is from LAPACK Version 3.12.0, path SRC/zpoequb.f(3). That's the footer, bestie, and it ate. 🎀💖