LAPACK: SRC/dlansy.f Source File

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00001       DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, 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, UPLO
00010       INTEGER            LDA, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DLANSY  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 *  real symmetric matrix A.
00022 *
00023 *  Description
00024 *  ===========
00025 *
00026 *  DLANSY returns the value
00027 *
00028 *     DLANSY = ( 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 DLANSY as described
00046 *          above.
00047 *
00048 *  UPLO    (input) CHARACTER*1
00049 *          Specifies whether the upper or lower triangular part of the
00050 *          symmetric matrix A is to be referenced.
00051 *          = 'U':  Upper triangular part of A is referenced
00052 *          = 'L':  Lower triangular part of A is referenced
00053 *
00054 *  N       (input) INTEGER
00055 *          The order of the matrix A.  N >= 0.  When N = 0, DLANSY is
00056 *          set to zero.
00057 *
00058 *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
00059 *          The symmetric matrix A.  If UPLO = 'U', the leading n by n
00060 *          upper triangular part of A contains the upper triangular part
00061 *          of the matrix A, and the strictly lower triangular part of A
00062 *          is not referenced.  If UPLO = 'L', the leading n by n lower
00063 *          triangular part of A contains the lower triangular part of
00064 *          the matrix A, and the strictly upper triangular part of A is
00065 *          not referenced.
00066 *
00067 *  LDA     (input) INTEGER
00068 *          The leading dimension of the array A.  LDA >= max(N,1).
00069 *
00070 *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
00071 *          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
00072 *          WORK is not referenced.
00073 *
00074 * =====================================================================
00075 *
00076 *     .. Parameters ..
00077       DOUBLE PRECISION   ONE, ZERO
00078       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00079 *     ..
00080 *     .. Local Scalars ..
00081       INTEGER            I, J
00082       DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
00083 *     ..
00084 *     .. External Subroutines ..
00085       EXTERNAL           DLASSQ
00086 *     ..
00087 *     .. External Functions ..
00088       LOGICAL            LSAME
00089       EXTERNAL           LSAME
00090 *     ..
00091 *     .. Intrinsic Functions ..
00092       INTRINSIC          ABS, MAX, SQRT
00093 *     ..
00094 *     .. Executable Statements ..
00095 *
00096       IF( N.EQ.0 ) THEN
00097          VALUE = ZERO
00098       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00099 *
00100 *        Find max(abs(A(i,j))).
00101 *
00102          VALUE = ZERO
00103          IF( LSAME( UPLO, 'U' ) ) THEN
00104             DO 20 J = 1, N
00105                DO 10 I = 1, J
00106                   VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00107    10          CONTINUE
00108    20       CONTINUE
00109          ELSE
00110             DO 40 J = 1, N
00111                DO 30 I = J, N
00112                   VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00113    30          CONTINUE
00114    40       CONTINUE
00115          END IF
00116       ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
00117      $         ( NORM.EQ.'1' ) ) THEN
00118 *
00119 *        Find normI(A) ( = norm1(A), since A is symmetric).
00120 *
00121          VALUE = ZERO
00122          IF( LSAME( UPLO, 'U' ) ) THEN
00123             DO 60 J = 1, N
00124                SUM = ZERO
00125                DO 50 I = 1, J - 1
00126                   ABSA = ABS( A( I, J ) )
00127                   SUM = SUM + ABSA
00128                   WORK( I ) = WORK( I ) + ABSA
00129    50          CONTINUE
00130                WORK( J ) = SUM + ABS( A( J, J ) )
00131    60       CONTINUE
00132             DO 70 I = 1, N
00133                VALUE = MAX( VALUE, WORK( I ) )
00134    70       CONTINUE
00135          ELSE
00136             DO 80 I = 1, N
00137                WORK( I ) = ZERO
00138    80       CONTINUE
00139             DO 100 J = 1, N
00140                SUM = WORK( J ) + ABS( A( J, J ) )
00141                DO 90 I = J + 1, N
00142                   ABSA = ABS( A( I, J ) )
00143                   SUM = SUM + ABSA
00144                   WORK( I ) = WORK( I ) + ABSA
00145    90          CONTINUE
00146                VALUE = MAX( VALUE, SUM )
00147   100       CONTINUE
00148          END IF
00149       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00150 *
00151 *        Find normF(A).
00152 *
00153          SCALE = ZERO
00154          SUM = ONE
00155          IF( LSAME( UPLO, 'U' ) ) THEN
00156             DO 110 J = 2, N
00157                CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
00158   110       CONTINUE
00159          ELSE
00160             DO 120 J = 1, N - 1
00161                CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
00162   120       CONTINUE
00163          END IF
00164          SUM = 2*SUM
00165          CALL DLASSQ( N, A, LDA+1, SCALE, SUM )
00166          VALUE = SCALE*SQRT( SUM )
00167       END IF
00168 *
00169       DLANSY = VALUE
00170       RETURN
00171 *
00172 *     End of DLANSY
00173 *
00174       END