SRC/clansb.f(3)

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🌸 NAME 🌸

SRC/clansb.f — that’s the name, short and iconic 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• real function clansb (norm, uplo, n, k, ab, ldab, work) — CLANSB 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.

🦋 Function/Subroutine Documentation 🦋

🌈 the function itself, no cap 🌈

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

CLANSB 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.

🎯 Purpose

CLANSB 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.

💖 Returns

CLANSB

CLANSB = ( 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. It specifies the value to be returned in CLANSB as described above.
• UPLO — UPLO is CHARACTER*1. It 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, CLANSB is set to zero.
• K — K is INTEGER. The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.
• AB — AB is COMPLEX 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 128 of file clansb.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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