laqhb(3)

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version 3.12.1 · 9 versions
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🎀 laqhb(3) 🎀

okay bestie, welcome to the laqhb page — the glow-up guide for row/col scale matrices 💅✨. It's a library functions manual situation, and we're gonna walk through every single one of these subroutines together, no cap.

✨ NAME ✨

laqhb — row/col scale matrix. that's the vibe. iconic, honestly 🫶

🌸 SYNOPSIS 🌸

💖 Functions

  • subroutine claqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. slay.
  • subroutine claqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
  • subroutine dlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
  • subroutine slaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
  • subroutine zlaqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.
  • subroutine zlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

🦋 Detailed Description 🦋

okay so this is where it gets juicy — the Function Documentation. we're going deep on each one, one at a time. buckle up 💀✨

👑 Function Documentation 👑

🧚 claqhb 🧚

subroutine claqhb (character uplo, integer n, integer kd, complex,
     dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real
     scond, real amax, character equed)

CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. literally its whole personality 💅

✨ Purpose ✨

CLAQHB equilibrates an Hermitian band matrix A using the scaling factors in the vector S.

🌸 Parameters 🌸

  • UPLO — UPLO is CHARACTER*1. Tells us 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.
  • KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
  • AB — AB is COMPLEX array, dimension (LDAB,N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A. (yes bestie, **H — Hermitian energy 👑)

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+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 140 of file claqhb.f.

🍓 claqsb 🍓

subroutine claqsb (character uplo, integer n, integer kd, complex,
     dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real
     scond, real amax, character equed)

CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. same energy, different name, still ate 💅

✨ Purpose ✨

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

🌸 Parameters 🌸

  • UPLO — UPLO is CHARACTER*1. Tells us 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.
  • KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
  • AB — AB is COMPLEX array, dimension (LDAB,N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A.

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+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 140 of file claqsb.f.

🌈 dlaqsb 🌈

subroutine dlaqsb (character uplo, integer n, integer kd, double precision,
     dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
     s, double precision scond, double precision amax, character equed)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. double precision edition, we love to see it ✨

✨ Purpose ✨

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

🌸 Parameters 🌸

  • UPLO — UPLO is CHARACTER*1. Tells us 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.
  • KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
  • AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A. (note: this one's **T, not **H — keep that energy, bestie 🙈)

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+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 139 of file dlaqsb.f.

🫶 subroutine slaqsb — the real-valued one, let's go

subroutine slaqsb (character uplo, integer n, integer kd, real, dimension(
    ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real
    amax, character equed)

okay so SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. ✨ That's the whole vibe. It's the glow-up pass for your matrix.

💖 Purpose

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

Literally just: here's A, here's S, let's make A behave. 🎀

🌸 Parameters

  • UPLO — UPLO is CHARACTER*1, and it tells us which triangle of the symmetric matrix A we're storing, bestie:
    • = 'U': Upper triangular ⬆️
    • = 'L': Lower triangular ⬇️
  • N — N is INTEGER, the order of the matrix A. Constraint: N >= 0. (Zero is allowed, she's valid. 💅)
  • KD — KD is INTEGER, the number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. Constraint: KD >= 0. 🦋
  • AB — AB is REAL array, dimension (LDAB,N). Okay so on entry, this holds the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A lives in the j-th column of the array AB like this:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, you get the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A. Same fit, new outfit. 🔥

  • LDAB — LDAB is INTEGER, the leading dimension of the array AB. Constraint: LDAB >= KD+1. Don't skimp. 🙈
  • S — S is REAL array, dimension (N). The scale factors for A. 🌈
  • SCOND — SCOND is REAL. The ratio of the smallest S(i) to the largest S(i). 🍓
  • AMAX — AMAX is REAL. The absolute value of the largest matrix entry. 👑
  • EQUED — EQUED is CHARACTER*1, and it reports whether or not equilibration was actually done:
    • = 'N': No equilibration. 😴
    • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). 💅 periodt

🧚 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 139 of file slaqsb.f.

💜 subroutine zlaqhb — Hermitian band matrix edition

subroutine zlaqhb (character uplo, integer n, integer kd, complex*16,
    dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
    s, double precision scond, double precision amax, character equed)

ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. 🦋 Same energy, complex flavour.

🌸 Purpose

ZLAQHB equilibrates a Hermitian band 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. Constraint: N >= 0. 💅
  • KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. Constraint: KD >= 0. ✨
  • AB — AB is COMPLEX*16 array, dimension (LDAB,N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A. Note the **H — conjugate transpose, she's fancy like that. 🔥

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. Constraint: LDAB >= KD+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 140 of file zlaqhb.f.

🌈 subroutine zlaqsb — complex symmetric/Hermitian band one

subroutine zlaqsb (character uplo, integer n, integer kd, complex*16,
    dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
    s, double precision scond, double precision amax, character equed)

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. 💖 (Yes, spbequ — that's what it says, don't come for me. 🫶)

🌸 Purpose

ZLAQSB equilibrates a symmetric band 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. Constraint: N >= 0. 💅
  • KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. Constraint: KD >= 0. ✨
  • AB — AB is COMPLEX*16 array, dimension (LDAB,N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A. 🔥

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. Constraint: LDAB >= KD+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 140 of file zlaqsb.f.

👑 Author

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and that's the whole page, bestie!! 🎀 This one's from LAPACK, Version 3.12.0, and it's the laqhb(3) page — go forth and scale those band matrices, ily, bye! 💜✨🦋

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