1
       2
       3
       4
       5
       6
       7
       8
       9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      21
      22
      23
      24
      25
      26
      27
      28
      29
      30
      31
      32
      33
      34
      35
      36
      37
      38
      39
      40
      41
      42
      43
      44
      45
      46
      47
      48
      49
      50
      51
      52
      53
      54
      55
      56
      57
      58
      59
      60
      61
      62
      63
      64
      65
      66
      67
      68
      69
      70
      71
      72
      73
      74
      75
      76
      77
      78
      79
      80
      81
      82
      83
      84
      85
      86
      87
      88
      89
      90
      91
      92
      93
      94
      95
      96
      97
      98
      99
     100
     101
     102
     103
     104
     105
     106
     107
     108
     109
     110
     111
     112
     113
     114
     115
     116
     117
     118
     119
     120
     121
     122
     123
     124
     125
     126
     127
     128
     129
     130
     131
     132
     133
     134
     135
     136
     137
     138
     139
     140
     141
     142
     143
     144
     145
     146
     147
     148
     149
     150
     151
     152
     153
     154
     155
     156
     157
     158
     159
     160
     161
     162
     163
     164
     165
     166
     167
     168
     169
     170
     171
     172
     173
     174
     175
     176
     177
     178
     179
     180
     181
     182
     183
     184
     185
     186
     187
     188
     189
     190
     191
     192
     193
     194
     195
     196
     197
     198
     199
     200
     201
     202
     203
     204
     205
     206
     207
     208
     209
     210
     211
     212
     213
     214
     215
     216
     217
     218
     219
     220
     221
     222
     223
     224
     225
     226
     227
     228
     229
     230
     231
     232
     233
     234
     235
     236
     237
     238
     239
     240
     241
     242
     243
     244
     245
     246
     247
     248
     249
     250
     251
     252
     253
     254
     255
     256
     257
     258
     259
     260
     261
     262
     263
     264
     265
     266
     267
     268
     269
     270
     271
     272
     273
     274
     275
     276
     277
      REAL             FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
     $                 WORK )
*
*  -- LAPACK auxiliary routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORM, UPLO
      INTEGER            LDA, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  SLANTR  returns the value of the one norm,  or the Frobenius norm, or
*  the  infinity norm,  or the  element of  largest absolute value  of a
*  trapezoidal or triangular matrix A.
*
*  Description
*  ===========
*
*  SLANTR returns the value
*
*     SLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*              (
*              ( norm1(A),         NORM = '1', 'O' or 'o'
*              (
*              ( normI(A),         NORM = 'I' or 'i'
*              (
*              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
*
*  where  norm1  denotes the  one norm of a matrix (maximum column sum),
*  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
*  normF  denotes the  Frobenius norm of a matrix (square root of sum of
*  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
*
*  Arguments
*  =========
*
*  NORM    (input) CHARACTER*1
*          Specifies the value to be returned in SLANTR as described
*          above.
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the matrix A is upper or lower trapezoidal.
*          = 'U':  Upper trapezoidal
*          = 'L':  Lower trapezoidal
*          Note that A is triangular instead of trapezoidal if M = N.
*
*  DIAG    (input) CHARACTER*1
*          Specifies whether or not the matrix A has unit diagonal.
*          = 'N':  Non-unit diagonal
*          = 'U':  Unit diagonal
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0, and if
*          UPLO = 'U', M <= N.  When M = 0, SLANTR is set to zero.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  N >= 0, and if
*          UPLO = 'L', N <= M.  When N = 0, SLANTR is set to zero.
*
*  A       (input) REAL array, dimension (LDA,N)
*          The trapezoidal matrix A (A is triangular if M = N).
*          If UPLO = 'U', the leading m by n upper trapezoidal part of
*          the array A contains the upper trapezoidal matrix, and the
*          strictly lower triangular part of A is not referenced.
*          If UPLO = 'L', the leading m by n lower trapezoidal part of
*          the array A contains the lower trapezoidal matrix, and the
*          strictly upper triangular part of A is not referenced.  Note
*          that when DIAG = 'U', the diagonal elements of A are not
*          referenced and are assumed to be one.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(M,1).
*
*  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
*          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*          referenced.
*
* =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UDIAG
      INTEGER            I, J
      REAL               SCALESUMVALUE
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLASSQ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABSMAXMINSQRT
*     ..
*     .. Executable Statements ..
*
      IFMIN( M, N ).EQ.0 ) THEN
         VALUE = ZERO
      ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
*        Find max(abs(A(i,j))).
*
         IF( LSAME( DIAG, 'U' ) ) THEN
            VALUE = ONE
            IF( LSAME( UPLO, 'U' ) ) THEN
               DO 20 J = 1, N
                  DO 10 I = 1MIN( M, J-1 )
                     VALUE = MAXVALUEABS( A( I, J ) ) )
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40 J = 1, N
                  DO 30 I = J + 1, M
                     VALUE = MAXVALUEABS( A( I, J ) ) )
   30             CONTINUE
   40          CONTINUE
            END IF
         ELSE
            VALUE = ZERO
            IF( LSAME( UPLO, 'U' ) ) THEN
               DO 60 J = 1, N
                  DO 50 I = 1MIN( M, J )
                     VALUE = MAXVALUEABS( A( I, J ) ) )
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80 J = 1, N
                  DO 70 I = J, M
                     VALUE = MAXVALUEABS( A( I, J ) ) )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
      ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
*
*        Find norm1(A).
*
         VALUE = ZERO
         UDIAG = LSAME( DIAG, 'U' )
         IF( LSAME( UPLO, 'U' ) ) THEN
            DO 110 J = 1, N
               IF( ( UDIAG ) .AND. ( J.LE.M ) ) THEN
                  SUM = ONE
                  DO 90 I = 1, J - 1
                     SUM = SUM + ABS( A( I, J ) )
   90             CONTINUE
               ELSE
                  SUM = ZERO
                  DO 100 I = 1MIN( M, J )
                     SUM = SUM + ABS( A( I, J ) )
  100             CONTINUE
               END IF
               VALUE = MAXVALUESUM )
  110       CONTINUE
         ELSE
            DO 140 J = 1, N
               IF( UDIAG ) THEN
                  SUM = ONE
                  DO 120 I = J + 1, M
                     SUM = SUM + ABS( A( I, J ) )
  120             CONTINUE
               ELSE
                  SUM = ZERO
                  DO 130 I = J, M
                     SUM = SUM + ABS( A( I, J ) )
  130             CONTINUE
               END IF
               VALUE = MAXVALUESUM )
  140       CONTINUE
         END IF
      ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
*        Find normI(A).
*
         IF( LSAME( UPLO, 'U' ) ) THEN
            IF( LSAME( DIAG, 'U' ) ) THEN
               DO 150 I = 1, M
                  WORK( I ) = ONE
  150          CONTINUE
               DO 170 J = 1, N
                  DO 160 I = 1MIN( M, J-1 )
                     WORK( I ) = WORK( I ) + ABS( A( I, J ) )
  160             CONTINUE
  170          CONTINUE
            ELSE
               DO 180 I = 1, M
                  WORK( I ) = ZERO
  180          CONTINUE
               DO 200 J = 1, N
                  DO 190 I = 1MIN( M, J )
                     WORK( I ) = WORK( I ) + ABS( A( I, J ) )
  190             CONTINUE
  200          CONTINUE
            END IF
         ELSE
            IF( LSAME( DIAG, 'U' ) ) THEN
               DO 210 I = 1, N
                  WORK( I ) = ONE
  210          CONTINUE
               DO 220 I = N + 1, M
                  WORK( I ) = ZERO
  220          CONTINUE
               DO 240 J = 1, N
                  DO 230 I = J + 1, M
                     WORK( I ) = WORK( I ) + ABS( A( I, J ) )
  230             CONTINUE
  240          CONTINUE
            ELSE
               DO 250 I = 1, M
                  WORK( I ) = ZERO
  250          CONTINUE
               DO 270 J = 1, N
                  DO 260 I = J, M
                     WORK( I ) = WORK( I ) + ABS( A( I, J ) )
  260             CONTINUE
  270          CONTINUE
            END IF
         END IF
         VALUE = ZERO
         DO 280 I = 1, M
            VALUE = MAXVALUE, WORK( I ) )
  280    CONTINUE
      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
*        Find normF(A).
*
         IF( LSAME( UPLO, 'U' ) ) THEN
            IF( LSAME( DIAG, 'U' ) ) THEN
               SCALE = ONE
               SUM = MIN( M, N )
               DO 290 J = 2, N
                  CALL SLASSQ( MIN( M, J-1 ), A( 1, J ), 1SCALESUM )
  290          CONTINUE
            ELSE
               SCALE = ZERO
               SUM = ONE
               DO 300 J = 1, N
                  CALL SLASSQ( MIN( M, J ), A( 1, J ), 1SCALESUM )
  300          CONTINUE
            END IF
         ELSE
            IF( LSAME( DIAG, 'U' ) ) THEN
               SCALE = ONE
               SUM = MIN( M, N )
               DO 310 J = 1, N
                  CALL SLASSQ( M-J, A( MIN( M, J+1 ), J ), 1SCALE,
     $                         SUM )
  310          CONTINUE
            ELSE
               SCALE = ZERO
               SUM = ONE
               DO 320 J = 1, N
                  CALL SLASSQ( M-J+1, A( J, J ), 1SCALESUM )
  320          CONTINUE
            END IF
         END IF
         VALUE = SCALE*SQRTSUM )
      END IF
*
      SLANTR = VALUE
      RETURN
*
*     End of SLANTR
*
      END