Dlangb Dlange Dlangt Dlansb Dlansp Dlanst Dlansy Dlantr

Dlansy() Function Dlansy ( Norm As  String, Byval Uplo As  String, N As  Long, A() As  Double, Optional Info As  Long  ) One norm, Frobenius norm, infinity norm, or largest absolute value of any element of a real symmetric matrix Purpose This routine returns the value of the one norm, the Frobenius norm, the infinity norm, or the largest absolute value of any element of a real symmetric matrix A. Returns Double max(abs(Aij)) when Norm = "M", norm1(A) when Norm = "1" or "O", normI(A) when Norm = "I", or normF(A) when Norm = "F" 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(Aij)) is not a consistent matrix norm. Parameters [in] Norm Specifies the value to be returned by Dlansy as described above. Note that normI(A) = norm1(A) since A is symmetric. [in] Uplo Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = "U": Only the upper triangular part is to be referenced. = "L": Only the lower triangular part is to be referenced. [in] N Order of the matrix A. (N >= 0) (If N = 0, returns 0) [in] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) N x N symmetric matrix A. Only the upper or lower triangular part is to be referenced in accordance with Uplo. [out] Info (Optional) = 0: Successful exit. = -1: The argument Norm had an illegal value. (Norm <> "M", "1", "O", "I", "F" nor "E") = -2: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -3: The argument N had an illegal value. (N < 0) = -4: The argument A() is invalid. Reference LAPACK Example Program Compute the norm of the symmetric matrix A, where ( 2.2 -0.11 -0.32 ) A = ( -0.11 2.93 0.81 ) ( -0.32 0.81 2.37 ) Sub Ex_Dlansy() Const N As Long = 3 Dim A(N - 1, N - 1) As Double Dim ANormM As Double, ANorm1 As Double, ANormI As Double, ANormF As Double A(0, 0) = 2.2: A(0, 1) = -0.11: A(0, 2) = -0.32 A(1, 1) = 2.93: A(1, 2) = 0.81 A(2, 2) = 2.37 ANormM = Dlansy("M", "U", N, A()) ANorm1 = Dlansy("1", "U", N, A()) ANormI = Dlansy("I", "U", N, A()) ANormF = Dlansy("F", "U", N, A()) Debug.Print "max(abs(Aij)), norm1(A), normI(A), normF(A) =" Debug.Print ANormM, ANorm1, ANormI, ANormF End Sub Example Results max(abs(Aij)), norm1(A), normI(A), normF(A) = 2.93 3.85 3.85 4.53684912687209