--- rpl/lapack/lapack/dlansp.f 2010/01/26 15:22:46 1.1.1.1 +++ rpl/lapack/lapack/dlansp.f 2014/01/27 09:28:20 1.13 @@ -1,9 +1,123 @@ +*> \brief \b DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANSP + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER NORM, UPLO +* INTEGER N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANSP returns the value of the one norm, or the Frobenius norm, or +*> the infinity norm, or the element of largest absolute value of a +*> real symmetric matrix A, supplied in packed form. +*> \endverbatim +*> +*> \return DLANSP +*> \verbatim +*> +*> DLANSP = ( 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 DLANSP as described +*> above. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> Specifies whether the upper or lower triangular part of the +*> symmetric matrix A is supplied. +*> = 'U': Upper triangular part of A is supplied +*> = 'L': Lower triangular part of A is supplied +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, DLANSP is +*> set to zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) +*> The upper or lower triangle of the symmetric matrix A, packed +*> columnwise in a linear array. The j-th column of A is stored +*> in the array AP as follows: +*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), +*> where LWORK >= N when NORM = 'I' or '1' or 'O'; 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 doubleOTHERauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, 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, UPLO @@ -13,59 +127,6 @@ DOUBLE PRECISION AP( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLANSP returns the value of the one norm, or the Frobenius norm, or -* the infinity norm, or the element of largest absolute value of a -* real symmetric matrix A, supplied in packed form. -* -* Description -* =========== -* -* DLANSP returns the value -* -* DLANSP = ( 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 DLANSP as described -* above. -* -* UPLO (input) CHARACTER*1 -* Specifies whether the upper or lower triangular part of the -* symmetric matrix A is supplied. -* = 'U': Upper triangular part of A is supplied -* = 'L': Lower triangular part of A is supplied -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, DLANSP is -* set to zero. -* -* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) -* The upper or lower triangle of the symmetric matrix A, packed -* columnwise in a linear array. The j-th column of A is stored -* in the array AP as follows: -* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, -* WORK is not referenced. -* * ===================================================================== * * .. Parameters .. @@ -80,11 +141,11 @@ EXTERNAL DLASSQ * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SQRT + INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * @@ -99,7 +160,8 @@ K = 1 DO 20 J = 1, N DO 10 I = K, K + J - 1 - VALUE = MAX( VALUE, ABS( AP( I ) ) ) + SUM = ABS( AP( I ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE K = K + J 20 CONTINUE @@ -107,7 +169,8 @@ K = 1 DO 40 J = 1, N DO 30 I = K, K + N - J - VALUE = MAX( VALUE, ABS( AP( I ) ) ) + SUM = ABS( AP( I ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE K = K + N - J + 1 40 CONTINUE @@ -132,7 +195,8 @@ K = K + 1 60 CONTINUE DO 70 I = 1, N - VALUE = MAX( VALUE, WORK( I ) ) + SUM = WORK( I ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE ELSE DO 80 I = 1, N @@ -147,7 +211,7 @@ WORK( I ) = WORK( I ) + ABSA K = K + 1 90 CONTINUE - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN