--- rpl/lapack/lapack/zlansy.f 2010/08/13 21:04:09 1.6 +++ rpl/lapack/lapack/zlansy.f 2015/11/26 11:44:24 1.14 @@ -1,9 +1,132 @@ +*> \brief \b ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLANSY + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER NORM, UPLO +* INTEGER LDA, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION WORK( * ) +* COMPLEX*16 A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLANSY 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. +*> \endverbatim +*> +*> \return ZLANSY +*> \verbatim +*> +*> ZLANSY = ( 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 ZLANSY 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 to be referenced. +*> = 'U': Upper triangular part of A is referenced +*> = 'L': Lower triangular part of A is referenced +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, ZLANSY is +*> set to zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The symmetric matrix A. If UPLO = 'U', the leading n by n +*> upper triangular part of A contains the upper triangular part +*> of the matrix A, and the strictly lower triangular part of A +*> is not referenced. If UPLO = 'L', the leading n by n lower +*> triangular part of A contains the lower triangular part of +*> the matrix A, and the strictly upper triangular part of A 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' 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 November 2015 +* +*> \ingroup complex16SYauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.6.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2015 * * .. Scalar Arguments .. CHARACTER NORM, UPLO @@ -14,64 +137,6 @@ COMPLEX*16 A( LDA, * ) * .. * -* Purpose -* ======= -* -* ZLANSY 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. -* -* Description -* =========== -* -* ZLANSY returns the value -* -* ZLANSY = ( 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 ZLANSY as described -* above. -* -* UPLO (input) CHARACTER*1 -* Specifies whether the upper or lower triangular part of the -* symmetric matrix A is to be referenced. -* = 'U': Upper triangular part of A is referenced -* = 'L': Lower triangular part of A is referenced -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. When N = 0, ZLANSY is -* set to zero. -* -* A (input) COMPLEX*16 array, dimension (LDA,N) -* The symmetric matrix A. If UPLO = 'U', the leading n by n -* upper triangular part of A contains the upper triangular part -* of the matrix A, and the strictly lower triangular part of A -* is not referenced. If UPLO = 'L', the leading n by n lower -* triangular part of A contains the lower triangular part of -* the matrix A, and the strictly upper triangular part of A 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' or '1' or 'O'; otherwise, -* WORK is not referenced. -* * ===================================================================== * * .. Parameters .. @@ -83,14 +148,14 @@ 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, MAX, SQRT + INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * @@ -104,13 +169,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J - 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 DO 40 J = 1, N DO 30 I = J, N - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF @@ -131,7 +198,8 @@ WORK( J ) = SUM + ABS( A( J, J ) ) 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 @@ -144,7 +212,7 @@ SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 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