--- rpl/lapack/lapack/zlansp.f 2010/01/26 15:22:46 1.1 +++ rpl/lapack/lapack/zlansp.f 2016/08/27 15:34:58 1.14 @@ -1,9 +1,124 @@ +*> \brief \b ZLANSP 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 ZLANSP + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER NORM, UPLO +* INTEGER N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION WORK( * ) +* COMPLEX*16 AP( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLANSP returns the value of the one norm, or the Frobenius norm, or +*> the infinity norm, or the element of largest absolute value of a +*> complex symmetric matrix A, supplied in packed form. +*> \endverbatim +*> +*> \return ZLANSP +*> \verbatim +*> +*> ZLANSP = ( 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 ZLANSP 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, ZLANSP is +*> set to zero. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX*16 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 complex16OTHERauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION ZLANSP( 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 @@ -14,59 +129,6 @@ COMPLEX*16 AP( * ) * .. * -* Purpose -* ======= -* -* ZLANSP returns the value of the one norm, or the Frobenius norm, or -* the infinity norm, or the element of largest absolute value of a -* complex symmetric matrix A, supplied in packed form. -* -* Description -* =========== -* -* ZLANSP returns the value -* -* ZLANSP = ( 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 ZLANSP 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, ZLANSP is -* set to zero. -* -* AP (input) COMPLEX*16 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 .. @@ -78,14 +140,14 @@ DOUBLE PRECISION ABSA, SCALE, SUM, VALUE * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ * .. * .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT + INTRINSIC ABS, DBLE, DIMAG, SQRT * .. * .. Executable Statements .. * @@ -100,7 +162,8 @@ 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 @@ -108,7 +171,8 @@ 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 @@ -133,7 +197,8 @@ 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 @@ -148,7 +213,7 @@ 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