d0/dc4/dlantr_8f_source.html

 *> \brief \b DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
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 *> [TGZ]</a>
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 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlantr.f">
 *> [TXT]</a>
 *> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
 *                        WORK )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          DIAG, NORM, UPLO
 *       INTEGER            LDA, M, N
 *       ..
 *       .. Array Arguments ..
 *       DOUBLE PRECISION   A( LDA, * ), WORK( * )
 *       ..
 *
 *
 *> \par Purpose:
 *  =============
 *>
 *> \verbatim
 *>
 *> 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.
 *> \endverbatim
 *>
 *> \return DLANTR
 *> \verbatim
 *>
 *>    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.
 *> \endverbatim
 *
 *  Arguments:
 *  ==========
 *
 *> \param[in] NORM
 *> \verbatim
 *>          NORM is CHARACTER*1
 *>          Specifies the value to be returned in DLANTR as described
 *>          above.
 *> \endverbatim
 *>
 *> \param[in] UPLO
 *> \verbatim
 *>          UPLO is 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.
 *> \endverbatim
 *>
 *> \param[in] DIAG
 *> \verbatim
 *>          DIAG is CHARACTER*1
 *>          Specifies whether or not the matrix A has unit diagonal.
 *>          = 'N':  Non-unit diagonal
 *>          = 'U':  Unit diagonal
 *> \endverbatim
 *>
 *> \param[in] M
 *> \verbatim
 *>          M is 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.
 *> \endverbatim
 *>
 *> \param[in] N
 *> \verbatim
 *>          N is 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.
 *> \endverbatim
 *>
 *> \param[in] A
 *> \verbatim
 *>          A is 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.
 *> \endverbatim
 *>
 *> \param[in] LDA
 *> \verbatim
 *>          LDA is INTEGER
 *>          The leading dimension of the array A.  LDA >= max(M,1).
 *> \endverbatim
 *>
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
 *>          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
 *>          referenced.
 *> \endverbatim
 *
 *  Authors:
 *  ========
 *
 *> \author Univ. of Tennessee
 *> \author Univ. of California Berkeley
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
 *> \ingroup lantr
 *
 *  =====================================================================
       DOUBLE PRECISION FUNCTION dlantr( NORM, UPLO, DIAG, M, N, A, LDA,
      $                 WORK )
 *
 *  -- LAPACK auxiliary routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIAG, NORM, UPLO
       INTEGER            LDA, M, N
 *     ..
 *     .. Array Arguments ..
       DOUBLE PRECISION   A( lda, * ), WORK( * )
 *     ..
 *
 * =====================================================================
 *
 *     .. 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, DISNAN
       EXTERNAL           lsame, disnan
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          abs, 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 )
                      sum = abs( a( i, j ) )
                      IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
    10             CONTINUE
    20          CONTINUE
             ELSE
                DO 40 j = 1, n
                   DO 30 i = j + 1, m
                      sum = abs( a( i, j ) )
                      IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
    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 )
                      sum = abs( a( i, j ) )
                      IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
    50             CONTINUE
    60          CONTINUE
             ELSE
                DO 80 j = 1, n
                   DO 70 i = j, m
                      sum = abs( a( i, j ) )
                      IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
    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
                IF( VALUE .LT. sum .OR. disnan( sum ) ) 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
                IF( VALUE .LT. sum .OR. disnan( sum ) ) 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, min( m, 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
             sum = work( i )
             IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   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
dlantr
double precision function dlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: dlantr.f:141