LAPACK: SRC/slantr.f Source File

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00001       REAL             FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
00002      $                 WORK )
00003 *
00004 *  -- LAPACK auxiliary routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          DIAG, NORM, UPLO
00011       INTEGER            LDA, M, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( LDA, * ), WORK( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  SLANTR  returns the value of the one norm,  or the Frobenius norm, or
00021 *  the  infinity norm,  or the  element of  largest absolute value  of a
00022 *  trapezoidal or triangular matrix A.
00023 *
00024 *  Description
00025 *  ===========
00026 *
00027 *  SLANTR returns the value
00028 *
00029 *     SLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00030 *              (
00031 *              ( norm1(A),         NORM = '1', 'O' or 'o'
00032 *              (
00033 *              ( normI(A),         NORM = 'I' or 'i'
00034 *              (
00035 *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00036 *
00037 *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
00038 *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00039 *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
00040 *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00041 *
00042 *  Arguments
00043 *  =========
00044 *
00045 *  NORM    (input) CHARACTER*1
00046 *          Specifies the value to be returned in SLANTR as described
00047 *          above.
00048 *
00049 *  UPLO    (input) CHARACTER*1
00050 *          Specifies whether the matrix A is upper or lower trapezoidal.
00051 *          = 'U':  Upper trapezoidal
00052 *          = 'L':  Lower trapezoidal
00053 *          Note that A is triangular instead of trapezoidal if M = N.
00054 *
00055 *  DIAG    (input) CHARACTER*1
00056 *          Specifies whether or not the matrix A has unit diagonal.
00057 *          = 'N':  Non-unit diagonal
00058 *          = 'U':  Unit diagonal
00059 *
00060 *  M       (input) INTEGER
00061 *          The number of rows of the matrix A.  M >= 0, and if
00062 *          UPLO = 'U', M <= N.  When M = 0, SLANTR is set to zero.
00063 *
00064 *  N       (input) INTEGER
00065 *          The number of columns of the matrix A.  N >= 0, and if
00066 *          UPLO = 'L', N <= M.  When N = 0, SLANTR is set to zero.
00067 *
00068 *  A       (input) REAL array, dimension (LDA,N)
00069 *          The trapezoidal matrix A (A is triangular if M = N).
00070 *          If UPLO = 'U', the leading m by n upper trapezoidal part of
00071 *          the array A contains the upper trapezoidal matrix, and the
00072 *          strictly lower triangular part of A is not referenced.
00073 *          If UPLO = 'L', the leading m by n lower trapezoidal part of
00074 *          the array A contains the lower trapezoidal matrix, and the
00075 *          strictly upper triangular part of A is not referenced.  Note
00076 *          that when DIAG = 'U', the diagonal elements of A are not
00077 *          referenced and are assumed to be one.
00078 *
00079 *  LDA     (input) INTEGER
00080 *          The leading dimension of the array A.  LDA >= max(M,1).
00081 *
00082 *  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
00083 *          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
00084 *          referenced.
00085 *
00086 * =====================================================================
00087 *
00088 *     .. Parameters ..
00089       REAL               ONE, ZERO
00090       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00091 *     ..
00092 *     .. Local Scalars ..
00093       LOGICAL            UDIAG
00094       INTEGER            I, J
00095       REAL               SCALE, SUM, VALUE
00096 *     ..
00097 *     .. External Subroutines ..
00098       EXTERNAL           SLASSQ
00099 *     ..
00100 *     .. External Functions ..
00101       LOGICAL            LSAME
00102       EXTERNAL           LSAME
00103 *     ..
00104 *     .. Intrinsic Functions ..
00105       INTRINSIC          ABS, MAX, MIN, SQRT
00106 *     ..
00107 *     .. Executable Statements ..
00108 *
00109       IF( MIN( M, N ).EQ.0 ) THEN
00110          VALUE = ZERO
00111       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00112 *
00113 *        Find max(abs(A(i,j))).
00114 *
00115          IF( LSAME( DIAG, 'U' ) ) THEN
00116             VALUE = ONE
00117             IF( LSAME( UPLO, 'U' ) ) THEN
00118                DO 20 J = 1, N
00119                   DO 10 I = 1, MIN( M, J-1 )
00120                      VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00121    10             CONTINUE
00122    20          CONTINUE
00123             ELSE
00124                DO 40 J = 1, N
00125                   DO 30 I = J + 1, M
00126                      VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00127    30             CONTINUE
00128    40          CONTINUE
00129             END IF
00130          ELSE
00131             VALUE = ZERO
00132             IF( LSAME( UPLO, 'U' ) ) THEN
00133                DO 60 J = 1, N
00134                   DO 50 I = 1, MIN( M, J )
00135                      VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00136    50             CONTINUE
00137    60          CONTINUE
00138             ELSE
00139                DO 80 J = 1, N
00140                   DO 70 I = J, M
00141                      VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00142    70             CONTINUE
00143    80          CONTINUE
00144             END IF
00145          END IF
00146       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00147 *
00148 *        Find norm1(A).
00149 *
00150          VALUE = ZERO
00151          UDIAG = LSAME( DIAG, 'U' )
00152          IF( LSAME( UPLO, 'U' ) ) THEN
00153             DO 110 J = 1, N
00154                IF( ( UDIAG ) .AND. ( J.LE.M ) ) THEN
00155                   SUM = ONE
00156                   DO 90 I = 1, J - 1
00157                      SUM = SUM + ABS( A( I, J ) )
00158    90             CONTINUE
00159                ELSE
00160                   SUM = ZERO
00161                   DO 100 I = 1, MIN( M, J )
00162                      SUM = SUM + ABS( A( I, J ) )
00163   100             CONTINUE
00164                END IF
00165                VALUE = MAX( VALUE, SUM )
00166   110       CONTINUE
00167          ELSE
00168             DO 140 J = 1, N
00169                IF( UDIAG ) THEN
00170                   SUM = ONE
00171                   DO 120 I = J + 1, M
00172                      SUM = SUM + ABS( A( I, J ) )
00173   120             CONTINUE
00174                ELSE
00175                   SUM = ZERO
00176                   DO 130 I = J, M
00177                      SUM = SUM + ABS( A( I, J ) )
00178   130             CONTINUE
00179                END IF
00180                VALUE = MAX( VALUE, SUM )
00181   140       CONTINUE
00182          END IF
00183       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00184 *
00185 *        Find normI(A).
00186 *
00187          IF( LSAME( UPLO, 'U' ) ) THEN
00188             IF( LSAME( DIAG, 'U' ) ) THEN
00189                DO 150 I = 1, M
00190                   WORK( I ) = ONE
00191   150          CONTINUE
00192                DO 170 J = 1, N
00193                   DO 160 I = 1, MIN( M, J-1 )
00194                      WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00195   160             CONTINUE
00196   170          CONTINUE
00197             ELSE
00198                DO 180 I = 1, M
00199                   WORK( I ) = ZERO
00200   180          CONTINUE
00201                DO 200 J = 1, N
00202                   DO 190 I = 1, MIN( M, J )
00203                      WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00204   190             CONTINUE
00205   200          CONTINUE
00206             END IF
00207          ELSE
00208             IF( LSAME( DIAG, 'U' ) ) THEN
00209                DO 210 I = 1, N
00210                   WORK( I ) = ONE
00211   210          CONTINUE
00212                DO 220 I = N + 1, M
00213                   WORK( I ) = ZERO
00214   220          CONTINUE
00215                DO 240 J = 1, N
00216                   DO 230 I = J + 1, M
00217                      WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00218   230             CONTINUE
00219   240          CONTINUE
00220             ELSE
00221                DO 250 I = 1, M
00222                   WORK( I ) = ZERO
00223   250          CONTINUE
00224                DO 270 J = 1, N
00225                   DO 260 I = J, M
00226                      WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00227   260             CONTINUE
00228   270          CONTINUE
00229             END IF
00230          END IF
00231          VALUE = ZERO
00232          DO 280 I = 1, M
00233             VALUE = MAX( VALUE, WORK( I ) )
00234   280    CONTINUE
00235       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00236 *
00237 *        Find normF(A).
00238 *
00239          IF( LSAME( UPLO, 'U' ) ) THEN
00240             IF( LSAME( DIAG, 'U' ) ) THEN
00241                SCALE = ONE
00242                SUM = MIN( M, N )
00243                DO 290 J = 2, N
00244                   CALL SLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
00245   290          CONTINUE
00246             ELSE
00247                SCALE = ZERO
00248                SUM = ONE
00249                DO 300 J = 1, N
00250                   CALL SLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
00251   300          CONTINUE
00252             END IF
00253          ELSE
00254             IF( LSAME( DIAG, 'U' ) ) THEN
00255                SCALE = ONE
00256                SUM = MIN( M, N )
00257                DO 310 J = 1, N
00258                   CALL SLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
00259      $                         SUM )
00260   310          CONTINUE
00261             ELSE
00262                SCALE = ZERO
00263                SUM = ONE
00264                DO 320 J = 1, N
00265                   CALL SLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
00266   320          CONTINUE
00267             END IF
00268          END IF
00269          VALUE = SCALE*SQRT( SUM )
00270       END IF
00271 *
00272       SLANTR = VALUE
00273       RETURN
00274 *
00275 *     End of SLANTR
00276 *
00277       END