--- rpl/lapack/lapack/dlanhs.f 2010/04/21 13:45:17 1.2 +++ rpl/lapack/lapack/dlanhs.f 2023/08/07 08:38:55 1.19 @@ -1,9 +1,114 @@ +*> \brief \b DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANHS + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER NORM +* INTEGER LDA, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANHS returns the value of the one norm, or the Frobenius norm, or +*> the infinity norm, or the element of largest absolute value of a +*> Hessenberg matrix A. +*> \endverbatim +*> +*> \return DLANHS +*> \verbatim +*> +*> DLANHS = ( 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 DLANHS as described +*> above. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, DLANHS is +*> set to zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The n by n upper Hessenberg matrix A; the part of A below the +*> first sub-diagonal is not referenced. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(N,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. +* +*> \ingroup doubleOTHERauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine -- * -- 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 @@ -13,53 +118,6 @@ DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLANHS returns the value of the one norm, or the Frobenius norm, or -* the infinity norm, or the element of largest absolute value of a -* Hessenberg matrix A. -* -* Description -* =========== -* -* DLANHS returns the value -* -* DLANHS = ( 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 DLANHS as described -* above. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, DLANHS is -* set to zero. -* -* A (input) DOUBLE PRECISION array, dimension (LDA,N) -* The n by n upper Hessenberg matrix A; the part of A below the -* first sub-diagonal is not referenced. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(N,1). -* -* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -* where LWORK >= N when NORM = 'I'; otherwise, WORK is not -* referenced. -* * ===================================================================== * * .. Parameters .. @@ -74,11 +132,11 @@ EXTERNAL DLASSQ * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT + INTRINSIC ABS, MIN, SQRT * .. * .. Executable Statements .. * @@ -91,7 +149,8 @@ VALUE = ZERO DO 20 J = 1, N DO 10 I = 1, MIN( N, J+1 ) - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN @@ -104,7 +163,7 @@ DO 30 I = 1, MIN( N, J+1 ) SUM = SUM + ABS( A( 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 * @@ -120,7 +179,8 @@ 70 CONTINUE VALUE = ZERO DO 80 I = 1, N - VALUE = MAX( VALUE, WORK( I ) ) + SUM = WORK( I ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 80 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN *