complex16HEauxiliary

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

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