SRC/slansb.f(3)

💖 SRC/slansb.f(3) 💖

okay so bestie, we're in the Library Functions Manual and this whole page is serving SRC/slansb.f — it's giving very specific LAPACK main-character energy, no cap ✨

✨ NAME ✨

SRC/slansb.f — that's the name, that's the vibe 🎀

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

real function slansb (norm, uplo, n, k, ab, ldab, work)

SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. periodt 💅

💅 Function/Subroutine Documentation 💅

real function slansb (character norm, character uplo, integer n, integer k,
       real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. it's literally the norm bestie, fr fr 🦋

🎀 Purpose 🎀

SLANSB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals. that's the whole assignment 💖

🎀 Returns 🎀

SLANSB returns this whole mood:

SLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
         (
         ( norm1(A),         NORM = '1', 'O' or 'o'
         (
         ( normI(A),         NORM = 'I' or 'i'
         (
         ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. ⚠️ not me learning that max-abs is not a consistent matrix norm, but okay 💀

🦋 Parameters 🦋

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANSB as described above. 💅
• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the band matrix A is supplied.
  • = 'U': Upper triangular part is supplied
  • = 'L': Lower triangular part is supplied
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANSB is set to zero. 😭 zero-order matrix but make it zero, iconic
• K — K is INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. 🦋
• AB — AB is REAL array, dimension (LDAB,N). The upper or lower triangle of the symmetric band matrix A, stored in the first K+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:
  • if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
  • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= K+1. 🔥
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. 🫶

👑 Author 👑

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

Definition at line 127 of file slansb.f.

👑 Author 👑

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