dlantr.f

          DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
         $                 WORK )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, NORM, UPLO
          INTEGER            LDA, M, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DLANTR  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
    *  ===========
    *
    *  DLANTR returns the value
    *
    *     DLANTR = ( 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 DLANTR 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, DLANTR 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, DLANTR is set to zero.
    *
    *  A       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
    *          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
    *          referenced.
    *
    * =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UDIAG
          INTEGER            I, J
          DOUBLE PRECISION   SCALE, SUM, VALUE
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLASSQ
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, MAX, MIN, SQRT
    *     ..
    *     .. Executable Statements ..
    *
          IF( MIN( 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 = 1, MIN( M, J-1 )
                         VALUE = MAX( VALUE, ABS( A( I, J ) ) )
       10             CONTINUE
       20          CONTINUE
                ELSE
                   DO 40 J = 1, N
                      DO 30 I = J + 1, M
                         VALUE = MAX( VALUE, ABS( 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 = 1, MIN( M, J )
                         VALUE = MAX( VALUE, ABS( A( I, J ) ) )
       50             CONTINUE
       60          CONTINUE
                ELSE
                   DO 80 J = 1, N
                      DO 70 I = J, M
                         VALUE = MAX( VALUE, ABS( 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 = 1, MIN( M, J )
                         SUM = SUM + ABS( A( I, J ) )
      100             CONTINUE
                   END IF
                   VALUE = MAX( VALUE, SUM )
      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 = MAX( VALUE, SUM )
      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 = 1, MIN( 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 = 1, MIN( 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 = MAX( VALUE, 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 DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
      290          CONTINUE
                ELSE
                   SCALE = ZERO
                   SUM = ONE
                   DO 300 J = 1, N
                      CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
      300          CONTINUE
                END IF
             ELSE
                IF( LSAME( DIAG, 'U' ) ) THEN
                   SCALE = ONE
                   SUM = MIN( M, N )
                   DO 310 J = 1, N
                      CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
         $                         SUM )
      310          CONTINUE
                ELSE
                   SCALE = ZERO
                   SUM = ONE
                   DO 320 J = 1, N
                      CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
      320          CONTINUE
                END IF
             END IF
             VALUE = SCALE*SQRT( SUM )
          END IF
    *
          DLANTR = VALUE
          RETURN
    *
    *     End of DLANTR
    *
          END