complexHEauxiliary(3)

NAME
complexHEauxiliary - complex

SYNOPSIS

  Functions
subroutine cheswapr (uplo, n, a, lda, i1, i2)
CHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix.
real function clanhe (norm, uplo, n, a, lda, work)
CLANHE 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 claqhe (uplo, n, a, lda, s, scond, amax, equed)
CLAQHE scales a Hermitian matrix.

Detailed Description

This is the group of complex auxiliary functions for HE matrices

Function Documentation

  subroutine cheswapr (character uplo, integer n, complex, dimension( lda, n ) a, integer lda, integer i1, integer i2)

CHESWAPR applies an elementary permutation on the rows and columns of a Hermitian matrix.

Purpose:

     CHESWAPR 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 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.

Definition at line 101 of file cheswapr.f.

  real function clanhe (character norm, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

CLANHE 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:

     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.

Returns
    CLANHE

        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.

Parameters
    NORM

              NORM is CHARACTER*1
              Specifies the value to be returned in CLANHE 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, CLANHE is
              set to zero.

    A

              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.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(N,1).

    WORK

              WORK is REAL 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.

Definition at line 123 of file clanhe.f.

  subroutine claqhe (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

CLAQHE scales a Hermitian matrix.

Purpose:

     CLAQHE 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 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 REAL array, dimension (N)
              The scale factors for A.

    SCOND

              SCOND is REAL
              Ratio of the smallest S(i) to the largest S(i).

    AMAX

              AMAX is REAL
              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.

Definition at line 133 of file claqhe.f.

Author

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