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lapack/SRC/dlangb.f
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*> \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.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLANGB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
* WORK )
*
* .. Scalar Arguments ..
* CHARACTER NORM
* INTEGER KL, KU, LDAB, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLANGB returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of an
*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
*> \endverbatim
*>
*> \return DLANGB
*> \verbatim
*>
*> DLANGB = ( 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 DLANGB as described
*> above.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0. When N = 0, DLANGB is
*> set to zero.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> The number of sub-diagonals of the matrix A. KL >= 0.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> The number of super-diagonals of the matrix A. KU >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
*> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
*> column of A is stored in the j-th column of the array AB as
*> follows:
*> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KL+KU+1.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
*> where LWORK >= N 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 doubleGBauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
$ 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..--
*
IMPLICIT NONE
* .. Scalar Arguments ..
CHARACTER NORM
INTEGER KL, KU, LDAB, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J, K, L
DOUBLE PRECISION SUM, VALUE, TEMP
* ..
* .. Local Arrays ..
DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
LOGICAL LSAME, DISNAN
EXTERNAL LSAME, DISNAN
* ..
* .. External Subroutines ..
EXTERNAL DLASSQ, DCOMBSSQ
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
IF( N.EQ.0 ) THEN
VALUE = ZERO
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
* Find max(abs(A(i,j))).
*
VALUE = ZERO
DO 20 J = 1, N
DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
TEMP = ABS( AB( I, J ) )
IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
10 CONTINUE
20 CONTINUE
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
*
* Find norm1(A).
*
VALUE = ZERO
DO 40 J = 1, N
SUM = ZERO
DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
SUM = SUM + ABS( AB( I, J ) )
30 CONTINUE
IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
40 CONTINUE
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
* Find normI(A).
*
DO 50 I = 1, N
WORK( I ) = ZERO
50 CONTINUE
DO 70 J = 1, N
K = KU + 1 - J
DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
60 CONTINUE
70 CONTINUE
VALUE = ZERO
DO 80 I = 1, N
TEMP = WORK( I )
IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
80 CONTINUE
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
* Find normF(A).
* SSQ(1) is scale
* SSQ(2) is sum-of-squares
* For better accuracy, sum each column separately.
*
SSQ( 1 ) = ZERO
SSQ( 2 ) = ONE
DO 90 J = 1, N
L = MAX( 1, J-KU )
K = KU + 1 - J + L
COLSSQ( 1 ) = ZERO
COLSSQ( 2 ) = ONE
CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1,
$ COLSSQ( 1 ), COLSSQ( 2 ) )
CALL DCOMBSSQ( SSQ, COLSSQ )
90 CONTINUE
VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANGB = VALUE
RETURN
*
* End of DLANGB
*
END
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