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NAMEcomplex16HEauxiliary - complex16SYNOPSISFunctionssubroutine zheswapr (UPLO, N, A, LDA, I1, I2) ZHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix. double precision function zlanhe (NORM, UPLO, N, A, LDA, WORK) ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. subroutine zlaqhe (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED) ZLAQHE scales a Hermitian matrix. Detailed DescriptionThis is the group of complex16 auxiliary functions for HE matricesFunction Documentationsubroutine zheswapr (character UPLO, integer N, complex*16, dimension( lda, n ) A, integer LDA, integer I1, integer I2)ZHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix.Purpose: ZHESWAPR 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*16 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 zheswapr.f. double precision function zlanhe (character NORM, character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) WORK)ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.Purpose: ZLANHE 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 ZLANHE
ZLANHE = ( 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 ZLANHE 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, ZLANHE is set to zero. A A is COMPLEX*16 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 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. Definition at line 123 of file zlanhe.f. subroutine zlaqhe (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED)ZLAQHE scales a Hermitian matrix.Purpose: ZLAQHE 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*16 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 DOUBLE PRECISION array, dimension (N) The scale factors for A. SCOND SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i). AMAX AMAX is DOUBLE PRECISION 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 zlaqhe.f. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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