zlantr_8f_source.html

*> \brief \b ZLANTR 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/

*

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*

*  Definition:

*  ===========

*

*       DOUBLE PRECISION FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N, A, LDA,

*                        WORK )

*

*       .. Scalar Arguments ..

*       CHARACTER          DIAG, NORM, UPLO

*       INTEGER            LDA, M, N

*       ..

*       .. Array Arguments ..

*       DOUBLE PRECISION   WORK( * )

*       COMPLEX*16         A( LDA, * )

*       ..

*

*

*> \par Purpose:

*  =============

*>

*> \verbatim

*>

*> ZLANTR  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 ZLANTR

*> \verbatim

*>

*>    ZLANTR = ( 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 ZLANTR 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, ZLANTR 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, ZLANTR is set to zero.

*> \endverbatim

*>

*> \param[in] A

*> \verbatim

*>          A is COMPLEX*16 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 complex16OTHERauxiliary

*

*  =====================================================================


      DOUBLE PRECISION FUNCTION zlantr( 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   work( * )

      COMPLEX*16         a( lda, * )

*     ..

*

* =====================================================================

*

*     .. 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 Functions ..

      LOGICAL            lsame, disnan

      EXTERNAL           lsame, disnan

*     ..

*     .. External Subroutines ..

      EXTERNAL           zlassq

*     ..

*     .. 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 )

.LT..OR.            IF( VALUE  SUM  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 ZLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )

  290          CONTINUE

            ELSE

               SCALE = ZERO

               SUM = ONE

               DO 300 J = 1, N

                  CALL ZLASSQ( 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 ZLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,

     $                         SUM )

  310          CONTINUE

            ELSE

               SCALE = ZERO

               SUM = ONE

               DO 320 J = 1, N

                  CALL ZLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )

  320          CONTINUE

            END IF

         END IF

         VALUE = SCALE*SQRT( SUM )

      END IF

*

      ZLANTR = VALUE

      RETURN

*

*     End of ZLANTR

*


      END

norm
norm(diag(diag(diag(inv(mat))) -id.SOL), 2) % destroy mumps instance id.JOB

zlassq
subroutine zlassq(n, x, incx, scl, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition zlassq.f90:137

disnan
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59

lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:53

zlantr
double precision function zlantr(norm, uplo, diag, m, n, a, lda, work)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlantr.f:142

min
#define min(a, b)
Definition macros.h:20