Zlangb Zlange Zlangt Zlanhb Zlanhe Zlanhp Zlanht Zlansb Zlansp Zlansy Zlantr

Zlansb() Function Zlansb ( Norm As  String, Uplo As  String, N As  Long, K As  Long, Ab() As  Complex, Optional Info As  Long  ) One norm, Frobenius norm, infinity norm, or largest absolute value of any element of a complex symmetric band 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 an n x n complex symmetric band matrix A, with k super/sub-diagonals. 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 Zlansb 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 band matrix A is supplied. = "U": Upper triangular part is supplied. = "L": Lower triangular part is supplied. [in] N Order of the matrix A. (N >= 0) (If N = 0, returns 0) [in] K Number of super-diagonals or sub-diagonals of the symmetric band matrix A. (K >= 0) [in] Ab() Array Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= K + 1, LAb2 >= N) N x N symmetric band matrix A in K+1 x N symmetric band matrix form. (Upper or lower part is to be stored 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 K had an illegal value. (K < 0) = -5: The argument Ab() is invalid. Reference LAPACK