laqhe(3)

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💅 laqhe(3) — Library Functions Manual

✨ NAME ✨

laqhe — literally just laqhe: row/col scale matrix. That's the whole name, bestie, no notes 💖

🦋 SYNOPSIS 🦋

🌸 Functions

  • subroutine claqhe (uplo, n, a, lda, s, scond, amax, equed) — CLAQHE scales a Hermitian matrix. 🎀
  • subroutine claqsy (uplo, n, a, lda, s, scond, amax, equed) — CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
  • subroutine dlaqsy (uplo, n, a, lda, s, scond, amax, equed) — DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
  • subroutine slaqsy (uplo, n, a, lda, s, scond, amax, equed) — SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
  • subroutine zlaqhe (uplo, n, a, lda, s, scond, amax, equed) — ZLAQHE scales a Hermitian matrix. 🌈
  • subroutine zlaqsy (uplo, n, a, lda, s, scond, amax, equed) — ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

🧚 Detailed Description

🔥 Function Documentation

⭐ subroutine claqhe (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

CLAQHE scales a Hermitian matrix.

Purpose:

CLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S.

Parameters

  • UPLO UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N N is INTEGER. The order of the matrix A. N >= 0.
  • A A is COMPLEX array, dimension (LDA,N).

On entry, the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).

  • LDA LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1).
  • S S is REAL array, dimension (N). The scale factors for A.
  • SCOND SCOND is REAL. Ratio of the smallest S(i) to the largest S(i).
  • AMAX AMAX is REAL. Absolute value of largest matrix entry.
  • EQUED EQUED is CHARACTER*1. Specifies whether or not equilibration was done.
    • = 'N': No equilibration.
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

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

Author

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

Definition at line 133 of file claqhe.f.

⭐ subroutine claqsy (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

CLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S.

Parameters

  • UPLO UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N N is INTEGER. The order of the matrix A. N >= 0.
  • A A is COMPLEX array, dimension (LDA,N).

On entry, the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).

  • LDA LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1).
  • S S is REAL array, dimension (N). The scale factors for A.
  • SCOND SCOND is REAL. Ratio of the smallest S(i) to the largest S(i).
  • AMAX AMAX is REAL. Absolute value of largest matrix entry.
  • EQUED EQUED is CHARACTER*1. Specifies whether or not equilibration was done.
    • = 'N': No equilibration.
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

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

Author

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

Definition at line 133 of file claqsy.f.

⭐ subroutine dlaqsy (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

DLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S.

Parameters

  • UPLO UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N N is INTEGER. The order of the matrix A. N >= 0.
  • A A is DOUBLE PRECISION array, dimension (LDA,N).

On entry, the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).

  • LDA LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1).
  • S S is DOUBLE PRECISION array, dimension (N). The scale factors for A.
  • SCOND SCOND is DOUBLE PRECISION. Ratio of the smallest S(i) to the largest S(i).
  • AMAX AMAX is DOUBLE PRECISION. Absolute value of largest matrix entry.
  • EQUED EQUED is CHARACTER*1. Specifies whether or not equilibration was done.
    • = 'N': No equilibration.
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

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

Author

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

Definition at line 132 of file dlaqsy.f.

⭐ subroutine slaqsy (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

SLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S.

Parameters

  • UPLO UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N N is INTEGER. The order of the matrix A. N >= 0.

okay bestie, the A parameter breakdown for SLAQSY keeps going in part 2 — don't go anywhere 🫶

  • A — A is REAL array, dimension (LDA,N). On entry, A is the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced — leave it alone, bestie. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', this is the equilibrated matrix: diag(S) * A * diag(S).

  • LDA — LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(N,1). No skimping, okay? 💅
  • S — S is REAL array, dimension (N). These are the scale factors for A. ✨
  • SCOND — SCOND is REAL. It's the ratio of the smallest S(i) to the largest S(i). Math bestie behavior.
  • AMAX — AMAX is REAL. Absolute value of the largest matrix entry. Big main-character energy.
  • EQUED — EQUED is CHARACTER*1. Specifies whether or not equilibration was done.
    • = 'N': No equilibration.
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done.

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

Author

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

Definition at line 132 of file slaqsy.f.

✨ subroutine zlaqhe — ZLAQHE scales a Hermitian matrix ✨

subroutine zlaqhe (character uplo, integer n, complex*16, dimension( lda, *
) a, integer lda, double precision, dimension( * ) s, double precision
scond, double precision amax, character equed)

Purpose

ZLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S. slay.

Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, A is the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).

  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1).
  • S — S is DOUBLE PRECISION array, dimension (N). The scale factors for A. 🎀
  • SCOND — SCOND is DOUBLE PRECISION. Ratio of the smallest S(i) to the largest S(i).
  • AMAX — AMAX is DOUBLE PRECISION. Absolute value of largest matrix entry.
  • EQUED — EQUED is CHARACTER*1. Specifies whether or not equilibration was done.
    • = 'N': No equilibration.
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done.

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

Author

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

Definition at line 133 of file zlaqhe.f.

🌈 subroutine zlaqsy — ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ 🌈

subroutine zlaqsy (character uplo, integer n, complex*16, dimension( lda, *
) a, integer lda, double precision, dimension( * ) s, double precision
scond, double precision amax, character equed)

Purpose

ZLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S.

Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, A is the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).

  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,1).
  • S — S is DOUBLE PRECISION array, dimension (N). The scale factors for A.
  • SCOND — SCOND is DOUBLE PRECISION. Ratio of the smallest S(i) to the largest S(i).
  • AMAX — AMAX is DOUBLE PRECISION. Absolute value of largest matrix entry.
  • EQUED — EQUED is CHARACTER*1. Specifies whether or not equilibration was done.
    • = 'N': No equilibration.
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done.

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

Author

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

Definition at line 133 of file zlaqsy.f.

🫶 Author

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