SLANTB(3)

🌸 NAME 🌸

SLANTB(3) is the manual name, and it sits under the Library Functions Manual umbrella. The source file path, exactly as the page gives it, is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slantb.f

Okay so this is the LAPACK page for a real function that returns norm values for a triangular band matrix. Very linear-algebra bestie, very “let me check that matrix for you” energy. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix. That’s the whole vibe check, bestie. 🦋

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🫶 Function/Subroutine Documentation 🫶

Here’s the full signature, verbatim:

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

SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

🎯 Purpose 🎯

The original purpose block is giving iconic documentation energy, so here it is exactly:

!>
!> SLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.
!>

Translation for the group chat: it’s an n by n triangular band matrix A, with ( k + 1 ) diagonals, and SLANTB gives you the norm value you asked for. Slay. ✨

💖 Returns 💖

SLANTB returns one of these, and the original decision tree is literally right here:

!>
!>    SLANTB = ( 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.
!>

So: 'M'/'m' gives you max(abs(A(i,j))); '1'/'O'/'o' gives you norm1(A); 'I'/'i' gives you normI(A); and 'F'/'f'/'E'/'e' gives you normF(A). And do not forget the note, bestie: max(abs(A(i,j))) is not a consistent matrix norm. That’s a real caveat, not a vibe suggestion. ⚠️

🌈 Parameters 🌈

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANTB as described above. Yes, this is the norm selector, the main character of the whole page.
• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• DIAG — DIAG is CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANTB is set to zero. Zero-size matrix? Handled. Periodt.
• K — K is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals of the matrix A if UPLO = 'L'. K >= 0.
• AB — AB is REAL array, dimension (LDAB,N). The upper or lower triangular 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). Note that when DIAG = 'U', the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. Those diagonal entries in AB are literally not referenced in unit mode, okay? Assumed to be one, no touchy.
• 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'; otherwise, WORK is not referenced.

👑 Author 👑

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

Definition at line 138 of file slantb.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. That’s the meta-author note, bestie — not a human, just the doc machine doing its thing. 🤖✨

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💖 That’s the whole page: LAPACK Version 3.12.0, source path /home/abui...RC/slantb.f(3). Footer folded in with love, no copied line, no cap. 💖