realGBauxiliary(3)

📦
version 3.11.0 · 2 versions
, in debian bookworm

💖 realGBauxiliary(3) 💖

okay bestie, welcome to the LAPACK group chat 🫶 this is the man page for realGBauxiliary and it is literally the whole little squad of real auxiliary functions for GB matrices. no cap. grab a snack, we're doing this. 🍓

✨ NAME ✨

realGBauxiliary — real 💅

🌸 SYNOPSIS 🌸

🎀 Functions 🎀

  • real function slangb (NORM, N, KL, KU, AB, LDAB, WORK) — SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 🔥
  • subroutine slaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED) — SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. 💫

🦋 Detailed Description 🦋

This is the group of real auxiliary functions for GB matrices. that's it, that's the vibe. ✨

👑 Function Documentation 👑

🌈 real function slangb (character NORM, integer N, integer KL, integer KU, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) WORK)

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. iconic behavior honestly. 💚

🎯 Purpose:

SLANGB  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the element of  largest absolute value  of an
n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.

💜 Returns

SLANGB

   SLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
            (
            ( norm1(A),         NORM = '1', 'O' or 'o'
            (
            ( normI(A),         NORM = 'I' or 'i'
            (
            ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. it's giving "chaotic but valid", periodt. 😭

⭐ Parameters

  • NORM

NORM is CHARACTER*1 Specifies the value to be returned in SLANGB as described above. bestie, this is the whole personality of the call. 💅

  • N

N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero. zero, no notes.

  • KL

KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0.

  • KU

KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0.

  • AB

AB is REAL array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
  • LDAB

LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. respect the leading dimension or perish 🫶

  • WORK

WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. so if you're not doing 'I', she simply does not see it. ghosted. 💀

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌟 subroutine slaqgb (integer M, integer N, integer KL, integer KU, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) R, real, dimension( * ) C, real ROWCND, real COLCND, real AMAX, character EQUED)

SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. equilibration era 💖

🎯 Purpose:

SLAQGB equilibrates a general M by N band matrix A with KL
subdiagonals and KU superdiagonals using the row and scaling factors
in the vectors R and C.

⭐ 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.

  • KL

KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.

  • KU

KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.

  • AB

AB is REAL array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix. she came in as one thing and left as another, glow-up fr fr ✨

  • LDAB

LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1. (yes bestie, the page literally says LDA here, we do not question the ancestors 😭)

  • R

R is REAL array, dimension (M) The row scale factors for A.

  • C

C is REAL array, dimension (N) The column scale factors for A.

  • ROWCND

ROWCND is REAL Ratio of the smallest R(i) to the largest R(i).

  • COLCND

COLCND is REAL Ratio of the smallest C(i) to the largest C(i).

  • AMAX

AMAX is REAL Absolute value of largest matrix entry.

  • EQUED

EQUED is CHARACTER*1 Specifies the form of equilibration that was done.

  • = 'N': No equilibration
  • = 'R': Row equilibration, i.e., A has been premultiplied by diag(R).
  • = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C).
  • = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

🧠 Internal Parameters:

THRESH is a threshold value used to decide if row or column scaling
should be done based on the ratio of the row or column scaling
factors.  If ROWCND < THRESH, row scaling is done, and if
COLCND < THRESH, column scaling is done.

LARGE and SMALL are threshold values used to decide if row scaling
should be done based on the absolute size of the largest matrix
element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

thresholds doing the decision-making so you don't have to 💅

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. not me being a whole auto-generated document and still serving looks 🙈

okay that's the whole page bestie, you ate it, you understood it, main character energy confirmed. 👑

and a lil sign-off for the credits section, because we always thank the people who made the thing: this is LAPACK, Version 3.11.0, dated Sun Nov 27 2022. 🎀✨🦋 periodt. 💜

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