geequ(3)

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version 3.12.1 · 9 versions
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💅 geequ(3) — Library Functions Manual 💅

okay so this is geequ from the <pink>Library Functions Manual</pink>, and it's literally the equilibration girlies' whole thing. Buckle up bestie, we're doing linear algebra self-care 💖

✨ NAME ✨

geequ — geequ: equilibration ✨

🎀 SYNOPSIS 🎀

Functions

  • subroutine cgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — CGEEQU
  • subroutine dgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — DGEEQU
  • subroutine sgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — SGEEQU
  • subroutine zgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — ZGEEQU

🫶 Detailed Description

no extra lore here, bestie — this section is just a heading in the original. The real tea is in the function documentation below 👇

🔥 Function Documentation 🔥

⭐ subroutine cgeequ ⭐

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

CGEEQU 💅

🦋 Purpose:

ok so what it actually does 👑

CGEEQU 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 absolute value 1.

R(i) and C(j) are restricted to be 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 works well in practice. (ngl that's kind of iconic of it.)

🌸 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 138 of file cgeequ.f.

⭐ subroutine dgeequ ⭐

subroutine dgeequ (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)

DGEEQU 🫶

🦋 Purpose:

DGEEQU 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 absolute value 1.

R(i) and C(j) are restricted to be 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 works well in practice.

🌸 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 137 of file dgeequ.f.

⭐ subroutine sgeequ ⭐

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

SGEEQU 🌈

🦋 Purpose:

SGEEQU 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 absolute value 1.

R(i) and C(j) are restricted to be 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 works well in practice.

🌸 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 — 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 137 of file sgeequ.f.

⭐ subroutine zgeequ ⭐

subroutine zgeequ (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)

ZGEEQU 💜

🦋 Purpose:

ZGEEQU 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 absolute value 1.

R(i) and C(j) are restricted to be 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 works well in practice.

...and that's literally where part 1 cuts off bestie 😭 the rest of zgeequ is coming in part 2, don't go anywhere 🌸

  • M 🌸 — it's an INTEGER, and it's the number of rows of the matrix A. Like, M >= 0, always. No negative rows bestie, that's not a thing.
  • N 🦋 — also an INTEGER, the number of columns of A. Same deal: N >= 0.
  • A 💜 — a COMPLEX*16 array, dimension (LDA,N). This is the actual M-by-N matrix whose equilibration factors we're out here computing. She's the main character of this whole function, periodt.
  • LDA ⭐ — INTEGER, the leading dimension of the array A. Gotta respect her: LDA >= max(1,M). Not optional, the vibes demand it.
  • R 🎀 — DOUBLE PRECISION array, dimension (M). If INFO = 0 or INFO > M, then R is where the row scale factors for A live. So she's holding the row receipts.
  • C 🍓 — DOUBLE PRECISION array, dimension (N). If INFO = 0, C contains the column scale factors for A. Column receipts, separate tab.
  • ROWCND ✨ — a DOUBLE PRECISION. If INFO = 0 or INFO > M, it holds the ratio of the smallest R(i) to the largest R(i). And here's the tea: if ROWCND >= 0.1 and AMAX is neither too large nor too small, it's genuinely not worth scaling by R. Like, why bother, the numbers are already fine.
  • COLCND 🌈 — DOUBLE PRECISION too. If INFO = 0, it contains the ratio of the smallest C(i) to the largest C(i). And if COLCND >= 0.1, it is not worth scaling by C. Same energy, column edition.
  • AMAX 🔥 — DOUBLE PRECISION. The absolute value of the largest matrix element. Now listen: if AMAX is very close to overflow or very close to underflow, the matrix should be scaled. That's a real warning, ngl, don't sleep on it — those are the danger zones 😭
  • INFO 👑 — INTEGER, and she's the whole status report, so let's break it all the way down:
    • = 0: successful exit 💖 everything slayed, we're done here.
    • < 0: if INFO = -i, then the i-th argument had an illegal value. Somebody passed something cursed 🙈
    • > 0: if INFO = i, and i is:
      • <= M: the i-th row of A is exactly zero. Like, completely zero. Empty. Nothing going on there 💀
      • > M: the (i-M)-th column of A is exactly zero. Same situation, column flavour.

👑 Author 👑

Say thank you to the institutions, bestie, they did the work:

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

Definition at line 138 of file zgeequ.f. ⭐

🫶 Author 🫶

This page was generated automatically by Doxygen for LAPACK straight from the source code. So like, don't come for the formatting, a robot wrote it 🧚

And that's the whole page, bestie — SHE'S DONE 💅 This was LAPACK, Version 3.12.0, page geequ(3), and you absolutely ate that reading comprehension. No cap. 🎀✨🦋

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