poequb(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

✨ NAME ✨

poequb — equilibration, power of 2 💅

(yeah bestie, this is the poequb(3) page — Library Functions Manual, section 3, and it's literally four subroutines that all do the same iconic thing in different precisions 🎀)

🌸 SYNOPSIS 🌸

Functions

subroutine cpoequb (n, a, lda, s, scond, amax, info)
    CPOEQUB
subroutine dpoequb (n, a, lda, s, scond, amax, info)
    DPOEQUB
subroutine spoequb (n, a, lda, s, scond, amax, info)
    SPOEQUB
subroutine zpoequb (n, a, lda, s, scond, amax, info)
    ZPOEQUB

🦋 DETAILED DESCRIPTION 🦋

okay so real talk — this whole page is the same routine living its best life in four different data types, and each one gets its own little write-up below. no cap, they're identical apart from the type of the matrix and the type of the scale factors. pick the one that matches your array and slay. ✨

💜 FUNCTION DOCUMENTATION 💜

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

CPOEQUB

🎀 Purpose

CPOEQUB 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 CPOEQU 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 — and this is the tradeoff, bestie — 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. (yes, zero is allowed, she's flexible 💖)
  • A — A is COMPLEX 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 — so don't stress about the rest, she's not looking 👀
  • 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. like, don't bother, it's giving unnecessary effort 💀
  • 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 118 of file cpoequb.f.

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

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, 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). same energy, different precision, we love consistency ✨

🌈 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.

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

SPOEQUB

🎀 Purpose

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). the single-precision girlies are eating too 🍓

🌈 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.

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

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). double-complex main character energy, honestly 👑

🌈 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 — DOUBLE PRECISION. This is the absolute value of the largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. No cap, handle that scaling situation bestie 🫶
  • INFO — INTEGER. The little report card of what happened:
    • = 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.

The definition is at line 118 of file zpoequb.f.

🤖 Author (the automated one) 🤖

Generated automatically by Doxygen for LAPACK from the source code. The robots really said “we got this one” 🤖💅

That’s the whole vibe check, bestie. Source/version is LAPACK Version 3.12.0 and the footer is giving poequb(3) energy — the date isn’t printed in this footer, but the icon behavior absolutely is 🌈✨

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