--- rpl/lapack/lapack/dlantb.f 2010/04/21 13:45:17 1.2 +++ rpl/lapack/lapack/dlantb.f 2017/06/17 11:06:23 1.16 @@ -1,10 +1,149 @@ +*> \brief \b DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANTB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB, +* LDAB, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIAG, NORM, UPLO +* INTEGER K, LDAB, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AB( LDAB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals. +*> \endverbatim +*> +*> \return DLANTB +*> \verbatim +*> +*> DLANTB = ( 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 DLANTB as described +*> above. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> Specifies whether the matrix A is upper or lower triangular. +*> = 'U': Upper triangular +*> = 'L': Lower triangular +*> \endverbatim +*> +*> \param[in] DIAG +*> \verbatim +*> DIAG is CHARACTER*1 +*> Specifies whether or not the matrix A is unit triangular. +*> = 'N': Non-unit triangular +*> = 'U': Unit triangular +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, DLANTB is +*> set to zero. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The number of super-diagonals of the matrix A if UPLO = 'U', +*> or the number of sub-diagonals of the matrix A if UPLO = 'L'. +*> K >= 0. +*> \endverbatim +*> +*> \param[in] AB +*> \verbatim +*> AB is DOUBLE PRECISION array, dimension (LDAB,N) +*> The upper or lower triangular band matrix A, stored in the +*> first k+1 rows of AB. The j-th column of A is stored +*> in the j-th column of the array AB as follows: +*> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; +*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). +*> Note that when DIAG = 'U', the elements of the array AB +*> corresponding to the diagonal elements of the matrix A are +*> not referenced, but are assumed to be one. +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= K+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 doubleOTHERauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB, $ LDAB, WORK ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- 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..-- -* November 2006 +* December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO @@ -14,74 +153,6 @@ DOUBLE PRECISION AB( LDAB, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals. -* -* Description -* =========== -* -* DLANTB returns the value -* -* DLANTB = ( 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 DLANTB as described -* above. -* -* UPLO (input) CHARACTER*1 -* Specifies whether the matrix A is upper or lower triangular. -* = 'U': Upper triangular -* = 'L': Lower triangular -* -* DIAG (input) CHARACTER*1 -* Specifies whether or not the matrix A is unit triangular. -* = 'N': Non-unit triangular -* = 'U': Unit triangular -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, DLANTB is -* set to zero. -* -* K (input) INTEGER -* The number of super-diagonals of the matrix A if UPLO = 'U', -* or the number of sub-diagonals of the matrix A if UPLO = 'L'. -* K >= 0. -* -* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) -* The upper or lower triangular band matrix A, stored in the -* first k+1 rows of AB. The j-th column of A is stored -* in the j-th column of the array AB as follows: -* if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; -* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). -* Note that when DIAG = 'U', the elements of the array AB -* corresponding to the diagonal elements of the matrix A are -* not referenced, but are assumed to be one. -* -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= K+1. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -* where LWORK >= N when NORM = 'I'; otherwise, WORK is not -* referenced. -* * ===================================================================== * * .. Parameters .. @@ -97,8 +168,8 @@ EXTERNAL DLASSQ * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT @@ -116,13 +187,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = MAX( K+2-J, 1 ), K - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = 2, MIN( N+1-J, K+1 ) - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF @@ -131,13 +204,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N DO 50 I = MAX( K+2-J, 1 ), K + 1 - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1, N DO 70 I = 1, MIN( N+1-J, K+1 ) - VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + SUM = ABS( AB( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE 80 CONTINUE END IF @@ -161,7 +236,7 @@ SUM = SUM + ABS( AB( I, J ) ) 100 CONTINUE END IF - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 110 CONTINUE ELSE DO 140 J = 1, N @@ -176,7 +251,7 @@ SUM = SUM + ABS( AB( I, J ) ) 130 CONTINUE END IF - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 140 CONTINUE END IF ELSE IF( LSAME( NORM, 'I' ) ) THEN @@ -230,7 +305,8 @@ END IF END IF DO 270 I = 1, N - VALUE = MAX( VALUE, WORK( I ) ) + SUM = WORK( I ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 270 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN *