.TH "complex16HEauxiliary" 3 "Sun Nov 27 2022" "Version 3.11.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME complex16HEauxiliary \- complex16 .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBzheswapr\fP (UPLO, N, A, LDA, I1, I2)" .br .RI "\fBZHESWAPR\fP applies an elementary permutation on the rows and columns of a Hermitian matrix\&. " .ti -1c .RI "double precision function \fBzlanhe\fP (NORM, UPLO, N, A, LDA, WORK)" .br .RI "\fBZLANHE\fP 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\&. " .ti -1c .RI "subroutine \fBzlaqhe\fP (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED)" .br .RI "\fBZLAQHE\fP scales a Hermitian matrix\&. " .in -1c .SH "Detailed Description" .PP This is the group of complex16 auxiliary functions for HE matrices .SH "Function Documentation" .PP .SS "subroutine zheswapr (character UPLO, integer N, complex*16, dimension( lda, n ) A, integer LDA, integer I1, integer I2)" .PP \fBZHESWAPR\fP applies an elementary permutation on the rows and columns of a Hermitian matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZHESWAPR applies an elementary permutation on the rows and the columns of a hermitian matrix\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fII1\fP .PP .nf I1 is INTEGER Index of the first row to swap .fi .PP .br \fII2\fP .PP .nf I2 is INTEGER Index of the second row to swap .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "double precision function zlanhe (character NORM, character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) WORK)" .PP \fBZLANHE\fP 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\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 ZLANHE .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fINORM\fP .PP .nf NORM is CHARACTER*1 Specifies the value to be returned in ZLANHE as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf 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 .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. When N = 0, ZLANHE is set to zero\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBZLAQHE\fP scales a Hermitian matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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 .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf 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)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf 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)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.