LAPACK 3.3.1 Linear Algebra PACKage

# dlanhs.f

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```00001       DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          NORM
00010       INTEGER            LDA, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DLANHS  returns the value of the one norm,  or the Frobenius norm, or
00020 *  the  infinity norm,  or the  element of  largest absolute value  of a
00021 *  Hessenberg matrix A.
00022 *
00023 *  Description
00024 *  ===========
00025 *
00026 *  DLANHS returns the value
00027 *
00028 *     DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00029 *              (
00030 *              ( norm1(A),         NORM = '1', 'O' or 'o'
00031 *              (
00032 *              ( normI(A),         NORM = 'I' or 'i'
00033 *              (
00034 *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00035 *
00036 *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
00037 *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00038 *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
00039 *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00040 *
00041 *  Arguments
00042 *  =========
00043 *
00044 *  NORM    (input) CHARACTER*1
00045 *          Specifies the value to be returned in DLANHS as described
00046 *          above.
00047 *
00048 *  N       (input) INTEGER
00049 *          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is
00050 *          set to zero.
00051 *
00052 *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
00053 *          The n by n upper Hessenberg matrix A; the part of A below the
00054 *          first sub-diagonal is not referenced.
00055 *
00056 *  LDA     (input) INTEGER
00057 *          The leading dimension of the array A.  LDA >= max(N,1).
00058 *
00059 *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
00060 *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00061 *          referenced.
00062 *
00063 * =====================================================================
00064 *
00065 *     .. Parameters ..
00066       DOUBLE PRECISION   ONE, ZERO
00067       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00068 *     ..
00069 *     .. Local Scalars ..
00070       INTEGER            I, J
00071       DOUBLE PRECISION   SCALE, SUM, VALUE
00072 *     ..
00073 *     .. External Subroutines ..
00074       EXTERNAL           DLASSQ
00075 *     ..
00076 *     .. External Functions ..
00077       LOGICAL            LSAME
00078       EXTERNAL           LSAME
00079 *     ..
00080 *     .. Intrinsic Functions ..
00081       INTRINSIC          ABS, MAX, MIN, SQRT
00082 *     ..
00083 *     .. Executable Statements ..
00084 *
00085       IF( N.EQ.0 ) THEN
00086          VALUE = ZERO
00087       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00088 *
00089 *        Find max(abs(A(i,j))).
00090 *
00091          VALUE = ZERO
00092          DO 20 J = 1, N
00093             DO 10 I = 1, MIN( N, J+1 )
00094                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00095    10       CONTINUE
00096    20    CONTINUE
00097       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00098 *
00099 *        Find norm1(A).
00100 *
00101          VALUE = ZERO
00102          DO 40 J = 1, N
00103             SUM = ZERO
00104             DO 30 I = 1, MIN( N, J+1 )
00105                SUM = SUM + ABS( A( I, J ) )
00106    30       CONTINUE
00107             VALUE = MAX( VALUE, SUM )
00108    40    CONTINUE
00109       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00110 *
00111 *        Find normI(A).
00112 *
00113          DO 50 I = 1, N
00114             WORK( I ) = ZERO
00115    50    CONTINUE
00116          DO 70 J = 1, N
00117             DO 60 I = 1, MIN( N, J+1 )
00118                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00119    60       CONTINUE
00120    70    CONTINUE
00121          VALUE = ZERO
00122          DO 80 I = 1, N
00123             VALUE = MAX( VALUE, WORK( I ) )
00124    80    CONTINUE
00125       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00126 *
00127 *        Find normF(A).
00128 *
00129          SCALE = ZERO
00130          SUM = ONE
00131          DO 90 J = 1, N
00132             CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
00133    90    CONTINUE
00134          VALUE = SCALE*SQRT( SUM )
00135       END IF
00136 *
00137       DLANHS = VALUE
00138       RETURN
00139 *
00140 *     End of DLANHS
00141 *
00142       END
```