LAPACK: SRC/clange.f Source File

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00001       REAL             FUNCTION CLANGE( NORM, M, 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, M, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       REAL               WORK( * )
00014       COMPLEX            A( LDA, * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  CLANGE  returns the value of the one norm,  or the Frobenius norm, or
00021 *  the  infinity norm,  or the  element of  largest absolute value  of a
00022 *  complex matrix A.
00023 *
00024 *  Description
00025 *  ===========
00026 *
00027 *  CLANGE returns the value
00028 *
00029 *     CLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00030 *              (
00031 *              ( norm1(A),         NORM = '1', 'O' or 'o'
00032 *              (
00033 *              ( normI(A),         NORM = 'I' or 'i'
00034 *              (
00035 *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00036 *
00037 *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
00038 *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00039 *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
00040 *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00041 *
00042 *  Arguments
00043 *  =========
00044 *
00045 *  NORM    (input) CHARACTER*1
00046 *          Specifies the value to be returned in CLANGE as described
00047 *          above.
00048 *
00049 *  M       (input) INTEGER
00050 *          The number of rows of the matrix A.  M >= 0.  When M = 0,
00051 *          CLANGE is set to zero.
00052 *
00053 *  N       (input) INTEGER
00054 *          The number of columns of the matrix A.  N >= 0.  When N = 0,
00055 *          CLANGE is set to zero.
00056 *
00057 *  A       (input) COMPLEX array, dimension (LDA,N)
00058 *          The m by n matrix A.
00059 *
00060 *  LDA     (input) INTEGER
00061 *          The leading dimension of the array A.  LDA >= max(M,1).
00062 *
00063 *  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
00064 *          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
00065 *          referenced.
00066 *
00067 * =====================================================================
00068 *
00069 *     .. Parameters ..
00070       REAL               ONE, ZERO
00071       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00072 *     ..
00073 *     .. Local Scalars ..
00074       INTEGER            I, J
00075       REAL               SCALE, SUM, VALUE
00076 *     ..
00077 *     .. External Functions ..
00078       LOGICAL            LSAME
00079       EXTERNAL           LSAME
00080 *     ..
00081 *     .. External Subroutines ..
00082       EXTERNAL           CLASSQ
00083 *     ..
00084 *     .. Intrinsic Functions ..
00085       INTRINSIC          ABS, MAX, MIN, SQRT
00086 *     ..
00087 *     .. Executable Statements ..
00088 *
00089       IF( MIN( M, N ).EQ.0 ) THEN
00090          VALUE = ZERO
00091       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00092 *
00093 *        Find max(abs(A(i,j))).
00094 *
00095          VALUE = ZERO
00096          DO 20 J = 1, N
00097             DO 10 I = 1, M
00098                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00099    10       CONTINUE
00100    20    CONTINUE
00101       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00102 *
00103 *        Find norm1(A).
00104 *
00105          VALUE = ZERO
00106          DO 40 J = 1, N
00107             SUM = ZERO
00108             DO 30 I = 1, M
00109                SUM = SUM + ABS( A( I, J ) )
00110    30       CONTINUE
00111             VALUE = MAX( VALUE, SUM )
00112    40    CONTINUE
00113       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00114 *
00115 *        Find normI(A).
00116 *
00117          DO 50 I = 1, M
00118             WORK( I ) = ZERO
00119    50    CONTINUE
00120          DO 70 J = 1, N
00121             DO 60 I = 1, M
00122                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00123    60       CONTINUE
00124    70    CONTINUE
00125          VALUE = ZERO
00126          DO 80 I = 1, M
00127             VALUE = MAX( VALUE, WORK( I ) )
00128    80    CONTINUE
00129       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00130 *
00131 *        Find normF(A).
00132 *
00133          SCALE = ZERO
00134          SUM = ONE
00135          DO 90 J = 1, N
00136             CALL CLASSQ( M, A( 1, J ), 1, SCALE, SUM )
00137    90    CONTINUE
00138          VALUE = SCALE*SQRT( SUM )
00139       END IF
00140 *
00141       CLANGE = VALUE
00142       RETURN
00143 *
00144 *     End of CLANGE
00145 *
00146       END