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complex16(3) LAPACK complex16(3)

NAME

complex16 -

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 (characterUPLO, integerN, complex*16, dimension( lda, n )A, integerLDA, integerI1, integerI2)

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.
Date:
December 2016

double precision function zlanhe (characterNORM, characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, 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.
Date:
December 2016

subroutine zlaqhe (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED)

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.
Date:
December 2016

Author

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