SRC/dpoequb.f(3)

✨ NAME ✨

SRC/dpoequb.f — that’s the name, bestie. Short, iconic, and to the point. This is the manual page for SRC/dpoequb.f from the Library Functions Manual. 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine dpoequb (n, a, lda, s, scond, amax, info)
    DPOEQUB

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💖 Function/Subroutine Documentation 💖

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

🌸 Purpose 🌸

Okay so DPOEQUB 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, where 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 DPOEQU 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 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 117 of file dpoequb.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole page. Footer tea: LAPACK Version 3.12.0, page SRC/dpoequb.f(3) — and the date? not on this footer, bestie, just version vibes. Mwah 💋✨. No cap, you ate. 🫶