*> \brief \b ZLANGB 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 ZLANGB + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, * WORK ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER KL, KU, LDAB, N * .. * .. Array Arguments .. * DOUBLE PRECISION WORK( * ) * COMPLEX*16 AB( LDAB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANGB 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 ZLANGB *> \verbatim *> *> ZLANGB = ( 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 ZLANGB as described *> above. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, ZLANGB 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 COMPLEX*16 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. * *> \date December 2016 * *> \ingroup complex16GBauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, $ WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER NORM INTEGER KL, KU, LDAB, N * .. * .. Array Arguments .. DOUBLE PRECISION WORK( * ) COMPLEX*16 AB( LDAB, * ) * .. * * ===================================================================== * * .. 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, TEMP * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ * .. * .. 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). * SCALE = ZERO SUM = ONE DO 90 J = 1, N L = MAX( 1, J-KU ) K = KU + 1 - J + L CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM ) 90 CONTINUE VALUE = SCALE*SQRT( SUM ) END IF * ZLANGB = VALUE RETURN * * End of ZLANGB * END