zlanhe.f

          DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          NORM, UPLO
          INTEGER            LDA, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   WORK( * )
          COMPLEX*16         A( LDA, * )
    *     ..
    *
    *  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.
    *
    *  Description
    *  ===========
    *
    *  ZLANHE returns the value
    *
    *     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.
    *
    *  Arguments
    *  =========
    *
    *  NORM    (input) CHARACTER*1
    *          Specifies the value to be returned in ZLANHE as described
    *          above.
    *
    *  UPLO    (input) 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       (input) INTEGER
    *          The order of the matrix A.  N >= 0.  When N = 0, ZLANHE is
    *          set to zero.
    *
    *  A       (input) 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     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(N,1).
    *
    *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
    *          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
    *          WORK is not referenced.
    *
    * =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J
          DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           ZLASSQ
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, DBLE, MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
          IF( N.EQ.0 ) THEN
             VALUE = ZERO
          ELSE IF( LSAME( NORM, 'M' ) ) THEN
    *
    *        Find max(abs(A(i,j))).
    *
             VALUE = ZERO
             IF( LSAME( UPLO, 'U' ) ) THEN
                DO 20 J = 1, N
                   DO 10 I = 1, J - 1
                      VALUE = MAX( VALUE, ABS( A( I, J ) ) )
       10          CONTINUE
                   VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) )
       20       CONTINUE
             ELSE
                DO 40 J = 1, N
                   VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) )
                   DO 30 I = J + 1, N
                      VALUE = MAX( VALUE, ABS( A( I, J ) ) )
       30          CONTINUE
       40       CONTINUE
             END IF
          ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
         $         ( NORM.EQ.'1' ) ) THEN
    *
    *        Find normI(A) ( = norm1(A), since A is hermitian).
    *
             VALUE = ZERO
             IF( LSAME( UPLO, 'U' ) ) THEN
                DO 60 J = 1, N
                   SUM = ZERO
                   DO 50 I = 1, J - 1
                      ABSA = ABS( A( I, J ) )
                      SUM = SUM + ABSA
                      WORK( I ) = WORK( I ) + ABSA
       50          CONTINUE
                   WORK( J ) = SUM + ABS( DBLE( A( J, J ) ) )
       60       CONTINUE
                DO 70 I = 1, N
                   VALUE = MAX( VALUE, WORK( I ) )
       70       CONTINUE
             ELSE
                DO 80 I = 1, N
                   WORK( I ) = ZERO
       80       CONTINUE
                DO 100 J = 1, N
                   SUM = WORK( J ) + ABS( DBLE( A( J, J ) ) )
                   DO 90 I = J + 1, N
                      ABSA = ABS( A( I, J ) )
                      SUM = SUM + ABSA
                      WORK( I ) = WORK( I ) + ABSA
       90          CONTINUE
                   VALUE = MAX( VALUE, SUM )
      100       CONTINUE
             END IF
          ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
    *
    *        Find normF(A).
    *
             SCALE = ZERO
             SUM = ONE
             IF( LSAME( UPLO, 'U' ) ) THEN
                DO 110 J = 2, N
                   CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
      110       CONTINUE
             ELSE
                DO 120 J = 1, N - 1
                   CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
      120       CONTINUE
             END IF
             SUM = 2*SUM
             DO 130 I = 1, N
                IF( DBLE( A( I, I ) ).NE.ZERO ) THEN
                   ABSA = ABS( DBLE( A( I, I ) ) )
                   IF( SCALE.LT.ABSA ) THEN
                      SUM = ONE + SUM*( SCALE / ABSA )**2
                      SCALE = ABSA
                   ELSE
                      SUM = SUM + ( ABSA / SCALE )**2
                   END IF
                END IF
      130    CONTINUE
             VALUE = SCALE*SQRT( SUM )
          END IF
    *
          ZLANHE = VALUE
          RETURN
    *
    *     End of ZLANHE
    *
          END