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    1:       DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
    2: *
    3: *  -- LAPACK auxiliary routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          NORM, UPLO
   10:       INTEGER            N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   AP( * ), WORK( * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DLANSP  returns the value of the one norm,  or the Frobenius norm, or
   20: *  the  infinity norm,  or the  element of  largest absolute value  of a
   21: *  real symmetric matrix A,  supplied in packed form.
   22: *
   23: *  Description
   24: *  ===========
   25: *
   26: *  DLANSP returns the value
   27: *
   28: *     DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   29: *              (
   30: *              ( norm1(A),         NORM = '1', 'O' or 'o'
   31: *              (
   32: *              ( normI(A),         NORM = 'I' or 'i'
   33: *              (
   34: *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   35: *
   36: *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
   37: *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   38: *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
   39: *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   40: *
   41: *  Arguments
   42: *  =========
   43: *
   44: *  NORM    (input) CHARACTER*1
   45: *          Specifies the value to be returned in DLANSP as described
   46: *          above.
   47: *
   48: *  UPLO    (input) CHARACTER*1
   49: *          Specifies whether the upper or lower triangular part of the
   50: *          symmetric matrix A is supplied.
   51: *          = 'U':  Upper triangular part of A is supplied
   52: *          = 'L':  Lower triangular part of A is supplied
   53: *
   54: *  N       (input) INTEGER
   55: *          The order of the matrix A.  N >= 0.  When N = 0, DLANSP is
   56: *          set to zero.
   57: *
   58: *  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
   59: *          The upper or lower triangle of the symmetric matrix A, packed
   60: *          columnwise in a linear array.  The j-th column of A is stored
   61: *          in the array AP as follows:
   62: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   63: *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   64: *
   65: *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
   66: *          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
   67: *          WORK is not referenced.
   68: *
   69: * =====================================================================
   70: *
   71: *     .. Parameters ..
   72:       DOUBLE PRECISION   ONE, ZERO
   73:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   74: *     ..
   75: *     .. Local Scalars ..
   76:       INTEGER            I, J, K
   77:       DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
   78: *     ..
   79: *     .. External Subroutines ..
   80:       EXTERNAL           DLASSQ
   81: *     ..
   82: *     .. External Functions ..
   83:       LOGICAL            LSAME
   84:       EXTERNAL           LSAME
   85: *     ..
   86: *     .. Intrinsic Functions ..
   87:       INTRINSIC          ABS, MAX, SQRT
   88: *     ..
   89: *     .. Executable Statements ..
   90: *
   91:       IF( N.EQ.0 ) THEN
   92:          VALUE = ZERO
   93:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
   94: *
   95: *        Find max(abs(A(i,j))).
   96: *
   97:          VALUE = ZERO
   98:          IF( LSAME( UPLO, 'U' ) ) THEN
   99:             K = 1
  100:             DO 20 J = 1, N
  101:                DO 10 I = K, K + J - 1
  102:                   VALUE = MAX( VALUE, ABS( AP( I ) ) )
  103:    10          CONTINUE
  104:                K = K + J
  105:    20       CONTINUE
  106:          ELSE
  107:             K = 1
  108:             DO 40 J = 1, N
  109:                DO 30 I = K, K + N - J
  110:                   VALUE = MAX( VALUE, ABS( AP( I ) ) )
  111:    30          CONTINUE
  112:                K = K + N - J + 1
  113:    40       CONTINUE
  114:          END IF
  115:       ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
  116:      $         ( NORM.EQ.'1' ) ) THEN
  117: *
  118: *        Find normI(A) ( = norm1(A), since A is symmetric).
  119: *
  120:          VALUE = ZERO
  121:          K = 1
  122:          IF( LSAME( UPLO, 'U' ) ) THEN
  123:             DO 60 J = 1, N
  124:                SUM = ZERO
  125:                DO 50 I = 1, J - 1
  126:                   ABSA = ABS( AP( K ) )
  127:                   SUM = SUM + ABSA
  128:                   WORK( I ) = WORK( I ) + ABSA
  129:                   K = K + 1
  130:    50          CONTINUE
  131:                WORK( J ) = SUM + ABS( AP( K ) )
  132:                K = K + 1
  133:    60       CONTINUE
  134:             DO 70 I = 1, N
  135:                VALUE = MAX( VALUE, WORK( I ) )
  136:    70       CONTINUE
  137:          ELSE
  138:             DO 80 I = 1, N
  139:                WORK( I ) = ZERO
  140:    80       CONTINUE
  141:             DO 100 J = 1, N
  142:                SUM = WORK( J ) + ABS( AP( K ) )
  143:                K = K + 1
  144:                DO 90 I = J + 1, N
  145:                   ABSA = ABS( AP( K ) )
  146:                   SUM = SUM + ABSA
  147:                   WORK( I ) = WORK( I ) + ABSA
  148:                   K = K + 1
  149:    90          CONTINUE
  150:                VALUE = MAX( VALUE, SUM )
  151:   100       CONTINUE
  152:          END IF
  153:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  154: *
  155: *        Find normF(A).
  156: *
  157:          SCALE = ZERO
  158:          SUM = ONE
  159:          K = 2
  160:          IF( LSAME( UPLO, 'U' ) ) THEN
  161:             DO 110 J = 2, N
  162:                CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
  163:                K = K + J
  164:   110       CONTINUE
  165:          ELSE
  166:             DO 120 J = 1, N - 1
  167:                CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
  168:                K = K + N - J + 1
  169:   120       CONTINUE
  170:          END IF
  171:          SUM = 2*SUM
  172:          K = 1
  173:          DO 130 I = 1, N
  174:             IF( AP( K ).NE.ZERO ) THEN
  175:                ABSA = ABS( AP( K ) )
  176:                IF( SCALE.LT.ABSA ) THEN
  177:                   SUM = ONE + SUM*( SCALE / ABSA )**2
  178:                   SCALE = ABSA
  179:                ELSE
  180:                   SUM = SUM + ( ABSA / SCALE )**2
  181:                END IF
  182:             END IF
  183:             IF( LSAME( UPLO, 'U' ) ) THEN
  184:                K = K + I + 1
  185:             ELSE
  186:                K = K + N - I + 1
  187:             END IF
  188:   130    CONTINUE
  189:          VALUE = SCALE*SQRT( SUM )
  190:       END IF
  191: *
  192:       DLANSP = VALUE
  193:       RETURN
  194: *
  195: *     End of DLANSP
  196: *
  197:       END