CHESWAPR applies an elementary permutation on the rows and the columns of


 a hermitian matrix.

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

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 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.

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.

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.

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 CLAQHE equilibrates a Hermitian matrix A using the scaling factors


 in the vector S.

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).

  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.

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