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**NAME**

complex16HEauxiliary

**SYNOPSIS**

Functionssubroutinezheswapr(UPLO, N, A, LDA, I1, I2)ZHESWAPRapplies an elementary permutation on the rows and columns of a Hermitian matrix. double precision functionzlanhe(NORM, UPLO, N, A, LDA, WORK)ZLANHEreturns 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. subroutinezlaqhe(UPLO, N, A, LDA, S, SCOND, AMAX, EQUED)ZLAQHEscales a Hermitian matrix.

**Detailed** **Description**

This is the group of complex16 auxiliary functions for HE matrices

**Function** **Documentation**

subroutinezheswapr(characterUPLO,integerN,complex*16,dimension(lda,n)A,integerLDA,integerI1,integerI2)ZHESWAPRapplies 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:UPLOUPLO 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.NN is INTEGER The order of the matrix A. N >= 0.AA 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.LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).I1I1 is INTEGER Index of the first row to swapI2I2 is INTEGER Index of the second row to swapAuthor:Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:December 2016doubleprecisionfunctionzlanhe(characterNORM,characterUPLO,integerN,complex*16,dimension(lda,*)A,integerLDA,doubleprecision,dimension(*)WORK)ZLANHEreturns 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:NORMNORM is CHARACTER*1 Specifies the value to be returned in ZLANHE as described above.UPLOUPLO 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 referencedNN is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHE is set to zero.AA 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.LDALDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).WORKWORK 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:December 2016subroutinezlaqhe(characterUPLO,integerN,complex*16,dimension(lda,*)A,integerLDA,doubleprecision,dimension(*)S,doubleprecisionSCOND,doubleprecisionAMAX,characterEQUED)ZLAQHEscales a Hermitian matrix.Purpose:ZLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S.Parameters:UPLOUPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangularNN is INTEGER The order of the matrix A. N >= 0.AA 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).LDALDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).SS is DOUBLE PRECISION array, dimension (N) The scale factors for A.SCONDSCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).AMAXAMAX is DOUBLE PRECISION Absolute value of largest matrix entry.EQUEDEQUED 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).InternalParameters: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.Date:December 2016

**Author**

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