SRC/clantb.f(3)

🎀 NAME 🎀

SRC/clantb.f — okay bestie, this is the Library Functions Manual page for SRC/clantb.f, and it's lowkey iconic ✨

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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. 💅

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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. 🫶

🎯 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. No cap, that's the whole job. 💜

🔁 Returns

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.
           !>

🧸 Parameters

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANTB as described above. It's giving norm-selector main character energy. 👑
• 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. 💀
• 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 👑

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Okay bestie, that's the whole page 💖 this little icon is from LAPACK Version 3.12.0, page SRC/clantb.f(3) 🎀✨