SRC/zlantb.f(3)

💅 NAME

okay bestie, welcome to SRC/zlantb.f(3) from the Library Functions Manual 🫶 — and the NAME is literally SRC/zlantb.f. slay.

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✨ SYNOPSIS

🎀 Functions/Subroutines

double precision function zlantb (norm, uplo, diag, n, k, ab, ldab,
           work)

ZLANTB 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. no cap 💖

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🦋 Function/Subroutine Documentation

double precision function zlantb (character norm, character uplo, character
       diag, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer
       ldab, double precision, dimension( * ) work)

ZLANTB 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:

ZLANTB 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

ZLANTB

!>
!>    ZLANTB = ( 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 bestie: max(abs(A(i,j))) is not a consistent matrix norm.

🌈 Parameters

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANTB 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, ZLANTB 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*16 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

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

Definition at line 139 of file zlantb.f.

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💀 Author

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie 💖 — LAPACK Version 3.12.0, source SRC/zlantb.f(3). you ate that 🫶✨