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## man page of LAPACK-3

### LAPACK-3: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute

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## NAME

LAPACK-3 - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A## SYNOPSIS

DOUBLE PRECISION FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK ) CHARACTER DIAG, NORM, UPLO INTEGER LDA, M, N DOUBLE PRECISION WORK( * ) COMPLEX*16 A( LDA, * )PURPOSE

ZLANTR returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A.## DESCRIPTION

ZLANTR returns the value ZLANTR = ( 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.## ARGUMENTS

NORM (input) CHARACTER*1 Specifies the value to be returned in ZLANTR as described above. UPLO (input) CHARACTER*1 Specifies whether the matrix A is upper or lower trapezoidal. = 'U': Upper trapezoidal = 'L': Lower trapezoidal Note that A is triangular instead of trapezoidal if M = N. DIAG (input) CHARACTER*1 Specifies whether or not the matrix A has unit diagonal. = 'N': Non-unit diagonal = 'U': Unit diagonal M (input) INTEGER The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, ZLANTR is set to zero. N (input) INTEGER The number of columns of the matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, ZLANTR is set to zero. A (input) COMPLEX*16 array, dimension (LDA,N) The trapezoidal matrix A (A is triangular if M = N). If UPLO = 'U', the leading m by n upper trapezoidal part of the array A contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading m by n lower trapezoidal part of the array A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(M,1). WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. LAPACK auxiliary routine (versionMarch 2011 LAPACK-3(3)

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