DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB, $ WORK ) * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER NORM INTEGER KL, KU, LDAB, N * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), WORK( * ) * .. * * Purpose * ======= * * 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. * * Description * =========== * * DLANGB returns the value * * 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. * * Arguments * ========= * * NORM (input) CHARACTER*1 * Specifies the value to be returned in DLANGB as described * above. * * N (input) INTEGER * The order of the matrix A. N >= 0. When N = 0, DLANGB is * set to zero. * * KL (input) INTEGER * The number of sub-diagonals of the matrix A. KL >= 0. * * KU (input) INTEGER * The number of super-diagonals of the matrix A. KU >= 0. * * AB (input) 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). * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KL+KU+1. * * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), * where LWORK >= N when NORM = 'I'; otherwise, WORK is not * referenced. * * ===================================================================== * * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, K, L DOUBLE PRECISION SCALE, SUM, VALUE * .. * .. External Subroutines .. EXTERNAL DLASSQ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. 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 ) VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) 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 VALUE = MAX( 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 VALUE = MAX( VALUE, WORK( I ) ) 80 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE DO 90 J = 1, N L = MAX( 1, J-KU ) K = KU + 1 - J + L CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM ) 90 CONTINUE VALUE = SCALE*SQRT( SUM ) END IF * DLANGB = VALUE RETURN * * End of DLANGB * END