226 lines
6.3 KiB
Fortran
226 lines
6.3 KiB
Fortran
*> \brief \b DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band 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 DLANGB + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangb.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/dlangb.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/dlangb.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 DLANGB( NORM, N, KL, KU, AB, LDAB,
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* WORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER NORM
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* INTEGER KL, KU, LDAB, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
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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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*> DLANGB 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 an
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*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
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*> \endverbatim
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*>
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*> \return DLANGB
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*> \verbatim
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*>
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*> DLANGB = ( 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 DLANGB 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, DLANGB is
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*> set to zero.
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*> \endverbatim
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*>
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*> \param[in] KL
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*> \verbatim
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*> KL is INTEGER
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*> The number of sub-diagonals of the matrix A. KL >= 0.
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*> \endverbatim
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*>
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*> \param[in] KU
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*> \verbatim
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*> KU is INTEGER
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*> The number of super-diagonals of the matrix A. KU >= 0.
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*> \endverbatim
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*>
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*> \param[in] AB
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*> \verbatim
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
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*> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
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*> column of A is stored in the j-th column of the array AB as
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*> follows:
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*> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KL+KU+1.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
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*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
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*> referenced.
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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 December 2016
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*
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*> \ingroup doubleGBauxiliary
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*
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* =====================================================================
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DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
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$ WORK )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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CHARACTER NORM
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INTEGER KL, KU, LDAB, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AB( LDAB, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, K, L
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DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
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* ..
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* .. External Subroutines ..
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EXTERNAL DLASSQ
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* ..
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* .. External Functions ..
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LOGICAL LSAME, DISNAN
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EXTERNAL LSAME, DISNAN
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, SQRT
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* ..
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* .. Executable Statements ..
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*
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IF( N.EQ.0 ) THEN
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VALUE = ZERO
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ELSE IF( LSAME( NORM, 'M' ) ) THEN
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*
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* Find max(abs(A(i,j))).
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*
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VALUE = ZERO
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DO 20 J = 1, N
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DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
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TEMP = ABS( AB( I, J ) )
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IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
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10 CONTINUE
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20 CONTINUE
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ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
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*
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* Find norm1(A).
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*
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VALUE = ZERO
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DO 40 J = 1, N
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SUM = ZERO
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DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
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SUM = SUM + ABS( AB( I, J ) )
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30 CONTINUE
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IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
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40 CONTINUE
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ELSE IF( LSAME( NORM, 'I' ) ) THEN
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*
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* Find normI(A).
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*
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DO 50 I = 1, N
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WORK( I ) = ZERO
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50 CONTINUE
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DO 70 J = 1, N
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K = KU + 1 - J
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DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
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WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
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60 CONTINUE
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70 CONTINUE
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VALUE = ZERO
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DO 80 I = 1, N
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TEMP = WORK( I )
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IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
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80 CONTINUE
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
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*
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* Find normF(A).
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*
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SCALE = ZERO
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SUM = ONE
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DO 90 J = 1, N
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L = MAX( 1, J-KU )
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K = KU + 1 - J + L
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CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
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90 CONTINUE
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VALUE = SCALE*SQRT( SUM )
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END IF
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*
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DLANGB = VALUE
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RETURN
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*
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* End of DLANGB
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*
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END
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