LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clantp.f
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00001 *> \brief \b CLANTP
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLANTP + 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/clantp.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clantp.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          DIAG, 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 *> CLANTP  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 *> triangular matrix A, supplied in packed form.
00041 *> \endverbatim
00042 *>
00043 *> \return CLANTP
00044 *> \verbatim
00045 *>
00046 *>    CLANTP = ( 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 CLANTP as described
00067 *>          above.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] UPLO
00071 *> \verbatim
00072 *>          UPLO is CHARACTER*1
00073 *>          Specifies whether the matrix A is upper or lower triangular.
00074 *>          = 'U':  Upper triangular
00075 *>          = 'L':  Lower triangular
00076 *> \endverbatim
00077 *>
00078 *> \param[in] DIAG
00079 *> \verbatim
00080 *>          DIAG is CHARACTER*1
00081 *>          Specifies whether or not the matrix A is unit triangular.
00082 *>          = 'N':  Non-unit triangular
00083 *>          = 'U':  Unit triangular
00084 *> \endverbatim
00085 *>
00086 *> \param[in] N
00087 *> \verbatim
00088 *>          N is INTEGER
00089 *>          The order of the matrix A.  N >= 0.  When N = 0, CLANTP is
00090 *>          set to zero.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] AP
00094 *> \verbatim
00095 *>          AP is COMPLEX array, dimension (N*(N+1)/2)
00096 *>          The upper or lower triangular matrix A, packed columnwise in
00097 *>          a linear array.  The j-th column of A is stored in the array
00098 *>          AP as follows:
00099 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00100 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00101 *>          Note that when DIAG = 'U', the elements of the array AP
00102 *>          corresponding to the diagonal elements of the matrix A are
00103 *>          not referenced, but are assumed to be one.
00104 *> \endverbatim
00105 *>
00106 *> \param[out] WORK
00107 *> \verbatim
00108 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00109 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00110 *>          referenced.
00111 *> \endverbatim
00112 *
00113 *  Authors:
00114 *  ========
00115 *
00116 *> \author Univ. of Tennessee 
00117 *> \author Univ. of California Berkeley 
00118 *> \author Univ. of Colorado Denver 
00119 *> \author NAG Ltd. 
00120 *
00121 *> \date November 2011
00122 *
00123 *> \ingroup complexOTHERauxiliary
00124 *
00125 *  =====================================================================
00126       REAL             FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )
00127 *
00128 *  -- LAPACK auxiliary routine (version 3.4.0) --
00129 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00130 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00131 *     November 2011
00132 *
00133 *     .. Scalar Arguments ..
00134       CHARACTER          DIAG, NORM, UPLO
00135       INTEGER            N
00136 *     ..
00137 *     .. Array Arguments ..
00138       REAL               WORK( * )
00139       COMPLEX            AP( * )
00140 *     ..
00141 *
00142 * =====================================================================
00143 *
00144 *     .. Parameters ..
00145       REAL               ONE, ZERO
00146       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00147 *     ..
00148 *     .. Local Scalars ..
00149       LOGICAL            UDIAG
00150       INTEGER            I, J, K
00151       REAL               SCALE, SUM, VALUE
00152 *     ..
00153 *     .. External Functions ..
00154       LOGICAL            LSAME
00155       EXTERNAL           LSAME
00156 *     ..
00157 *     .. External Subroutines ..
00158       EXTERNAL           CLASSQ
00159 *     ..
00160 *     .. Intrinsic Functions ..
00161       INTRINSIC          ABS, MAX, SQRT
00162 *     ..
00163 *     .. Executable Statements ..
00164 *
00165       IF( N.EQ.0 ) THEN
00166          VALUE = ZERO
00167       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00168 *
00169 *        Find max(abs(A(i,j))).
00170 *
00171          K = 1
00172          IF( LSAME( DIAG, 'U' ) ) THEN
00173             VALUE = ONE
00174             IF( LSAME( UPLO, 'U' ) ) THEN
00175                DO 20 J = 1, N
00176                   DO 10 I = K, K + J - 2
00177                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00178    10             CONTINUE
00179                   K = K + J
00180    20          CONTINUE
00181             ELSE
00182                DO 40 J = 1, N
00183                   DO 30 I = K + 1, K + N - J
00184                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00185    30             CONTINUE
00186                   K = K + N - J + 1
00187    40          CONTINUE
00188             END IF
00189          ELSE
00190             VALUE = ZERO
00191             IF( LSAME( UPLO, 'U' ) ) THEN
00192                DO 60 J = 1, N
00193                   DO 50 I = K, K + J - 1
00194                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00195    50             CONTINUE
00196                   K = K + J
00197    60          CONTINUE
00198             ELSE
00199                DO 80 J = 1, N
00200                   DO 70 I = K, K + N - J
00201                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00202    70             CONTINUE
00203                   K = K + N - J + 1
00204    80          CONTINUE
00205             END IF
00206          END IF
00207       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00208 *
00209 *        Find norm1(A).
00210 *
00211          VALUE = ZERO
00212          K = 1
00213          UDIAG = LSAME( DIAG, 'U' )
00214          IF( LSAME( UPLO, 'U' ) ) THEN
00215             DO 110 J = 1, N
00216                IF( UDIAG ) THEN
00217                   SUM = ONE
00218                   DO 90 I = K, K + J - 2
00219                      SUM = SUM + ABS( AP( I ) )
00220    90             CONTINUE
00221                ELSE
00222                   SUM = ZERO
00223                   DO 100 I = K, K + J - 1
00224                      SUM = SUM + ABS( AP( I ) )
00225   100             CONTINUE
00226                END IF
00227                K = K + J
00228                VALUE = MAX( VALUE, SUM )
00229   110       CONTINUE
00230          ELSE
00231             DO 140 J = 1, N
00232                IF( UDIAG ) THEN
00233                   SUM = ONE
00234                   DO 120 I = K + 1, K + N - J
00235                      SUM = SUM + ABS( AP( I ) )
00236   120             CONTINUE
00237                ELSE
00238                   SUM = ZERO
00239                   DO 130 I = K, K + N - J
00240                      SUM = SUM + ABS( AP( I ) )
00241   130             CONTINUE
00242                END IF
00243                K = K + N - J + 1
00244                VALUE = MAX( VALUE, SUM )
00245   140       CONTINUE
00246          END IF
00247       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00248 *
00249 *        Find normI(A).
00250 *
00251          K = 1
00252          IF( LSAME( UPLO, 'U' ) ) THEN
00253             IF( LSAME( DIAG, 'U' ) ) THEN
00254                DO 150 I = 1, N
00255                   WORK( I ) = ONE
00256   150          CONTINUE
00257                DO 170 J = 1, N
00258                   DO 160 I = 1, J - 1
00259                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00260                      K = K + 1
00261   160             CONTINUE
00262                   K = K + 1
00263   170          CONTINUE
00264             ELSE
00265                DO 180 I = 1, N
00266                   WORK( I ) = ZERO
00267   180          CONTINUE
00268                DO 200 J = 1, N
00269                   DO 190 I = 1, J
00270                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00271                      K = K + 1
00272   190             CONTINUE
00273   200          CONTINUE
00274             END IF
00275          ELSE
00276             IF( LSAME( DIAG, 'U' ) ) THEN
00277                DO 210 I = 1, N
00278                   WORK( I ) = ONE
00279   210          CONTINUE
00280                DO 230 J = 1, N
00281                   K = K + 1
00282                   DO 220 I = J + 1, N
00283                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00284                      K = K + 1
00285   220             CONTINUE
00286   230          CONTINUE
00287             ELSE
00288                DO 240 I = 1, N
00289                   WORK( I ) = ZERO
00290   240          CONTINUE
00291                DO 260 J = 1, N
00292                   DO 250 I = J, N
00293                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00294                      K = K + 1
00295   250             CONTINUE
00296   260          CONTINUE
00297             END IF
00298          END IF
00299          VALUE = ZERO
00300          DO 270 I = 1, N
00301             VALUE = MAX( VALUE, WORK( I ) )
00302   270    CONTINUE
00303       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00304 *
00305 *        Find normF(A).
00306 *
00307          IF( LSAME( UPLO, 'U' ) ) THEN
00308             IF( LSAME( DIAG, 'U' ) ) THEN
00309                SCALE = ONE
00310                SUM = N
00311                K = 2
00312                DO 280 J = 2, N
00313                   CALL CLASSQ( J-1, AP( K ), 1, SCALE, SUM )
00314                   K = K + J
00315   280          CONTINUE
00316             ELSE
00317                SCALE = ZERO
00318                SUM = ONE
00319                K = 1
00320                DO 290 J = 1, N
00321                   CALL CLASSQ( J, AP( K ), 1, SCALE, SUM )
00322                   K = K + J
00323   290          CONTINUE
00324             END IF
00325          ELSE
00326             IF( LSAME( DIAG, 'U' ) ) THEN
00327                SCALE = ONE
00328                SUM = N
00329                K = 2
00330                DO 300 J = 1, N - 1
00331                   CALL CLASSQ( N-J, AP( K ), 1, SCALE, SUM )
00332                   K = K + N - J + 1
00333   300          CONTINUE
00334             ELSE
00335                SCALE = ZERO
00336                SUM = ONE
00337                K = 1
00338                DO 310 J = 1, N
00339                   CALL CLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
00340                   K = K + N - J + 1
00341   310          CONTINUE
00342             END IF
00343          END IF
00344          VALUE = SCALE*SQRT( SUM )
00345       END IF
00346 *
00347       CLANTP = VALUE
00348       RETURN
00349 *
00350 *     End of CLANTP
00351 *
00352       END
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