DPOEQU(3)

🦋 DPOEQU(3) — Library Functions Manual 🦋

Okay bestie, welcome to the DPOEQU(3) page in the Library Functions Manual ✨. This one is giving serious linear-algebra main character energy, and we're gonna get through every detail together.

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💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpoequ.f

That's the file this page is about, periodt. 🫶

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine DPOEQU (n, a, lda, s, scond, amax, info) — DPOEQU

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💅 Function/Subroutine Documentation 💅

subroutine DPOEQU (integer n, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) s, double precision scond,
       double precision amax, integer info)

DPOEQU — iconic, honestly. 💫

🎀 Purpose 🎀

DPOEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, with 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. No cap, that's the whole flex. 🔥

🌈 Parameters 🌈

• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The N-by-N symmetric 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 111 of file dpoequ.f.

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🫶 Author 🫶

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