numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/dlangt.f | 6106B | -rw-r--r-- |
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*> \brief \b DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLANGT + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangt.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangt.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangt.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), DL( * ), DU( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLANGT 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 tridiagonal matrix A. *> \endverbatim *> *> \return DLANGT *> \verbatim *> *> DLANGT = ( 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 DLANGT as described *> above. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, DLANGT is *> set to zero. *> \endverbatim *> *> \param[in] DL *> \verbatim *> DL is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) sub-diagonal elements of A. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of A. *> \endverbatim *> *> \param[in] DU *> \verbatim *> DU is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) super-diagonal elements of A. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup langt * * ===================================================================== DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU ) * * -- 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 NORM INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), DL( * ), DU( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION ANORM, SCALE, SUM, TEMP * .. * .. 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 IF( ANORM.LT.ABS( DL( I ) ) .OR. $ DISNAN( ABS( DL( I ) ) ) ) $ ANORM = ABS(DL(I)) IF( ANORM.LT.ABS( D( I ) ) .OR. DISNAN( ABS( D( I ) ) ) ) $ ANORM = ABS(D(I)) IF( ANORM.LT.ABS( DU( I ) ) .OR. $ DISNAN (ABS( DU( I ) ) ) ) $ ANORM = ABS(DU(I)) 10 CONTINUE ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN * * Find norm1(A). * IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE ANORM = ABS( D( 1 ) )+ABS( DL( 1 ) ) TEMP = ABS( D( N ) )+ABS( DU( N-1 ) ) IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP DO 20 I = 2, N - 1 TEMP = ABS( D( I ) )+ABS( DL( I ) )+ABS( DU( I-1 ) ) IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP 20 CONTINUE END IF ELSE IF( LSAME( NORM, 'I' ) ) THEN * * Find normI(A). * IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE ANORM = ABS( D( 1 ) )+ABS( DU( 1 ) ) TEMP = ABS( D( N ) )+ABS( DL( N-1 ) ) IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP DO 30 I = 2, N - 1 TEMP = ABS( D( I ) )+ABS( DU( I ) )+ABS( DL( I-1 ) ) IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP 30 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. $ ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE CALL DLASSQ( N, D, 1, SCALE, SUM ) IF( N.GT.1 ) THEN CALL DLASSQ( N-1, DL, 1, SCALE, SUM ) CALL DLASSQ( N-1, DU, 1, SCALE, SUM ) END IF ANORM = SCALE*SQRT( SUM ) END IF * DLANGT = ANORM RETURN * * End of DLANGT * END