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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / internal / testdata / dsterftest / dlanst.f

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+*> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*> \htmlonly
+*> Download DLANST + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanst.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanst.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanst.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          NORM
+*       INTEGER            N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * ), E( * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DLANST  returns the value of the one norm,  or the Frobenius norm, or
+*> the  infinity norm,  or the  element of  largest absolute value  of a
+*> real symmetric tridiagonal matrix A.
+*> \endverbatim
+*>
+*> \return DLANST
+*> \verbatim
+*>
+*>    DLANST = ( 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 DLANST as described
+*>          above.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.  When N = 0, DLANST is
+*>          set to zero.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          The diagonal elements of A.
+*> \endverbatim
+*>
+*> \param[in] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (N-1)
+*>          The (n-1) sub-diagonal or super-diagonal elements of A.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERauxiliary
+*
+*  =====================================================================
+      DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
+*
+*  -- LAPACK auxiliary routine (version 3.4.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     September 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          NORM
+      INTEGER            N
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   D( * ), E( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE, ZERO
+      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I
+      DOUBLE PRECISION   ANORM, SCALE, SUM
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME, DISNAN
+      EXTERNAL           LSAME, DISNAN
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           DLASSQ
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+      IF( N.LE.0 ) THEN
+         ANORM = ZERO
+      ELSE IF( LSAME( NORM, 'M' ) ) THEN
+*
+*        Find max(abs(A(i,j))).
+*
+         ANORM = ABS( D( N ) )
+         DO 10 I = 1, N - 1
+            SUM = ABS( D( I ) )
+            IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+            SUM = ABS( E( I ) )
+            IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+   10    CONTINUE
+      ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
+     $         LSAME( NORM, 'I' ) ) THEN
+*
+*        Find norm1(A).
+*
+         IF( N.EQ.1 ) THEN
+            ANORM = ABS( D( 1 ) )
+         ELSE
+            ANORM = ABS( D( 1 ) )+ABS( E( 1 ) )
+            SUM = ABS( E( N-1 ) )+ABS( D( N ) )
+            IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+            DO 20 I = 2, N - 1
+               SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) )
+               IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
+   20       CONTINUE
+         END IF
+      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
+*
+*        Find normF(A).
+*
+         SCALE = ZERO
+         SUM = ONE
+         IF( N.GT.1 ) THEN
+            CALL DLASSQ( N-1, E, 1, SCALE, SUM )
+            SUM = 2*SUM
+         END IF
+         CALL DLASSQ( N, D, 1, SCALE, SUM )
+         ANORM = SCALE*SQRT( SUM )
+      END IF
+*
+      DLANST = ANORM
+      RETURN
+*
+*     End of DLANST
+*
+      END