
NAMEcomplexHEauxiliary  complexSYNOPSISFunctionssubroutine cheswapr (UPLO, N, A, LDA, I1, I2) CHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix. real function clanhe (NORM, UPLO, N, A, LDA, WORK) CLANHE returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. subroutine claqhe (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED) CLAQHE scales a Hermitian matrix. Detailed DescriptionThis is the group of complex auxiliary functions for HE matricesFunction Documentationsubroutine cheswapr (character UPLO, integer N, complex, dimension( lda, n ) A, integer LDA, integer I1, integer I2)CHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix.Purpose: CHESWAPR applies an elementary permutation on the rows and the columns of a hermitian matrix. Parameters UPLO
UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the NB diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF. On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). I1 I1 is INTEGER Index of the first row to swap I2 I2 is INTEGER Index of the second row to swap Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 101 of file cheswapr.f. real function clanhe (character NORM, character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) WORK)CLANHE returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.Purpose: CLANHE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A. Returns CLANHE
CLANHE = ( 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 CLANHE as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced N N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHE is set to zero. A A is COMPLEX array, dimension (LDA,N) The hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1). WORK WORK is REAL 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. Definition at line 123 of file clanhe.f. subroutine claqhe (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, character EQUED)CLAQHE scales a Hermitian matrix.Purpose: CLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S. Parameters UPLO
UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1). S S is REAL array, dimension (N) The scale factors for A. SCOND SCOND is REAL Ratio of the smallest S(i) to the largest S(i). AMAX AMAX is REAL Absolute value of largest matrix entry. EQUED EQUED is CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). Internal Parameters: THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done. Author Univ. of Tennessee
Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 133 of file claqhe.f. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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