laqge(3)

🌸 laqge(3) — laqge: row/col scale matrix 💅

okay bestie, this page is from the Library Functions Manual and it’s all about laqge, whose whole thing is literally row/col scale matrix ✨

✨ NAME ✨

• laqge — laqge: row/col scale matrix

🌈 SYNOPSIS 🌈

💖 Functions 💖

subroutine claqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
subroutine dlaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
subroutine slaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
subroutine zlaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)

• claqge — CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
• dlaqge — DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
• slaqge — SLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
• zlaqge — ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

🫶 Detailed Description

okay so this is the detailed rundown, bestie — the whole page is the function documentation for these four subroutines 💜

🧚 Function Documentation 🧚

💅 subroutine claqge

subroutine claqge (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose

CLAQGE equilibrates a general M by N matrix A using the row and column 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.
• A — A is COMPLEX array, dimension (LDA,N). On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• 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.

Author

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

Definition at line 141 of file claqge.f.

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💅 subroutine dlaqge

subroutine dlaqge (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, character equed)

DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose

DLAQGE equilibrates a general M by N matrix A using the row and column 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.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• 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.

Definition at line 140 of file dlaqge.f.

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💅 subroutine slaqge

subroutine slaqge (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

SLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose

SLAQGE equilibrates a general M by N matrix A using the row and column 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.
• A — A is REAL array, dimension (LDA,N). On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• 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.

Author

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

Definition at line 140 of file slaqge.f.

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💅 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.

Purpose

ZLAQGE equilibrates a general M by N matrix A using the row and column 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.
• A —

Okay so back to the parameter lineup, bestie — we’re still in Function Documentation, just picking up the args that didn’t fit in part one 💅

• A — this one is a 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, bestie 🔥
• LDA — LDA is INTEGER, the leading dimension of the array A. Must satisfy LDA >= max(M,1) ✨
• R — R is a DOUBLE PRECISION array, dimension (M). These are the row scale factors for A 🎀
• C — C is a 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).

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🔥 Internal Parameters 🔥

• THRESH — 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 — 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 🫶

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👑 Author 👑

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

Definition at line 141 of file zlaqge.f. ��

🦋 Author (the Doxygen one) 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie — LAPACK, Version 3.12.0, page laqge(3), signed off with love, zero skipped parameters, and all the vibes 💖✨🎀