laqhp(3)

📦
version 3.12.1 · 9 versions
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💅 laqhp — row/col scale matrix ✨

okay so bestie, welcome to laqhp(3) from the Library Functions Manual 💖 this page is basically the group chat for six subroutines that all do the same iconic thing — they equilibrate your matrix using the scaling factors in the vector S, i.e. they swap A out for diag(S) * A * diag(S) (row/col scale, hence the NAME, periodt 👑). And the whole time the matrix stays in packed storage, because we're efficient like that 🎀

🌸 SYNOPSIS 🌸

Functions

  • claqhp — CLAQHP scales a Hermitian matrix stored in packed form.
  • claqsp — CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
  • dlaqsp — DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
  • slaqsp — SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
  • zlaqhp — ZLAQHP scales a Hermitian matrix stored in packed form.
  • zlaqsp — ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

🦋 Detailed Description 🦋

💜 Function Documentation 💜

claqhp — the complex Hermitian packed one 💫

subroutine claqhp (character uplo, integer n, complex, dimension( * ) ap,
    real, dimension( * ) s, real scond, real amax, character equed)

CLAQHP scales a Hermitian matrix stored in packed form.

🌟 Purpose:

CLAQHP equilibrates a Hermitian matrix A using the scaling factors in the vector S. that's the whole job bestie, and she does it flawlessly ✨

🎀 Parameters

  • UPLO — CHARACTER*1. says which triangle of the Hermitian matrix A we're storing:
    • 'U': Upper triangular
    • 'L': Lower triangular
  • N — INTEGER. the order of the matrix A. lowkey important: N >= 0.
  • AP — COMPLEX array, dimension (N*(N+1)/2). On entry, this holds the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. the j-th column of A lives in AP like this:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, it's the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A. same fit, new energy 🫶

  • S — REAL array, dimension (N). the scale factors for A.
  • SCOND — REAL. ratio of the smallest S(i) to the largest S(i).
  • AMAX — REAL. absolute value of largest matrix entry.
  • EQUED — CHARACTER*1. tells you 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 125 of file claqhp.f.

claqsp — complex, symmetric/Hermitian, packed 💅

subroutine claqsp (character uplo, integer n, complex, dimension( * ) ap,
    real, dimension( * ) s, real scond, real amax, character equed)

CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

🌟 Purpose:

CLAQSP equilibrates a symmetric matrix A using the scaling factors in the vector S. no notes, she ate 🔥

🎀 Parameters

  • UPLO — CHARACTER*1. which triangle of the symmetric matrix A is stored, choose your fighter:
    • 'U': Upper triangular
    • 'L': Lower triangular
  • N — INTEGER. the order of the matrix A. N >= 0, always.
  • AP — COMPLEX array, dimension (N*(N+1)/2). On entry: the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. here's the mapping for the j-th column of A:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit: the equilibrated matrix diag(S) * A * diag(S), sitting in the same storage format as A 💖

  • S — REAL array, dimension (N). The scale factors for A.
  • SCOND — REAL. Ratio of the smallest S(i) to the largest S(i).
  • AMAX — REAL. Absolute value of largest matrix entry.
  • EQUED — 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 125 of file claqsp.f.

dlaqsp — double precision edition 🧊

subroutine dlaqsp (character uplo, integer n, double precision, dimension( *
    ) ap, double precision, dimension( * ) s, double precision scond, double
    precision amax, character equed)

DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

🌟 Purpose:

DLAQSP equilibrates a symmetric matrix A using the scaling factors in the vector S. double the precision, double the slay 💀✨

🎀 Parameters

  • UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
    • 'U': Upper triangular
    • 'L': Lower triangular
  • N — INTEGER. The order of the matrix A. N >= 0.
  • AP — DOUBLE PRECISION array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. the j-th column of A is stored in AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A 🌈

  • S — DOUBLE PRECISION array, dimension (N). The scale factors for A.
  • SCOND — DOUBLE PRECISION. Ratio of the smallest S(i) to the largest S(i).
  • AMAX — DOUBLE PRECISION. Absolute value of largest matrix entry.
  • EQUED — 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 124 of file dlaqsp.f.

slaqsp — single precision, single-minded focus 🍓

subroutine slaqsp (character uplo, integer n, real, dimension( * ) ap, real,
    dimension( * ) s, real scond, real amax, character equed)

SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

🌟 Purpose:

SLAQSP equilibrates a symmetric matrix A using the scaling factors in the vector S. main character energy fr fr 👑

🎀 Parameters

  • UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
    • 'U': Upper triangular
    • 'L': Lower triangular
  • N — INTEGER. The order of the matrix A. N >= 0.
  • AP — REAL array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. the j-th column of A is stored in AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A ⭐

  • S — REAL array, dimension (N). The scale factors for A.
  • SCOND — REAL. Ratio of the smallest S(i) to the largest S(i).
  • AMAX — REAL. Absolute value of largest matrix entry.
  • EQUED — 🫶 hold that thought, bestie — more of this page is coming in part 2 💖
  • EQUED is CHARACTER*1 — it's the receipts, bestie 💅 it tells you whether equilibration was actually done or not.
    • = 'N': no equilibration, we left it alone.
    • = '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 124 of file slaqsp.f.

🌸 zlaqhp 🌸

subroutine zlaqhp (character uplo, integer n, complex*16, dimension( * ) ap,
    double precision, dimension( * ) s, double precision scond, double
    precision amax, character equed)

ZLAQHP scales a Hermitian matrix stored in packed form. That's the whole elevator pitch, no cap 🛗✨

🎯 Purpose

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

🧩 Parameters

  • UPLO is CHARACTER*1 — bestie, this is the "which half are we storing" switch for the Hermitian matrix A.
    • = 'U': upper triangular
    • = 'L': lower triangular
  • N is INTEGER — the order of the matrix A. Constraint check: N >= 0 🫶
  • AP is COMPLEX*16 array, dimension (N*(N+1)/2) — the packed triangle, living its best linear-array life. On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A. It literally reinvented itself, icon behaviour 💅

  • S is DOUBLE PRECISION array, dimension (N) — the scale factors for A. The main characters tbh.
  • SCOND is DOUBLE PRECISION — ratio of the smallest S(i) to the largest S(i). The little-to-big vibe check 📏
  • AMAX is DOUBLE PRECISION — absolute value of largest matrix entry. The biggest fish in the matrix pond 🐟
  • EQUED is CHARACTER*1 — the receipts again, telling you if equilibration happened.
    • = '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 125 of file zlaqhp.f.

💜 zlaqsp 💜

subroutine zlaqsp (character uplo, integer n, complex*16, dimension( * ) ap,
    double precision, dimension( * ) s, double precision scond, double
    precision amax, character equed)

ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. Family reunion of the scaling routines fr fr 🫂✨

🎯 Purpose

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

🧩 Parameters

  • UPLO is CHARACTER*1 — strikes again. Tells you whether the upper or lower triangular part of the symmetric matrix A is stored.
    • = 'U': upper triangular
    • = 'L': lower triangular
  • N is INTEGER — the order of the matrix A. N >= 0, always check bestie 🫶
  • AP is COMPLEX*16 array, dimension (N*(N+1)/2) — the packed triangle, same deal, symmetric edition. On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A. Glow-up complete ✨

  • S is DOUBLE PRECISION array, dimension (N) — the scale factors for A.
  • SCOND is DOUBLE PRECISION — ratio of the smallest S(i) to the largest S(i).
  • AMAX is DOUBLE PRECISION — absolute value of largest matrix entry.
  • EQUED is CHARACTER*1 — did we equilibrate or not, that is the question 🎭
    • = '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 125 of file zlaqsp.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page bestie, you ate that 🎀 This lil beauty is from LAPACK, Version 3.12.0, page laqhp(3) — go forth and equilibrate responsibly, mwah 💖✨🫶
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