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version 1.11, 2012/12/14 12:30:23
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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. |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DLANST + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanst.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanst.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanst.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER NORM |
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* INTEGER N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION D( * ), E( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DLANST returns the value of the one norm, or the Frobenius norm, or |
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*> the infinity norm, or the element of largest absolute value of a |
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*> real symmetric tridiagonal matrix A. |
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*> \endverbatim |
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*> |
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*> \return DLANST |
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*> \verbatim |
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*> |
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*> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
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*> ( |
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*> ( norm1(A), NORM = '1', 'O' or 'o' |
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*> ( |
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*> ( normI(A), NORM = 'I' or 'i' |
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*> ( |
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*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
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*> |
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*> where norm1 denotes the one norm of a matrix (maximum column sum), |
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*> normI denotes the infinity norm of a matrix (maximum row sum) and |
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*> normF denotes the Frobenius norm of a matrix (square root of sum of |
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*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] NORM |
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*> \verbatim |
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*> NORM is CHARACTER*1 |
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*> Specifies the value to be returned in DLANST as described |
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*> above. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. When N = 0, DLANST is |
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*> set to zero. |
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*> \endverbatim |
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*> |
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*> \param[in] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> The diagonal elements of A. |
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*> \endverbatim |
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*> |
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*> \param[in] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> The (n-1) sub-diagonal or super-diagonal elements of A. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date September 2012 |
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* |
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*> \ingroup auxOTHERauxiliary |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) |
DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM |
CHARACTER NORM |
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DOUBLE PRECISION D( * ), E( * ) |
DOUBLE PRECISION D( * ), E( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLANST returns the value of the one norm, or the Frobenius norm, or |
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* the infinity norm, or the element of largest absolute value of a |
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* real symmetric tridiagonal matrix A. |
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* |
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* Description |
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* =========== |
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* |
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* DLANST returns the value |
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* |
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* DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' |
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* ( |
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* ( norm1(A), NORM = '1', 'O' or 'o' |
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* ( |
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* ( normI(A), NORM = 'I' or 'i' |
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* ( |
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* ( normF(A), NORM = 'F', 'f', 'E' or 'e' |
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* |
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* where norm1 denotes the one norm of a matrix (maximum column sum), |
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* normI denotes the infinity norm of a matrix (maximum row sum) and |
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* normF denotes the Frobenius norm of a matrix (square root of sum of |
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* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. |
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* |
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* Arguments |
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* ========= |
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* |
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* NORM (input) CHARACTER*1 |
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* Specifies the value to be returned in DLANST as described |
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* above. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. When N = 0, DLANST is |
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* set to zero. |
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* |
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* D (input) DOUBLE PRECISION array, dimension (N) |
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* The diagonal elements of A. |
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* |
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* E (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) sub-diagonal or super-diagonal elements of A. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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DOUBLE PRECISION ANORM, SCALE, SUM |
DOUBLE PRECISION ANORM, SCALE, SUM |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME, DISNAN |
EXTERNAL LSAME |
EXTERNAL LSAME, DISNAN |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DLASSQ |
EXTERNAL DLASSQ |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, MAX, SQRT |
INTRINSIC ABS, SQRT |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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* |
* |
ANORM = ABS( D( N ) ) |
ANORM = ABS( D( N ) ) |
DO 10 I = 1, N - 1 |
DO 10 I = 1, N - 1 |
ANORM = MAX( ANORM, ABS( D( I ) ) ) |
SUM = ABS( D( I ) ) |
ANORM = MAX( ANORM, ABS( E( I ) ) ) |
IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM |
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SUM = ABS( E( I ) ) |
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IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM |
10 CONTINUE |
10 CONTINUE |
ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. |
ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. |
$ LSAME( NORM, 'I' ) ) THEN |
$ LSAME( NORM, 'I' ) ) THEN |
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IF( N.EQ.1 ) THEN |
IF( N.EQ.1 ) THEN |
ANORM = ABS( D( 1 ) ) |
ANORM = ABS( D( 1 ) ) |
ELSE |
ELSE |
ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), |
ANORM = ABS( D( 1 ) )+ABS( E( 1 ) ) |
$ ABS( E( N-1 ) )+ABS( D( N ) ) ) |
SUM = ABS( E( N-1 ) )+ABS( D( N ) ) |
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IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM |
DO 20 I = 2, N - 1 |
DO 20 I = 2, N - 1 |
ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+ |
SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) ) |
$ ABS( E( I-1 ) ) ) |
IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM |
20 CONTINUE |
20 CONTINUE |
END IF |
END IF |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN |