SRC/dlantb.f(3)

✨ NAME ✨

SRC/dlantb.f — okay bestie, this is the page for dlantb from the SRC/dlantb.f(3) Library Functions Manual. It’s a LAPACK function page, and it’s giving “triangular band matrix norm realness.” 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

• double precision function dlantb (norm, uplo, diag, n, k, ab, ldab, work) — DLANTB 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. ✨

💖 FUNCTION/SUBROUTINE DOCUMENTATION 💖

🫶 double precision function dlantb (...)

Here’s the full signature, exactly as it appears:

double precision function dlantb (character norm, character
     uplo, character diag, integer n, integer k, double precision, dimension(
     ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

DLANTB 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

okay so the Purpose block is literally:

!>
!> DLANTB  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.
!>

🦋 Returns

DLANTB picks its value based on NORM like this:

!>
!>    DLANTB = ( 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.
!>

🚨 Heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. That’s literally in the original, so it’s not me being dramatic. 😭

🌈 Parameters

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANTB as described above. ✨
• 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, DLANTB is set to zero.
• 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 DOUBLE PRECISION 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.
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= K+1.
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

👑 AUTHOR 👑

The author block credits:

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

📌 DEFINITION AT LINE 📌

Definition at line 138 of file dlantb.f. 📍

🧚 AUTHOR 🧚

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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okay that’s the whole page, bestie — it’s from the SRC/dlantb.f(3) manual, and the footer says LAPACK Version 3.12.0. Slay, stay cozy, and may your norms stay iconic. 💅💖🎀