LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clansp.f
Go to the documentation of this file.
00001 *> \brief \b CLANSP
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLANSP + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clansp.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clansp.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clansp.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION CLANSP( NORM, UPLO, N, AP, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM, UPLO
00025 *       INTEGER            N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               WORK( * )
00029 *       COMPLEX            AP( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> CLANSP  returns the value of the one norm,  or the Frobenius norm, or
00039 *> the  infinity norm,  or the  element of  largest absolute value  of a
00040 *> complex symmetric matrix A,  supplied in packed form.
00041 *> \endverbatim
00042 *>
00043 *> \return CLANSP
00044 *> \verbatim
00045 *>
00046 *>    CLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00047 *>             (
00048 *>             ( norm1(A),         NORM = '1', 'O' or 'o'
00049 *>             (
00050 *>             ( normI(A),         NORM = 'I' or 'i'
00051 *>             (
00052 *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00053 *>
00054 *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
00055 *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00056 *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
00057 *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00058 *> \endverbatim
00059 *
00060 *  Arguments:
00061 *  ==========
00062 *
00063 *> \param[in] NORM
00064 *> \verbatim
00065 *>          NORM is CHARACTER*1
00066 *>          Specifies the value to be returned in CLANSP as described
00067 *>          above.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] UPLO
00071 *> \verbatim
00072 *>          UPLO is CHARACTER*1
00073 *>          Specifies whether the upper or lower triangular part of the
00074 *>          symmetric matrix A is supplied.
00075 *>          = 'U':  Upper triangular part of A is supplied
00076 *>          = 'L':  Lower triangular part of A is supplied
00077 *> \endverbatim
00078 *>
00079 *> \param[in] N
00080 *> \verbatim
00081 *>          N is INTEGER
00082 *>          The order of the matrix A.  N >= 0.  When N = 0, CLANSP is
00083 *>          set to zero.
00084 *> \endverbatim
00085 *>
00086 *> \param[in] AP
00087 *> \verbatim
00088 *>          AP is COMPLEX array, dimension (N*(N+1)/2)
00089 *>          The upper or lower triangle of the symmetric matrix A, packed
00090 *>          columnwise in a linear array.  The j-th column of A is stored
00091 *>          in the array AP as follows:
00092 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00093 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00094 *> \endverbatim
00095 *>
00096 *> \param[out] WORK
00097 *> \verbatim
00098 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00099 *>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
00100 *>          WORK is not referenced.
00101 *> \endverbatim
00102 *
00103 *  Authors:
00104 *  ========
00105 *
00106 *> \author Univ. of Tennessee 
00107 *> \author Univ. of California Berkeley 
00108 *> \author Univ. of Colorado Denver 
00109 *> \author NAG Ltd. 
00110 *
00111 *> \date November 2011
00112 *
00113 *> \ingroup complexOTHERauxiliary
00114 *
00115 *  =====================================================================
00116       REAL             FUNCTION CLANSP( NORM, UPLO, N, AP, WORK )
00117 *
00118 *  -- LAPACK auxiliary routine (version 3.4.0) --
00119 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00120 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00121 *     November 2011
00122 *
00123 *     .. Scalar Arguments ..
00124       CHARACTER          NORM, UPLO
00125       INTEGER            N
00126 *     ..
00127 *     .. Array Arguments ..
00128       REAL               WORK( * )
00129       COMPLEX            AP( * )
00130 *     ..
00131 *
00132 * =====================================================================
00133 *
00134 *     .. Parameters ..
00135       REAL               ONE, ZERO
00136       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00137 *     ..
00138 *     .. Local Scalars ..
00139       INTEGER            I, J, K
00140       REAL               ABSA, SCALE, SUM, VALUE
00141 *     ..
00142 *     .. External Functions ..
00143       LOGICAL            LSAME
00144       EXTERNAL           LSAME
00145 *     ..
00146 *     .. External Subroutines ..
00147       EXTERNAL           CLASSQ
00148 *     ..
00149 *     .. Intrinsic Functions ..
00150       INTRINSIC          ABS, AIMAG, MAX, REAL, SQRT
00151 *     ..
00152 *     .. Executable Statements ..
00153 *
00154       IF( N.EQ.0 ) THEN
00155          VALUE = ZERO
00156       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00157 *
00158 *        Find max(abs(A(i,j))).
00159 *
00160          VALUE = ZERO
00161          IF( LSAME( UPLO, 'U' ) ) THEN
00162             K = 1
00163             DO 20 J = 1, N
00164                DO 10 I = K, K + J - 1
00165                   VALUE = MAX( VALUE, ABS( AP( I ) ) )
00166    10          CONTINUE
00167                K = K + J
00168    20       CONTINUE
00169          ELSE
00170             K = 1
00171             DO 40 J = 1, N
00172                DO 30 I = K, K + N - J
00173                   VALUE = MAX( VALUE, ABS( AP( I ) ) )
00174    30          CONTINUE
00175                K = K + N - J + 1
00176    40       CONTINUE
00177          END IF
00178       ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
00179      $         ( NORM.EQ.'1' ) ) THEN
00180 *
00181 *        Find normI(A) ( = norm1(A), since A is symmetric).
00182 *
00183          VALUE = ZERO
00184          K = 1
00185          IF( LSAME( UPLO, 'U' ) ) THEN
00186             DO 60 J = 1, N
00187                SUM = ZERO
00188                DO 50 I = 1, J - 1
00189                   ABSA = ABS( AP( K ) )
00190                   SUM = SUM + ABSA
00191                   WORK( I ) = WORK( I ) + ABSA
00192                   K = K + 1
00193    50          CONTINUE
00194                WORK( J ) = SUM + ABS( AP( K ) )
00195                K = K + 1
00196    60       CONTINUE
00197             DO 70 I = 1, N
00198                VALUE = MAX( VALUE, WORK( I ) )
00199    70       CONTINUE
00200          ELSE
00201             DO 80 I = 1, N
00202                WORK( I ) = ZERO
00203    80       CONTINUE
00204             DO 100 J = 1, N
00205                SUM = WORK( J ) + ABS( AP( K ) )
00206                K = K + 1
00207                DO 90 I = J + 1, N
00208                   ABSA = ABS( AP( K ) )
00209                   SUM = SUM + ABSA
00210                   WORK( I ) = WORK( I ) + ABSA
00211                   K = K + 1
00212    90          CONTINUE
00213                VALUE = MAX( VALUE, SUM )
00214   100       CONTINUE
00215          END IF
00216       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00217 *
00218 *        Find normF(A).
00219 *
00220          SCALE = ZERO
00221          SUM = ONE
00222          K = 2
00223          IF( LSAME( UPLO, 'U' ) ) THEN
00224             DO 110 J = 2, N
00225                CALL CLASSQ( J-1, AP( K ), 1, SCALE, SUM )
00226                K = K + J
00227   110       CONTINUE
00228          ELSE
00229             DO 120 J = 1, N - 1
00230                CALL CLASSQ( N-J, AP( K ), 1, SCALE, SUM )
00231                K = K + N - J + 1
00232   120       CONTINUE
00233          END IF
00234          SUM = 2*SUM
00235          K = 1
00236          DO 130 I = 1, N
00237             IF( REAL( AP( K ) ).NE.ZERO ) THEN
00238                ABSA = ABS( REAL( AP( K ) ) )
00239                IF( SCALE.LT.ABSA ) THEN
00240                   SUM = ONE + SUM*( SCALE / ABSA )**2
00241                   SCALE = ABSA
00242                ELSE
00243                   SUM = SUM + ( ABSA / SCALE )**2
00244                END IF
00245             END IF
00246             IF( AIMAG( AP( K ) ).NE.ZERO ) THEN
00247                ABSA = ABS( AIMAG( AP( K ) ) )
00248                IF( SCALE.LT.ABSA ) THEN
00249                   SUM = ONE + SUM*( SCALE / ABSA )**2
00250                   SCALE = ABSA
00251                ELSE
00252                   SUM = SUM + ( ABSA / SCALE )**2
00253                END IF
00254             END IF
00255             IF( LSAME( UPLO, 'U' ) ) THEN
00256                K = K + I + 1
00257             ELSE
00258                K = K + N - I + 1
00259             END IF
00260   130    CONTINUE
00261          VALUE = SCALE*SQRT( SUM )
00262       END IF
00263 *
00264       CLANSP = VALUE
00265       RETURN
00266 *
00267 *     End of CLANSP
00268 *
00269       END
 All Files Functions