complex16GBauxiliary(3)

📦
version 3.11.0 · 2 versions
, in debian bookworm

💅 complex16GBauxiliary — the LAPACK page, but make it make sense

okay so bestie, this is a page out of the LAPACK manual (you know, the linear algebra girlies). It's for complex16GBauxiliary(3), and no cap, it's a whole little group of complex16 auxiliary functions that do their thing on GB matrices — that's general band matrices, iykyk. Two functions in the squad. Let's get into it. 🎀

✨ NAME ✨

complex16GBauxiliary — complex16 💖

✨ SYNOPSIS ✨

🦋 Functions

  • double precision function zlangb (NORM, N, KL, KU, AB, LDAB, WORK) — ZLANGB hands you back the value of the 1-norm, the Frobenius norm, the infinity-norm, or literally just the largest absolute value of any element of a general band matrix. pick your fighter. 💅
  • subroutine zlaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED) — ZLAQGB scales a general band matrix, using row and column scaling factors that were computed by sgbequ. slay.

✨ Detailed Description ✨

This is the group of complex16 auxiliary functions for GB matrices. that's it, that's the vibe. 🌸

✨ Function Documentation ✨

💜 double precision function zlangb (character NORM, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) WORK)

ZLANGB 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:

ZLANGB  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

ZLANGB 👑

ZLANGB = ( 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). 📐

heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. it's just... a vibe. don't @ me. 💀

🫶 Parameters

  • NORM

NORM is CHARACTER*1 Specifies the value to be returned in ZLANGB as described above. pick one, girl. 🌈

  • N

N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANGB is set to zero. (empty matrix, empty feelings, zero.) 🍓

  • 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 COMPLEX*16 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. (yes, it's a real requirement, respect it. 🎀)

  • WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. she's only here when she's needed. main character energy. 👑

🫶 Author

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

💜 subroutine zlaqgb (integer M, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED)

ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ. it's giving glow-up for your matrix. ✨🦋

🫶 Purpose:

ZLAQGB 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 COMPLEX*16 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. (before/after pic fr fr. 📸)

  • LDAB

LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1. (yes bestie, the original says LDA here, not LDAB. we don't make the rules, we just report them. 🙈)

  • R

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

  • C

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

  • ROWCND

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

  • COLCND

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

  • AMAX

AMAX is DOUBLE PRECISION 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.

🫶 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. (the robots wrote this one, we just gave it a makeover 💅)

and that's the whole page, bestie!! this was LAPACK Version 3.11.0, dated Sun Nov 27 2022 — so if you're citing her, that's the era. periodt. 💖✨🎀🦋🌸

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