LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
slanst.f
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00001 *> \brief \b SLANST
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SLANST + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slanst.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slanst.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION SLANST( NORM, N, D, E )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM
00025 *       INTEGER            N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               D( * ), E( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> SLANST  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 tridiagonal matrix A.
00040 *> \endverbatim
00041 *>
00042 *> \return SLANST
00043 *> \verbatim
00044 *>
00045 *>    SLANST = ( 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 SLANST as described
00066 *>          above.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] N
00070 *> \verbatim
00071 *>          N is INTEGER
00072 *>          The order of the matrix A.  N >= 0.  When N = 0, SLANST is
00073 *>          set to zero.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] D
00077 *> \verbatim
00078 *>          D is REAL array, dimension (N)
00079 *>          The diagonal elements of A.
00080 *> \endverbatim
00081 *>
00082 *> \param[in] E
00083 *> \verbatim
00084 *>          E is REAL array, dimension (N-1)
00085 *>          The (n-1) sub-diagonal or super-diagonal elements of A.
00086 *> \endverbatim
00087 *
00088 *  Authors:
00089 *  ========
00090 *
00091 *> \author Univ. of Tennessee 
00092 *> \author Univ. of California Berkeley 
00093 *> \author Univ. of Colorado Denver 
00094 *> \author NAG Ltd. 
00095 *
00096 *> \date November 2011
00097 *
00098 *> \ingroup auxOTHERauxiliary
00099 *
00100 *  =====================================================================
00101       REAL             FUNCTION SLANST( NORM, N, D, E )
00102 *
00103 *  -- LAPACK auxiliary routine (version 3.4.0) --
00104 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00105 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00106 *     November 2011
00107 *
00108 *     .. Scalar Arguments ..
00109       CHARACTER          NORM
00110       INTEGER            N
00111 *     ..
00112 *     .. Array Arguments ..
00113       REAL               D( * ), E( * )
00114 *     ..
00115 *
00116 *  =====================================================================
00117 *
00118 *     .. Parameters ..
00119       REAL               ONE, ZERO
00120       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00121 *     ..
00122 *     .. Local Scalars ..
00123       INTEGER            I
00124       REAL               ANORM, SCALE, SUM
00125 *     ..
00126 *     .. External Functions ..
00127       LOGICAL            LSAME
00128       EXTERNAL           LSAME
00129 *     ..
00130 *     .. External Subroutines ..
00131       EXTERNAL           SLASSQ
00132 *     ..
00133 *     .. Intrinsic Functions ..
00134       INTRINSIC          ABS, MAX, SQRT
00135 *     ..
00136 *     .. Executable Statements ..
00137 *
00138       IF( N.LE.0 ) THEN
00139          ANORM = ZERO
00140       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00141 *
00142 *        Find max(abs(A(i,j))).
00143 *
00144          ANORM = ABS( D( N ) )
00145          DO 10 I = 1, N - 1
00146             ANORM = MAX( ANORM, ABS( D( I ) ) )
00147             ANORM = MAX( ANORM, ABS( E( I ) ) )
00148    10    CONTINUE
00149       ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
00150      $         LSAME( NORM, 'I' ) ) THEN
00151 *
00152 *        Find norm1(A).
00153 *
00154          IF( N.EQ.1 ) THEN
00155             ANORM = ABS( D( 1 ) )
00156          ELSE
00157             ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
00158      $              ABS( E( N-1 ) )+ABS( D( N ) ) )
00159             DO 20 I = 2, N - 1
00160                ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
00161      $                 ABS( E( I-1 ) ) )
00162    20       CONTINUE
00163          END IF
00164       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00165 *
00166 *        Find normF(A).
00167 *
00168          SCALE = ZERO
00169          SUM = ONE
00170          IF( N.GT.1 ) THEN
00171             CALL SLASSQ( N-1, E, 1, SCALE, SUM )
00172             SUM = 2*SUM
00173          END IF
00174          CALL SLASSQ( N, D, 1, SCALE, SUM )
00175          ANORM = SCALE*SQRT( SUM )
00176       END IF
00177 *
00178       SLANST = ANORM
00179       RETURN
00180 *
00181 *     End of SLANST
00182 *
00183       END
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