SRC/zlaqge.f(3)

📦
version 3.12.1 · 4 versions
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✨ NAME ✨

okay bestie, this is the page for SRC/zlaqge.f, and it's coming at you from the Library Functions Manual 💅. It's a LAPACK function page, and we're about to get into some matrix-equilibration business. Periodt.

🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

subroutine zlaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
           ZLAQGE scales a general rectangular matrix, using row and column
           scaling factors computed by sgeequ.

💖 Function/Subroutine Documentation 💖

🌟 subroutine zlaqge 🌟

subroutine zlaqge (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, character equed)

ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. It's giving very "let me fix your vibes" energy for a matrix 🔥.

🎀 Purpose 🎀

ZLAQGE equilibrates a general M by N matrix A using the row and column scaling factors in the vectors R and C. Obsessed with a balanced matrix, honestly.

💅 Parameters 💅

  • M — okay so M is INTEGER, and it's the number of rows of the matrix A. M >= 0. 🫶
  • N — N is INTEGER, and it's the number of columns of the matrix A. N >= 0. 🌸
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, it's the M by N matrix A. On exit, it's the equilibrated matrix. See EQUED for the form of the equilibrated matrix. 🦋
  • LDA — LDA is INTEGER, and it's the leading dimension of the array A. LDA >= max(M,1). Don't skip this, bestie. 🎀
  • R — R is DOUBLE PRECISION array, dimension (M). These are the row scale factors for A. 💜
  • C — C is DOUBLE PRECISION array, dimension (N). These are the column scale factors for A. 💖
  • ROWCND — ROWCND is DOUBLE PRECISION. It's the ratio of the smallest R(i) to the largest R(i). 💫
  • COLCND — COLCND is DOUBLE PRECISION. It's the ratio of the smallest C(i) to the largest C(i). ✨
  • AMAX — AMAX is DOUBLE PRECISION. It's the absolute value of the largest matrix entry. 🍓
  • EQUED — EQUED is CHARACTER*1. It 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.

Definition at line 141 of file zlaqge.f. 🫡

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. ✨

mwah 💋 LAPACK Version 3.12.0 and this page is SRC/zlaqge.f(3) — bye bestie, go equilibrate something cute 🫶✨

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