/home/abui.../spoequb.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

okay bestie, welcome to the Library Functions Manual page for spoequb.f(3) ✨ — yes, we're doing Fortran linear algebra and we're gonna make it cute.

💖 NAME

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

✨ SYNOPSIS

Functions/Subroutines

  • subroutine SPOEQUB (n, a, lda, s, scond, amax, info) — the main character 💅

🦋 FUNCTION/SUBROUTINE DOCUMENTATION

subroutine SPOEQUB (integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)

SPOEQUB — yep, that's the subroutine, bestie 🫶

🌸 PURPOSE

okay so SPOEQUB 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, 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 SPOEQU 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). periodt 🌈

💅 PARAMETERS

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is REAL 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 REAL array, dimension (N). If INFO = 0, S contains the scale factors for A.
  • SCOND — SCOND is REAL. 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 REAL. 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 spoequb.f

Definition at line 117 of file spoequb.f.

Author

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