--- name: "complex16HEauxiliary" section: "3" platform: "linux" package: "liblapack-doc" version: "3.11.0-2" release: "Debian 12 (Bookworm)" platforms: ["linux"] url: "https://new.carta.tech/complex16HEauxiliary" --- # complex16HEauxiliary(3) complex16 ## NAME complex16HEauxiliary - complex16 ## SYNOPSIS ### Functions subroutine **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 Description This is the group of complex16 auxiliary functions for HE matrices ## Function Documentation ### subroutine 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. ### 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. ### 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. ## Author Generated automatically by Doxygen for LAPACK from the source code.