SRC/slansy.f(3)

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NAME

SRC/slansy.f

SYNOPSIS

Functions/Subroutines

• real function slansy (norm, uplo, n, a, lda, work) — SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

Function/Subroutine Documentation

real function slansy (character norm, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. 💅

Purpose

!>
!> SLANSY  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real symmetric matrix A.
!>

Returns

SLANSY:

!>
!>    SLANSY = ( 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 SLANSY as described above. 🌈
• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
  • = 'U': Upper triangular part of A is referenced
  • = 'L': Lower triangular part of A is referenced
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANSY is set to zero. 🫶
• A — A is REAL array, dimension (LDA,N). The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(N,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 121 of file slansy.f.

Author

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