zlanhb.f(3) [debian man page]
zlanhb.f(3) LAPACK zlanhb.f(3) NAME
zlanhb.f - SYNOPSIS
Functions/Subroutines DOUBLE PRECISION function zlanhb (NORM, UPLO, N, K, AB, LDAB, WORK) ZLANHB Function/Subroutine Documentation DOUBLE PRECISION function zlanhb (characterNORM, characterUPLO, integerN, integerK, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK) ZLANHB Purpose: ZLANHB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals. Returns: ZLANHB ZLANHB = ( 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 ZLANHB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangle of the hermitian band matrix A, stored in the first K+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is DOUBLE PRECISION 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. Date: November 2011 Definition at line 132 of file zlanhb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 zlanhb.f(3)
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dlansb.f(3) LAPACK dlansb.f(3) NAME
dlansb.f - SYNOPSIS
Functions/Subroutines DOUBLE PRECISION function dlansb (NORM, UPLO, N, K, AB, LDAB, WORK) DLANSB Function/Subroutine Documentation DOUBLE PRECISION function dlansb (characterNORM, characterUPLO, integerN, integerK, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK) DLANSB Purpose: DLANSB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals. Returns: DLANSB DLANSB = ( 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 DLANSB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular part is supplied = 'L': Lower triangular part is supplied N N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANSB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangle of the symmetric band matrix A, stored in the first K+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is DOUBLE PRECISION 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. Date: November 2011 Definition at line 129 of file dlansb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlansb.f(3)