.TH ZLANTP 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME ZLANTP - the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form .SH SYNOPSIS .TP 17 DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK ) .TP 17 .ti +4 CHARACTER DIAG, NORM, UPLO .TP 17 .ti +4 INTEGER N .TP 17 .ti +4 DOUBLE PRECISION WORK( * ) .TP 17 .ti +4 COMPLEX*16 AP( * ) .SH PURPOSE ZLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form. .SH DESCRIPTION ZLANTP returns the value .br ZLANTP = ( max(abs(A(i,j))), NORM = \(aqM\(aq or \(aqm\(aq .br ( .br ( norm1(A), NORM = \(aq1\(aq, \(aqO\(aq or \(aqo\(aq .br ( .br ( normI(A), NORM = \(aqI\(aq or \(aqi\(aq .br ( .br ( normF(A), NORM = \(aqF\(aq, \(aqf\(aq, \(aqE\(aq or \(aqe\(aq 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. .SH ARGUMENTS .TP 8 NORM (input) CHARACTER*1 Specifies the value to be returned in ZLANTP as described above. .TP 8 UPLO (input) CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = \(aqU\(aq: Upper triangular .br = \(aqL\(aq: Lower triangular .TP 8 DIAG (input) CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = \(aqN\(aq: Non-unit triangular .br = \(aqU\(aq: Unit triangular .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANTP is set to zero. .TP 8 AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. Note that when DIAG = \(aqU\(aq, the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = \(aqI\(aq; otherwise, WORK is not referenced.