.TH "complexHEauxiliary" 3 "Sun Nov 27 2022" "Version 3.11.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
complexHEauxiliary \- complex
.SH SYNOPSIS
.br
.PP
.SS "Functions"
.in +1c
.ti -1c
.RI "subroutine \fBcheswapr\fP (UPLO, N, A, LDA, I1, I2)"
.br
.RI "\fBCHESWAPR\fP applies an elementary permutation on the rows and columns of a Hermitian matrix\&. "
.ti -1c
.RI "real function \fBclanhe\fP (NORM, UPLO, N, A, LDA, WORK)"
.br
.RI "\fBCLANHE\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 \fBclaqhe\fP (UPLO, N, A, LDA, S, SCOND, AMAX, EQUED)"
.br
.RI "\fBCLAQHE\fP scales a Hermitian matrix\&. "
.in -1c
.SH "Detailed Description"
.PP
This is the group of complex auxiliary functions for HE matrices
.SH "Function Documentation"
.PP
.SS "subroutine cheswapr (character UPLO, integer N, complex, dimension( lda, n ) A, integer LDA, integer I1, integer I2)"
.PP
\fBCHESWAPR\fP applies an elementary permutation on the rows and columns of a Hermitian matrix\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
CHESWAPR 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 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 "real function clanhe (character NORM, character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) WORK)"
.PP
\fBCLANHE\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
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\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
CLANHE
.PP
.nf
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\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP
.PP
.nf
NORM is CHARACTER*1
Specifies the value to be returned in CLANHE 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, CLANHE is
set to zero\&.
.fi
.PP
.br
\fIA\fP
.PP
.nf
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\&.
.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 REAL 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 claqhe (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, character EQUED)"
.PP
\fBCLAQHE\fP scales a Hermitian matrix\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
CLAQHE 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 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 REAL array, dimension (N)
The scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP
.PP
.nf
SCOND is REAL
Ratio of the smallest S(i) to the largest S(i)\&.
.fi
.PP
.br
\fIAMAX\fP
.PP
.nf
AMAX is REAL
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\&.