LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
slansy.f
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00001 *> \brief \b SLANSY
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SLANSY + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slansy.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM, UPLO
00025 *       INTEGER            LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               A( LDA, * ), WORK( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> SLANSY  returns the value of the one norm,  or the Frobenius norm, or
00038 *> the  infinity norm,  or the  element of  largest absolute value  of a
00039 *> real symmetric matrix A.
00040 *> \endverbatim
00041 *>
00042 *> \return SLANSY
00043 *> \verbatim
00044 *>
00045 *>    SLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00046 *>             (
00047 *>             ( norm1(A),         NORM = '1', 'O' or 'o'
00048 *>             (
00049 *>             ( normI(A),         NORM = 'I' or 'i'
00050 *>             (
00051 *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00052 *>
00053 *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
00054 *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00055 *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
00056 *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00057 *> \endverbatim
00058 *
00059 *  Arguments:
00060 *  ==========
00061 *
00062 *> \param[in] NORM
00063 *> \verbatim
00064 *>          NORM is CHARACTER*1
00065 *>          Specifies the value to be returned in SLANSY as described
00066 *>          above.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] UPLO
00070 *> \verbatim
00071 *>          UPLO is CHARACTER*1
00072 *>          Specifies whether the upper or lower triangular part of the
00073 *>          symmetric matrix A is to be referenced.
00074 *>          = 'U':  Upper triangular part of A is referenced
00075 *>          = 'L':  Lower triangular part of A is referenced
00076 *> \endverbatim
00077 *>
00078 *> \param[in] N
00079 *> \verbatim
00080 *>          N is INTEGER
00081 *>          The order of the matrix A.  N >= 0.  When N = 0, SLANSY is
00082 *>          set to zero.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] A
00086 *> \verbatim
00087 *>          A is REAL array, dimension (LDA,N)
00088 *>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
00089 *>          upper triangular part of A contains the upper triangular part
00090 *>          of the matrix A, and the strictly lower triangular part of A
00091 *>          is not referenced.  If UPLO = 'L', the leading n by n lower
00092 *>          triangular part of A contains the lower triangular part of
00093 *>          the matrix A, and the strictly upper triangular part of A is
00094 *>          not referenced.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] LDA
00098 *> \verbatim
00099 *>          LDA is INTEGER
00100 *>          The leading dimension of the array A.  LDA >= max(N,1).
00101 *> \endverbatim
00102 *>
00103 *> \param[out] WORK
00104 *> \verbatim
00105 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00106 *>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
00107 *>          WORK is not referenced.
00108 *> \endverbatim
00109 *
00110 *  Authors:
00111 *  ========
00112 *
00113 *> \author Univ. of Tennessee 
00114 *> \author Univ. of California Berkeley 
00115 *> \author Univ. of Colorado Denver 
00116 *> \author NAG Ltd. 
00117 *
00118 *> \date November 2011
00119 *
00120 *> \ingroup realSYauxiliary
00121 *
00122 *  =====================================================================
00123       REAL             FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK )
00124 *
00125 *  -- LAPACK auxiliary routine (version 3.4.0) --
00126 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00127 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00128 *     November 2011
00129 *
00130 *     .. Scalar Arguments ..
00131       CHARACTER          NORM, UPLO
00132       INTEGER            LDA, N
00133 *     ..
00134 *     .. Array Arguments ..
00135       REAL               A( LDA, * ), WORK( * )
00136 *     ..
00137 *
00138 * =====================================================================
00139 *
00140 *     .. Parameters ..
00141       REAL               ONE, ZERO
00142       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00143 *     ..
00144 *     .. Local Scalars ..
00145       INTEGER            I, J
00146       REAL               ABSA, SCALE, SUM, VALUE
00147 *     ..
00148 *     .. External Subroutines ..
00149       EXTERNAL           SLASSQ
00150 *     ..
00151 *     .. External Functions ..
00152       LOGICAL            LSAME
00153       EXTERNAL           LSAME
00154 *     ..
00155 *     .. Intrinsic Functions ..
00156       INTRINSIC          ABS, MAX, SQRT
00157 *     ..
00158 *     .. Executable Statements ..
00159 *
00160       IF( N.EQ.0 ) THEN
00161          VALUE = ZERO
00162       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00163 *
00164 *        Find max(abs(A(i,j))).
00165 *
00166          VALUE = ZERO
00167          IF( LSAME( UPLO, 'U' ) ) THEN
00168             DO 20 J = 1, N
00169                DO 10 I = 1, J
00170                   VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00171    10          CONTINUE
00172    20       CONTINUE
00173          ELSE
00174             DO 40 J = 1, N
00175                DO 30 I = J, N
00176                   VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00177    30          CONTINUE
00178    40       CONTINUE
00179          END IF
00180       ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
00181      $         ( NORM.EQ.'1' ) ) THEN
00182 *
00183 *        Find normI(A) ( = norm1(A), since A is symmetric).
00184 *
00185          VALUE = ZERO
00186          IF( LSAME( UPLO, 'U' ) ) THEN
00187             DO 60 J = 1, N
00188                SUM = ZERO
00189                DO 50 I = 1, J - 1
00190                   ABSA = ABS( A( I, J ) )
00191                   SUM = SUM + ABSA
00192                   WORK( I ) = WORK( I ) + ABSA
00193    50          CONTINUE
00194                WORK( J ) = SUM + ABS( A( J, J ) )
00195    60       CONTINUE
00196             DO 70 I = 1, N
00197                VALUE = MAX( VALUE, WORK( I ) )
00198    70       CONTINUE
00199          ELSE
00200             DO 80 I = 1, N
00201                WORK( I ) = ZERO
00202    80       CONTINUE
00203             DO 100 J = 1, N
00204                SUM = WORK( J ) + ABS( A( J, J ) )
00205                DO 90 I = J + 1, N
00206                   ABSA = ABS( A( I, J ) )
00207                   SUM = SUM + ABSA
00208                   WORK( I ) = WORK( I ) + ABSA
00209    90          CONTINUE
00210                VALUE = MAX( VALUE, SUM )
00211   100       CONTINUE
00212          END IF
00213       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00214 *
00215 *        Find normF(A).
00216 *
00217          SCALE = ZERO
00218          SUM = ONE
00219          IF( LSAME( UPLO, 'U' ) ) THEN
00220             DO 110 J = 2, N
00221                CALL SLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
00222   110       CONTINUE
00223          ELSE
00224             DO 120 J = 1, N - 1
00225                CALL SLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
00226   120       CONTINUE
00227          END IF
00228          SUM = 2*SUM
00229          CALL SLASSQ( N, A, LDA+1, SCALE, SUM )
00230          VALUE = SCALE*SQRT( SUM )
00231       END IF
00232 *
00233       SLANSY = VALUE
00234       RETURN
00235 *
00236 *     End of SLANSY
00237 *
00238       END
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