LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
slantp.f
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00001 *> \brief \b SLANTP
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SLANTP + 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/slantp.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slantp.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          DIAG, NORM, UPLO
00025 *       INTEGER            N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               AP( * ), WORK( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> SLANTP  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 *> triangular matrix A, supplied in packed form.
00040 *> \endverbatim
00041 *>
00042 *> \return SLANTP
00043 *> \verbatim
00044 *>
00045 *>    SLANTP = ( 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 SLANTP as described
00066 *>          above.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] UPLO
00070 *> \verbatim
00071 *>          UPLO is CHARACTER*1
00072 *>          Specifies whether the matrix A is upper or lower triangular.
00073 *>          = 'U':  Upper triangular
00074 *>          = 'L':  Lower triangular
00075 *> \endverbatim
00076 *>
00077 *> \param[in] DIAG
00078 *> \verbatim
00079 *>          DIAG is CHARACTER*1
00080 *>          Specifies whether or not the matrix A is unit triangular.
00081 *>          = 'N':  Non-unit triangular
00082 *>          = 'U':  Unit triangular
00083 *> \endverbatim
00084 *>
00085 *> \param[in] N
00086 *> \verbatim
00087 *>          N is INTEGER
00088 *>          The order of the matrix A.  N >= 0.  When N = 0, SLANTP is
00089 *>          set to zero.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] AP
00093 *> \verbatim
00094 *>          AP is REAL array, dimension (N*(N+1)/2)
00095 *>          The upper or lower triangular matrix A, packed columnwise in
00096 *>          a linear array.  The j-th column of A is stored in the array
00097 *>          AP as follows:
00098 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00099 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00100 *>          Note that when DIAG = 'U', the elements of the array AP
00101 *>          corresponding to the diagonal elements of the matrix A are
00102 *>          not referenced, but are assumed to be one.
00103 *> \endverbatim
00104 *>
00105 *> \param[out] WORK
00106 *> \verbatim
00107 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00108 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00109 *>          referenced.
00110 *> \endverbatim
00111 *
00112 *  Authors:
00113 *  ========
00114 *
00115 *> \author Univ. of Tennessee 
00116 *> \author Univ. of California Berkeley 
00117 *> \author Univ. of Colorado Denver 
00118 *> \author NAG Ltd. 
00119 *
00120 *> \date November 2011
00121 *
00122 *> \ingroup realOTHERauxiliary
00123 *
00124 *  =====================================================================
00125       REAL             FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
00126 *
00127 *  -- LAPACK auxiliary routine (version 3.4.0) --
00128 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00129 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00130 *     November 2011
00131 *
00132 *     .. Scalar Arguments ..
00133       CHARACTER          DIAG, NORM, UPLO
00134       INTEGER            N
00135 *     ..
00136 *     .. Array Arguments ..
00137       REAL               AP( * ), WORK( * )
00138 *     ..
00139 *
00140 * =====================================================================
00141 *
00142 *     .. Parameters ..
00143       REAL               ONE, ZERO
00144       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00145 *     ..
00146 *     .. Local Scalars ..
00147       LOGICAL            UDIAG
00148       INTEGER            I, J, K
00149       REAL               SCALE, SUM, VALUE
00150 *     ..
00151 *     .. External Subroutines ..
00152       EXTERNAL           SLASSQ
00153 *     ..
00154 *     .. External Functions ..
00155       LOGICAL            LSAME
00156       EXTERNAL           LSAME
00157 *     ..
00158 *     .. Intrinsic Functions ..
00159       INTRINSIC          ABS, MAX, SQRT
00160 *     ..
00161 *     .. Executable Statements ..
00162 *
00163       IF( N.EQ.0 ) THEN
00164          VALUE = ZERO
00165       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00166 *
00167 *        Find max(abs(A(i,j))).
00168 *
00169          K = 1
00170          IF( LSAME( DIAG, 'U' ) ) THEN
00171             VALUE = ONE
00172             IF( LSAME( UPLO, 'U' ) ) THEN
00173                DO 20 J = 1, N
00174                   DO 10 I = K, K + J - 2
00175                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00176    10             CONTINUE
00177                   K = K + J
00178    20          CONTINUE
00179             ELSE
00180                DO 40 J = 1, N
00181                   DO 30 I = K + 1, K + N - J
00182                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00183    30             CONTINUE
00184                   K = K + N - J + 1
00185    40          CONTINUE
00186             END IF
00187          ELSE
00188             VALUE = ZERO
00189             IF( LSAME( UPLO, 'U' ) ) THEN
00190                DO 60 J = 1, N
00191                   DO 50 I = K, K + J - 1
00192                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00193    50             CONTINUE
00194                   K = K + J
00195    60          CONTINUE
00196             ELSE
00197                DO 80 J = 1, N
00198                   DO 70 I = K, K + N - J
00199                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00200    70             CONTINUE
00201                   K = K + N - J + 1
00202    80          CONTINUE
00203             END IF
00204          END IF
00205       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00206 *
00207 *        Find norm1(A).
00208 *
00209          VALUE = ZERO
00210          K = 1
00211          UDIAG = LSAME( DIAG, 'U' )
00212          IF( LSAME( UPLO, 'U' ) ) THEN
00213             DO 110 J = 1, N
00214                IF( UDIAG ) THEN
00215                   SUM = ONE
00216                   DO 90 I = K, K + J - 2
00217                      SUM = SUM + ABS( AP( I ) )
00218    90             CONTINUE
00219                ELSE
00220                   SUM = ZERO
00221                   DO 100 I = K, K + J - 1
00222                      SUM = SUM + ABS( AP( I ) )
00223   100             CONTINUE
00224                END IF
00225                K = K + J
00226                VALUE = MAX( VALUE, SUM )
00227   110       CONTINUE
00228          ELSE
00229             DO 140 J = 1, N
00230                IF( UDIAG ) THEN
00231                   SUM = ONE
00232                   DO 120 I = K + 1, K + N - J
00233                      SUM = SUM + ABS( AP( I ) )
00234   120             CONTINUE
00235                ELSE
00236                   SUM = ZERO
00237                   DO 130 I = K, K + N - J
00238                      SUM = SUM + ABS( AP( I ) )
00239   130             CONTINUE
00240                END IF
00241                K = K + N - J + 1
00242                VALUE = MAX( VALUE, SUM )
00243   140       CONTINUE
00244          END IF
00245       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00246 *
00247 *        Find normI(A).
00248 *
00249          K = 1
00250          IF( LSAME( UPLO, 'U' ) ) THEN
00251             IF( LSAME( DIAG, 'U' ) ) THEN
00252                DO 150 I = 1, N
00253                   WORK( I ) = ONE
00254   150          CONTINUE
00255                DO 170 J = 1, N
00256                   DO 160 I = 1, J - 1
00257                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00258                      K = K + 1
00259   160             CONTINUE
00260                   K = K + 1
00261   170          CONTINUE
00262             ELSE
00263                DO 180 I = 1, N
00264                   WORK( I ) = ZERO
00265   180          CONTINUE
00266                DO 200 J = 1, N
00267                   DO 190 I = 1, J
00268                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00269                      K = K + 1
00270   190             CONTINUE
00271   200          CONTINUE
00272             END IF
00273          ELSE
00274             IF( LSAME( DIAG, 'U' ) ) THEN
00275                DO 210 I = 1, N
00276                   WORK( I ) = ONE
00277   210          CONTINUE
00278                DO 230 J = 1, N
00279                   K = K + 1
00280                   DO 220 I = J + 1, N
00281                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00282                      K = K + 1
00283   220             CONTINUE
00284   230          CONTINUE
00285             ELSE
00286                DO 240 I = 1, N
00287                   WORK( I ) = ZERO
00288   240          CONTINUE
00289                DO 260 J = 1, N
00290                   DO 250 I = J, N
00291                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00292                      K = K + 1
00293   250             CONTINUE
00294   260          CONTINUE
00295             END IF
00296          END IF
00297          VALUE = ZERO
00298          DO 270 I = 1, N
00299             VALUE = MAX( VALUE, WORK( I ) )
00300   270    CONTINUE
00301       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00302 *
00303 *        Find normF(A).
00304 *
00305          IF( LSAME( UPLO, 'U' ) ) THEN
00306             IF( LSAME( DIAG, 'U' ) ) THEN
00307                SCALE = ONE
00308                SUM = N
00309                K = 2
00310                DO 280 J = 2, N
00311                   CALL SLASSQ( J-1, AP( K ), 1, SCALE, SUM )
00312                   K = K + J
00313   280          CONTINUE
00314             ELSE
00315                SCALE = ZERO
00316                SUM = ONE
00317                K = 1
00318                DO 290 J = 1, N
00319                   CALL SLASSQ( J, AP( K ), 1, SCALE, SUM )
00320                   K = K + J
00321   290          CONTINUE
00322             END IF
00323          ELSE
00324             IF( LSAME( DIAG, 'U' ) ) THEN
00325                SCALE = ONE
00326                SUM = N
00327                K = 2
00328                DO 300 J = 1, N - 1
00329                   CALL SLASSQ( N-J, AP( K ), 1, SCALE, SUM )
00330                   K = K + N - J + 1
00331   300          CONTINUE
00332             ELSE
00333                SCALE = ZERO
00334                SUM = ONE
00335                K = 1
00336                DO 310 J = 1, N
00337                   CALL SLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
00338                   K = K + N - J + 1
00339   310          CONTINUE
00340             END IF
00341          END IF
00342          VALUE = SCALE*SQRT( SUM )
00343       END IF
00344 *
00345       SLANTP = VALUE
00346       RETURN
00347 *
00348 *     End of SLANTP
00349 *
00350       END
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