d6/dc8/clantp_8f_source.html

 *> \brief \b CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
 *> Download CLANTP + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clantp.f">
 *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clantp.f">
 *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clantp.f">
 *> [TXT]</a>
 *> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       REAL             FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          DIAG, NORM, UPLO
 *       INTEGER            N
 *       ..
 *       .. Array Arguments ..
 *       REAL               WORK( * )
 *       COMPLEX            AP( * )
 *       ..
 *
 *
 *> \par Purpose:
 *  =============
 *>
 *> \verbatim
 *>
 *> CLANTP  returns the value of the one norm,  or the Frobenius norm, or
 *> the  infinity norm,  or the  element of  largest absolute value  of a
 *> triangular matrix A, supplied in packed form.
 *> \endverbatim
 *>
 *> \return CLANTP
 *> \verbatim
 *>
 *>    CLANTP = ( 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 CLANTP as described
 *>          above.
 *> \endverbatim
 *>
 *> \param[in] UPLO
 *> \verbatim
 *>          UPLO is CHARACTER*1
 *>          Specifies whether the matrix A is upper or lower triangular.
 *>          = 'U':  Upper triangular
 *>          = 'L':  Lower triangular
 *> \endverbatim
 *>
 *> \param[in] DIAG
 *> \verbatim
 *>          DIAG is CHARACTER*1
 *>          Specifies whether or not the matrix A is unit triangular.
 *>          = 'N':  Non-unit triangular
 *>          = 'U':  Unit triangular
 *> \endverbatim
 *>
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
 *>          The order of the matrix A.  N >= 0.  When N = 0, CLANTP is
 *>          set to zero.
 *> \endverbatim
 *>
 *> \param[in] AP
 *> \verbatim
 *>          AP is COMPLEX array, dimension (N*(N+1)/2)
 *>          The upper or lower triangular matrix A, packed columnwise in
 *>          a linear array.  The j-th column of A is stored in the array
 *>          AP as follows:
 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
 *>          Note that when DIAG = 'U', the elements of the array AP
 *>          corresponding to the diagonal elements of the matrix A are
 *>          not referenced, but are assumed to be one.
 *> \endverbatim
 *>
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
 *>          where LWORK >= N 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.
 *
 *> \date December 2016
 *
 *> \ingroup complexOTHERauxiliary
 *
 *  =====================================================================
       REAL             FUNCTION clantp( NORM, UPLO, DIAG, N, AP, WORK )
 *
 *  -- LAPACK auxiliary routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIAG, NORM, UPLO
       INTEGER            N
 *     ..
 *     .. Array Arguments ..
       REAL               WORK( * )
       COMPLEX            AP( * )
 *     ..
 *
 * =====================================================================
 *
 *     .. Parameters ..
       REAL               ONE, ZERO
       parameter( one = 1.0e+0, zero = 0.0e+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            UDIAG
       INTEGER            I, J, K
       REAL               SCALE, SUM, VALUE
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, SISNAN
       EXTERNAL           lsame, sisnan
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           classq
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          abs, sqrt
 *     ..
 *     .. Executable Statements ..
 *
       IF( n.EQ.0 ) THEN
          VALUE = zero
       ELSE IF( lsame( norm, 'M' ) ) THEN
 *
 *        Find max(abs(A(i,j))).
 *
          k = 1
          IF( lsame( diag, 'U' ) ) THEN
             VALUE = one
             IF( lsame( uplo, 'U' ) ) THEN
                DO 20 j = 1, n
                   DO 10 i = k, k + j - 2
                      sum = abs( ap( i ) )
                      IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
    10             CONTINUE
                   k = k + j
    20          CONTINUE
             ELSE
                DO 40 j = 1, n
                   DO 30 i = k + 1, k + n - j
                      sum = abs( ap( i ) )
                      IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
    30             CONTINUE
                   k = k + n - j + 1
    40          CONTINUE
             END IF
          ELSE
             VALUE = zero
             IF( lsame( uplo, 'U' ) ) THEN
                DO 60 j = 1, n
                   DO 50 i = k, k + j - 1
                      sum = abs( ap( i ) )
                      IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
    50             CONTINUE
                   k = k + j
    60          CONTINUE
             ELSE
                DO 80 j = 1, n
                   DO 70 i = k, k + n - j
                      sum = abs( ap( i ) )
                      IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
    70             CONTINUE
                   k = k + n - j + 1
    80          CONTINUE
             END IF
          END IF
       ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
 *
 *        Find norm1(A).
 *
          VALUE = zero
          k = 1
          udiag = lsame( diag, 'U' )
          IF( lsame( uplo, 'U' ) ) THEN
             DO 110 j = 1, n
                IF( udiag ) THEN
                   sum = one
                   DO 90 i = k, k + j - 2
                      sum = sum + abs( ap( i ) )
    90             CONTINUE
                ELSE
                   sum = zero
                   DO 100 i = k, k + j - 1
                      sum = sum + abs( ap( i ) )
   100             CONTINUE
                END IF
                k = k + j
                IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
   110       CONTINUE
          ELSE
             DO 140 j = 1, n
                IF( udiag ) THEN
                   sum = one
                   DO 120 i = k + 1, k + n - j
                      sum = sum + abs( ap( i ) )
   120             CONTINUE
                ELSE
                   sum = zero
                   DO 130 i = k, k + n - j
                      sum = sum + abs( ap( i ) )
   130             CONTINUE
                END IF
                k = k + n - j + 1
                IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
   140       CONTINUE
          END IF
       ELSE IF( lsame( norm, 'I' ) ) THEN
 *
 *        Find normI(A).
 *
          k = 1
          IF( lsame( uplo, 'U' ) ) THEN
             IF( lsame( diag, 'U' ) ) THEN
                DO 150 i = 1, n
                   work( i ) = one
   150          CONTINUE
                DO 170 j = 1, n
                   DO 160 i = 1, j - 1
                      work( i ) = work( i ) + abs( ap( k ) )
                      k = k + 1
   160             CONTINUE
                   k = k + 1
   170          CONTINUE
             ELSE
                DO 180 i = 1, n
                   work( i ) = zero
   180          CONTINUE
                DO 200 j = 1, n
                   DO 190 i = 1, j
                      work( i ) = work( i ) + abs( ap( k ) )
                      k = k + 1
   190             CONTINUE
   200          CONTINUE
             END IF
          ELSE
             IF( lsame( diag, 'U' ) ) THEN
                DO 210 i = 1, n
                   work( i ) = one
   210          CONTINUE
                DO 230 j = 1, n
                   k = k + 1
                   DO 220 i = j + 1, n
                      work( i ) = work( i ) + abs( ap( k ) )
                      k = k + 1
   220             CONTINUE
   230          CONTINUE
             ELSE
                DO 240 i = 1, n
                   work( i ) = zero
   240          CONTINUE
                DO 260 j = 1, n
                   DO 250 i = j, n
                      work( i ) = work( i ) + abs( ap( k ) )
                      k = k + 1
   250             CONTINUE
   260          CONTINUE
             END IF
          END IF
          VALUE = zero
          DO 270 i = 1, n
             sum = work( i )
             IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
   270    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 = n
                k = 2
                DO 280 j = 2, n
                   CALL classq( j-1, ap( k ), 1, scale, sum )
                   k = k + j
   280          CONTINUE
             ELSE
                scale = zero
                sum = one
                k = 1
                DO 290 j = 1, n
                   CALL classq( j, ap( k ), 1, scale, sum )
                   k = k + j
   290          CONTINUE
             END IF
          ELSE
             IF( lsame( diag, 'U' ) ) THEN
                scale = one
                sum = n
                k = 2
                DO 300 j = 1, n - 1
                   CALL classq( n-j, ap( k ), 1, scale, sum )
                   k = k + n - j + 1
   300          CONTINUE
             ELSE
                scale = zero
                sum = one
                k = 1
                DO 310 j = 1, n
                   CALL classq( n-j+1, ap( k ), 1, scale, sum )
                   k = k + n - j + 1
   310          CONTINUE
             END IF
          END IF
          VALUE = scale*sqrt( sum )
       END IF
 *
       clantp = VALUE
       RETURN
 *
 *     End of CLANTP
 *
       END
classq
subroutine classq(N, X, INCX, SCALE, SUMSQ)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f:108

clantp
real function clantp(NORM, UPLO, DIAG, N, AP, WORK)
CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
Definition: clantp.f:127