--- rpl/lapack/lapack/zlangb.f 2010/12/21 13:53:50 1.7 +++ rpl/lapack/lapack/zlangb.f 2012/12/14 12:30:31 1.11 @@ -1,10 +1,134 @@ +*> \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 September 2012 +* +*> \ingroup complex16GBauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, $ WORK ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.4.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* September 2012 * * .. Scalar Arguments .. CHARACTER NORM @@ -15,61 +139,6 @@ COMPLEX*16 AB( LDAB, * ) * .. * -* Purpose -* ======= -* -* 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. -* -* Description -* =========== -* -* ZLANGB returns the value -* -* 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. -* -* Arguments -* ========= -* -* NORM (input) CHARACTER*1 -* Specifies the value to be returned in ZLANGB as described -* above. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, ZLANGB 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) 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). -* -* 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 .. @@ -78,11 +147,11 @@ * .. * .. Local Scalars .. INTEGER I, J, K, L - DOUBLE PRECISION SCALE, SUM, VALUE + DOUBLE PRECISION SCALE, SUM, VALUE, TEMP * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ @@ -101,7 +170,8 @@ 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 ) ) ) + 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 @@ -114,7 +184,7 @@ 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 ) + IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM 40 CONTINUE ELSE IF( LSAME( NORM, 'I' ) ) THEN * @@ -131,7 +201,8 @@ 70 CONTINUE VALUE = ZERO DO 80 I = 1, N - VALUE = MAX( VALUE, WORK( I ) ) + TEMP = WORK( I ) + IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP 80 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN *