laqgb(3)

📦
version 3.12.1 · 9 versions
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💅 laqgb — row/col scale matrix (yes that's the whole name, iconic)

okay so bestie, welcome to laqgb(3) from the Library Functions Manual. This is a family of four Fortran subroutines — claqgb, dlaqgb, slaqgb, zlaqgb — and they all do the same lil job in different precisions: they equilibrate a general band matrix using row and column scaling factors. Spoiler: the factors come from sgbequ. We'll get there. Sit down, hydrate, let's go 💖

✨ NAME ✨

laqgb — laqgb: row/col scale matrix. That's it. That's the name. Ten out of ten, no notes 🎀

🦋 SYNOPSIS ✨

🌸 Functions

  • subroutine claqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed) — CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
  • subroutine dlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed) — DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
  • 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.
  • 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 computed by sgbequ.
💀 notice how all four have the exact same argument list? That's the whole vibe of this page. Same energy, different precision. iykyk.

🔥 Detailed Description ✨

Bestie there is literally nothing extra hiding in here — the detailed description section is where the actual Function Documentation lives. So let's meet the cast 🌈

👑 Function Documentation ✨

💜 subroutine claqgb 🌸

subroutine claqgb (integer m, integer n, integer kl, integer ku,
                   complex, dimension( ldab, * ) ab, integer ldab,
                   real, dimension( * ) r, real, dimension( * ) c,
                   real rowcnd, real colcnd, real amax,
                   character equed)

CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

⭐ Purpose:

!>
!> CLAQGB 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.
!>

So it takes your band matrix A and your scaling vectors R and C, and it equilibrates the whole situation. Main character behaviour honestly 🫶

🎀 Parameters

  • M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= 0. Respect the constraint, bestie.
  • N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. Constraint: KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. Constraint: KU >= 0.
  • AB — AB is COMPLEX 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. ✨

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. The page says LDA >= KL+KU+1 — yep, it really does say LDA there, and I'm not about to "fix" it for you, so quoting it exactly, periodt 💅
  • 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 158 of file claqgb.f.

🦋 subroutine dlaqgb 💖

subroutine dlaqgb (integer m, integer n, integer kl, integer ku,
                   double precision, dimension( ldab, * ) ab, integer ldab,
                   double precision, dimension( * ) r,
                   double precision, dimension( * ) c,
                   double precision rowcnd, double precision colcnd,
                   double precision amax, character equed)

DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

⭐ Purpose:

!>
!> DLAQGB 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.
!>

Same mission, double precision edition. She upgraded 💅✨

🎀 Parameters

  • M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. Constraint: KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. Constraint: KU >= 0.
  • AB — AB is DOUBLE PRECISION 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.

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. Again the page says LDA >= KL+KU+1 — same quirk as before, copying it faithfully 🫶
  • 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 157 of file dlaqgb.f.

🌈 subroutine slaqgb ⭐

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.

⭐ 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.
!>

Single precision queen, doing exactly what her sisters do 🎀

🎀 Parameters

  • M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. Constraint: KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. Constraint: 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.

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDA >= KL+KU+1 — yes, LDA, exactly as written on the page, no cap 🫶
  • 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 — this bestie is a CHARACTER*1 and it specifies the form of equilibration that was done. The vibe-check options are:
    • '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 — 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.

🌸 Author

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

The receipt says: Definition at line 157 of file slaqgb.f.

🦋 subroutine zlaqgb

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.

✨ 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.
  • LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDA >= KL+KU+1. (yes, the page literally says LDA, not LDAB — keep it exact, bestie)
  • 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 — 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.

🌸 Author

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

The receipt says: Definition at line 158 of file zlaqgb.f.

🌈 Author

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