CLANTB(3)

🎀 NAME 🎀

Okay bestie, welcome to the CLANTB(3) page from the Library Functions Manual ✨ — this is the LAPACK zone, and the NAME line points at the file:

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

CLANTB 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. It's giving “one function, many norm moods” and honestly? iconic. 💅

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💅 Function/Subroutine Documentation 💅

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

CLANTB 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. Same queen, full signature reveal. 🦋

🫶 Purpose

CLANTB 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

CLANTB

!>    CLANTB = ( 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. Important vibe check: that one is not a consistent matrix norm, no cap. 💀

🌸 Parameters

NORM

NORM is CHARACTER*1 — Specifies the value to be returned in CLANTB 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, CLANTB 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 COMPLEX 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. So don't come for those diagonal entries — they're not even being read, bestie. 🫶

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 139 of file clantb.f.

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✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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