julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
156 lines
4.5 KiB
FortranFixed
156 lines
4.5 KiB
FortranFixed
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 3.2) --
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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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* November 2006
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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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* Purpose
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* =======
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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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*
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* Description
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* ===========
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*
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* DLANGB returns the value
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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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*
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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 DLANGB 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, DLANGB is
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* set to zero.
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*
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* KL (input) INTEGER
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* The number of sub-diagonals of the matrix A. KL >= 0.
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*
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* KU (input) INTEGER
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* The number of super-diagonals of the matrix A. KU >= 0.
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*
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* AB (input) 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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*
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* LDAB (input) INTEGER
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* The leading dimension of the array AB. LDAB >= KL+KU+1.
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*
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* WORK (workspace) 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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*
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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
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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
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EXTERNAL LSAME
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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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VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
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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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VALUE = MAX( 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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VALUE = MAX( VALUE, WORK( I ) )
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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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