LAPACK: SRC/slantp.f Source File

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00001       REAL             FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          DIAG, NORM, UPLO
00010       INTEGER            N
00011 *     ..
00012 *     .. Array Arguments ..
00013       REAL               AP( * ), WORK( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  SLANTP  returns the value of the one norm,  or the Frobenius norm, or
00020 *  the  infinity norm,  or the  element of  largest absolute value  of a
00021 *  triangular matrix A, supplied in packed form.
00022 *
00023 *  Description
00024 *  ===========
00025 *
00026 *  SLANTP returns the value
00027 *
00028 *     SLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00029 *              (
00030 *              ( norm1(A),         NORM = '1', 'O' or 'o'
00031 *              (
00032 *              ( normI(A),         NORM = 'I' or 'i'
00033 *              (
00034 *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00035 *
00036 *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
00037 *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00038 *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
00039 *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00040 *
00041 *  Arguments
00042 *  =========
00043 *
00044 *  NORM    (input) CHARACTER*1
00045 *          Specifies the value to be returned in SLANTP as described
00046 *          above.
00047 *
00048 *  UPLO    (input) CHARACTER*1
00049 *          Specifies whether the matrix A is upper or lower triangular.
00050 *          = 'U':  Upper triangular
00051 *          = 'L':  Lower triangular
00052 *
00053 *  DIAG    (input) CHARACTER*1
00054 *          Specifies whether or not the matrix A is unit triangular.
00055 *          = 'N':  Non-unit triangular
00056 *          = 'U':  Unit triangular
00057 *
00058 *  N       (input) INTEGER
00059 *          The order of the matrix A.  N >= 0.  When N = 0, SLANTP is
00060 *          set to zero.
00061 *
00062 *  AP      (input) REAL array, dimension (N*(N+1)/2)
00063 *          The upper or lower triangular matrix A, packed columnwise in
00064 *          a linear array.  The j-th column of A is stored in the array
00065 *          AP as follows:
00066 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00067 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00068 *          Note that when DIAG = 'U', the elements of the array AP
00069 *          corresponding to the diagonal elements of the matrix A are
00070 *          not referenced, but are assumed to be one.
00071 *
00072 *  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
00073 *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00074 *          referenced.
00075 *
00076 * =====================================================================
00077 *
00078 *     .. Parameters ..
00079       REAL               ONE, ZERO
00080       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00081 *     ..
00082 *     .. Local Scalars ..
00083       LOGICAL            UDIAG
00084       INTEGER            I, J, K
00085       REAL               SCALE, SUM, VALUE
00086 *     ..
00087 *     .. External Subroutines ..
00088       EXTERNAL           SLASSQ
00089 *     ..
00090 *     .. External Functions ..
00091       LOGICAL            LSAME
00092       EXTERNAL           LSAME
00093 *     ..
00094 *     .. Intrinsic Functions ..
00095       INTRINSIC          ABS, MAX, SQRT
00096 *     ..
00097 *     .. Executable Statements ..
00098 *
00099       IF( N.EQ.0 ) THEN
00100          VALUE = ZERO
00101       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00102 *
00103 *        Find max(abs(A(i,j))).
00104 *
00105          K = 1
00106          IF( LSAME( DIAG, 'U' ) ) THEN
00107             VALUE = ONE
00108             IF( LSAME( UPLO, 'U' ) ) THEN
00109                DO 20 J = 1, N
00110                   DO 10 I = K, K + J - 2
00111                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00112    10             CONTINUE
00113                   K = K + J
00114    20          CONTINUE
00115             ELSE
00116                DO 40 J = 1, N
00117                   DO 30 I = K + 1, K + N - J
00118                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00119    30             CONTINUE
00120                   K = K + N - J + 1
00121    40          CONTINUE
00122             END IF
00123          ELSE
00124             VALUE = ZERO
00125             IF( LSAME( UPLO, 'U' ) ) THEN
00126                DO 60 J = 1, N
00127                   DO 50 I = K, K + J - 1
00128                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00129    50             CONTINUE
00130                   K = K + J
00131    60          CONTINUE
00132             ELSE
00133                DO 80 J = 1, N
00134                   DO 70 I = K, K + N - J
00135                      VALUE = MAX( VALUE, ABS( AP( I ) ) )
00136    70             CONTINUE
00137                   K = K + N - J + 1
00138    80          CONTINUE
00139             END IF
00140          END IF
00141       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00142 *
00143 *        Find norm1(A).
00144 *
00145          VALUE = ZERO
00146          K = 1
00147          UDIAG = LSAME( DIAG, 'U' )
00148          IF( LSAME( UPLO, 'U' ) ) THEN
00149             DO 110 J = 1, N
00150                IF( UDIAG ) THEN
00151                   SUM = ONE
00152                   DO 90 I = K, K + J - 2
00153                      SUM = SUM + ABS( AP( I ) )
00154    90             CONTINUE
00155                ELSE
00156                   SUM = ZERO
00157                   DO 100 I = K, K + J - 1
00158                      SUM = SUM + ABS( AP( I ) )
00159   100             CONTINUE
00160                END IF
00161                K = K + J
00162                VALUE = MAX( VALUE, SUM )
00163   110       CONTINUE
00164          ELSE
00165             DO 140 J = 1, N
00166                IF( UDIAG ) THEN
00167                   SUM = ONE
00168                   DO 120 I = K + 1, K + N - J
00169                      SUM = SUM + ABS( AP( I ) )
00170   120             CONTINUE
00171                ELSE
00172                   SUM = ZERO
00173                   DO 130 I = K, K + N - J
00174                      SUM = SUM + ABS( AP( I ) )
00175   130             CONTINUE
00176                END IF
00177                K = K + N - J + 1
00178                VALUE = MAX( VALUE, SUM )
00179   140       CONTINUE
00180          END IF
00181       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00182 *
00183 *        Find normI(A).
00184 *
00185          K = 1
00186          IF( LSAME( UPLO, 'U' ) ) THEN
00187             IF( LSAME( DIAG, 'U' ) ) THEN
00188                DO 150 I = 1, N
00189                   WORK( I ) = ONE
00190   150          CONTINUE
00191                DO 170 J = 1, N
00192                   DO 160 I = 1, J - 1
00193                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00194                      K = K + 1
00195   160             CONTINUE
00196                   K = K + 1
00197   170          CONTINUE
00198             ELSE
00199                DO 180 I = 1, N
00200                   WORK( I ) = ZERO
00201   180          CONTINUE
00202                DO 200 J = 1, N
00203                   DO 190 I = 1, J
00204                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00205                      K = K + 1
00206   190             CONTINUE
00207   200          CONTINUE
00208             END IF
00209          ELSE
00210             IF( LSAME( DIAG, 'U' ) ) THEN
00211                DO 210 I = 1, N
00212                   WORK( I ) = ONE
00213   210          CONTINUE
00214                DO 230 J = 1, N
00215                   K = K + 1
00216                   DO 220 I = J + 1, N
00217                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00218                      K = K + 1
00219   220             CONTINUE
00220   230          CONTINUE
00221             ELSE
00222                DO 240 I = 1, N
00223                   WORK( I ) = ZERO
00224   240          CONTINUE
00225                DO 260 J = 1, N
00226                   DO 250 I = J, N
00227                      WORK( I ) = WORK( I ) + ABS( AP( K ) )
00228                      K = K + 1
00229   250             CONTINUE
00230   260          CONTINUE
00231             END IF
00232          END IF
00233          VALUE = ZERO
00234          DO 270 I = 1, N
00235             VALUE = MAX( VALUE, WORK( I ) )
00236   270    CONTINUE
00237       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00238 *
00239 *        Find normF(A).
00240 *
00241          IF( LSAME( UPLO, 'U' ) ) THEN
00242             IF( LSAME( DIAG, 'U' ) ) THEN
00243                SCALE = ONE
00244                SUM = N
00245                K = 2
00246                DO 280 J = 2, N
00247                   CALL SLASSQ( J-1, AP( K ), 1, SCALE, SUM )
00248                   K = K + J
00249   280          CONTINUE
00250             ELSE
00251                SCALE = ZERO
00252                SUM = ONE
00253                K = 1
00254                DO 290 J = 1, N
00255                   CALL SLASSQ( J, AP( K ), 1, SCALE, SUM )
00256                   K = K + J
00257   290          CONTINUE
00258             END IF
00259          ELSE
00260             IF( LSAME( DIAG, 'U' ) ) THEN
00261                SCALE = ONE
00262                SUM = N
00263                K = 2
00264                DO 300 J = 1, N - 1
00265                   CALL SLASSQ( N-J, AP( K ), 1, SCALE, SUM )
00266                   K = K + N - J + 1
00267   300          CONTINUE
00268             ELSE
00269                SCALE = ZERO
00270                SUM = ONE
00271                K = 1
00272                DO 310 J = 1, N
00273                   CALL SLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
00274                   K = K + N - J + 1
00275   310          CONTINUE
00276             END IF
00277          END IF
00278          VALUE = SCALE*SQRT( SUM )
00279       END IF
00280 *
00281       SLANTP = VALUE
00282       RETURN
00283 *
00284 *     End of SLANTP
00285 *
00286       END