geequb(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

okay bestie, welcome to geequb(3) from the Library Functions Manual — she does equilibration with power of 2 energy, and honestly? iconic. ✨

🎀 NAME 🎀

  • geequb — geequb: equilibration, power of 2

🌸 SYNOPSIS 🌸

💅 Functions 💅

cgeequb — CGEEQUB

subroutine cgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)

dgeequb — DGEEQUB

subroutine dgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)

sgeequb — SGEEQUB

subroutine sgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)

zgeequb — ZGEEQUB

subroutine zgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)

🦋 Detailed Description 🦋

the detailed deets live in Function Documentation below — no cap, that's where the whole breakdown is. 💖

👑 Function Documentation 👑

🧚 subroutine cgeequb 🧚

subroutine cgeequb (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

CGEEQUB

✨ Purpose ✨

okay so CGEEQUB computes row and column scalings — the whole goal is to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C returns the column scale factors, and they're chosen to try to make the largest element in each row and column of the matrix B (with elements B(i,j)=R(i)*A(i,j)*C(j)) have an absolute value of at most the radix. 🫶

R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice — lowkey reliable. 💅

This routine differs from CGEEQU 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 entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). 😭 that range is the whole personality, fr.

🎀 Parameters 🎀

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). The M-by-N matrix whose equilibration factors are to be computed.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • R — R is REAL array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A.
  • C — C is REAL array, dimension (N). If INFO = 0, C contains the column scale factors for A.
  • ROWCND — ROWCND is REAL. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R.
  • COLCND — COLCND is REAL. If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C.
  • 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, and i is
      • <= M: the i-th row of A is exactly zero
      • > M: the (i-M)-th column of A is exactly zero

💜 Author 💜

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 145 of file cgeequb.f.

🧚 subroutine dgeequb 🧚

subroutine dgeequb (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)

DGEEQUB

✨ Purpose ✨

okay so DGEEQUB computes row and column scalings — the whole goal is to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C returns the column scale factors, and they're chosen to try to make the largest element in each row and column of the matrix B (with elements B(i,j)=R(i)*A(i,j)*C(j)) have an absolute value of at most the radix. 🫶

R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice — lowkey reliable. 💅

This routine differs from DGEEQU 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 entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). 😭 that range is the whole personality, fr.

🎀 Parameters 🎀

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). The M-by-N matrix whose equilibration factors are to be computed.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • R — R is DOUBLE PRECISION array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A.
  • C — C is DOUBLE PRECISION array, dimension (N). If INFO = 0, C contains the column scale factors for A.
  • ROWCND — ROWCND is DOUBLE PRECISION. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R.
  • COLCND — COLCND is DOUBLE PRECISION. If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C.
  • 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, and i is
      • <= M: the i-th row of A is exactly zero
      • > M: the (i-M)-th column of A is exactly zero

💜 Author 💜

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 144 of file dgeequb.f.

🧚 subroutine sgeequb 🧚

subroutine sgeequb (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

SGEEQUB

✨ Purpose ✨

okay so SGEEQUB computes row and column scalings — the whole goal is to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C returns the column scale factors, and they're chosen to try to make the largest element in each row and column of the matrix B (with elements B(i,j)=R(i)*A(i,j)*C(j)) have an absolute value of at most the radix. 🫶

R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice — lowkey reliable. 💅

This routine differs from SGEEQU 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 entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). 😭 that range is the whole personality, fr.

🎀 Parameters 🎀

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • A — A is REAL array, dimension (LDA,N). The M-by-N matrix whose equilibration factors are to be computed.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • R — R is REAL array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A.
  • C — C is REAL array, dimension (N). If INFO = 0, C contains the column scale factors for A.
  • ROWCND — ROWCND is REAL. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R.
  • COLCND — COLCND is REAL. If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C.
  • 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

(bestie, the original page cuts off right here mid-INFO — part 2 picks it up, so don't close the tab 💅✨)

  • INFO — it's an INTEGER, bestie, and it's the vibe check for the whole call:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value 🙈
    • > 0: if INFO = i, and i is
      • <= M: the i-th row of A is exactly zero 😭
      • > M: the (i-M)-th column of A is exactly zero 😭

💜 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 144 of file sgeequb.f.

🦋 The ZGEEQUB era

subroutine zgeequb (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, double precision, dimension( * ) r, double precision,
    dimension( * ) c, double precision rowcnd, double precision colcnd,
    double precision amax, integer info)

⭐ ZGEEQUB

Purpose:

ok so this one is the complex*16 sibling of the whole situation we just discussed, and it ATE 💅

ZGEEQUB computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most the radix. iconic behavior honestly ✨

R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Heads up though — use of these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice. no cap, it just vibes 🫶

🎀 This routine differs from ZGEEQU 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 entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). lowkey important, don't skip this one.

🌸 Parameters

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0. (yes, it can be zero, we love a flexible king 👑)
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). The M-by-N matrix whose equilibration factors are to be computed. main character matrix energy 🦋
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). respect the leading dimension bestie, it WILL catch you 💀
  • R — R is DOUBLE PRECISION array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A.
  • C — C is DOUBLE PRECISION array, dimension (N). If INFO = 0, C contains the column scale factors for A.
  • ROWCND — ROWCND is DOUBLE PRECISION. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. like, don't bother, it's fine ✨
  • COLCND — COLCND is DOUBLE PRECISION. If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C. same energy, different axis 🫶
  • 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. like actually should. please. 🙏
  • INFO — INFO is INTEGER, the final report card:
    • = 0: successful exit 🔥
    • < 0: if INFO = -i, the i-th argument had an illegal value 🙈
    • > 0: if INFO = i, and i is
      • <= M: the i-th row of A is exactly zero 😭
      • > M: the (i-M)-th column of A is exactly zero 😭

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 145 of file zgeequb.f.

🎀 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing its little job 🤖✨

and that's the whole page bestie, ily, go equilibrate something 💖 this was geeque b(3) from LAPACK, Version 3.12.0 — mwah, see u next manpage 🫶🌈🦋

📦 where this page comes from