SRC/slaqsb.f(3)

🌈 NAME 🌈

okay bestie, this is the SRC/slaqsb.f page from the Library Functions Manual 💅 — it's all about the slaqsb subroutine.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• ```fortran subroutine slaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)

SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by `spbequ`.

# 💖 Function/Subroutine Documentation 💖

## 🦋 subroutine slaqsb 🦋

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

SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by `spbequ`.

### 🌸 Purpose:

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

### 💜 Parameters

- **`UPLO`** — `UPLO is CHARACTER*1`. It says 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 REAL array, dimension (LDAB,N)`. On entry, this is 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`. no cap 🫶

- **`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  - `= 'Y'`: Equilibration was done, i.e., `A` has been replaced by `diag(S) * A * diag(S)`.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 139 of file `slaqsb.f`.

# 🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page bestie 💖 — this was LAPACK `Version 3.12.0` for `SRC/slaqsb.f(3)`, and the top-level author note says it was generated automatically by Doxygen for LAPACK from the source code. byeee 🫶✨