*> \brief \b SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SLANSY + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * REAL FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM, UPLO * INTEGER LDA, N * .. * .. Array Arguments .. * REAL A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLANSY 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. *> \endverbatim *> *> \return SLANSY *> \verbatim *> *> SLANSY = ( 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 SLANSY 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, SLANSY is *> set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL 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 REAL 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. * *> \ingroup realSYauxiliary * * ===================================================================== REAL FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * IMPLICIT NONE * .. Scalar Arguments .. CHARACTER NORM, UPLO INTEGER LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL ABSA, SUM, VALUE * .. * .. Local Arrays .. REAL SSQ( 2 ), COLSSQ( 2 ) * .. * .. External Functions .. LOGICAL LSAME, SISNAN EXTERNAL LSAME, SISNAN * .. * .. External Subroutines .. EXTERNAL SLASSQ, SCOMBSSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN VALUE = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J, N SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. $ ( NORM.EQ.'1' ) ) THEN * * Find normI(A) ( = norm1(A), since A is symmetric). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N SUM = ZERO DO 50 I = 1, J - 1 ABSA = ABS( A( I, J ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 50 CONTINUE WORK( J ) = SUM + ABS( A( J, J ) ) 60 CONTINUE DO 70 I = 1, N SUM = WORK( I ) IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 70 CONTINUE ELSE DO 80 I = 1, N WORK( I ) = ZERO 80 CONTINUE DO 100 J = 1, N SUM = WORK( J ) + ABS( A( J, J ) ) DO 90 I = J + 1, N ABSA = ABS( A( I, J ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 90 CONTINUE IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SSQ(1) is scale * SSQ(2) is sum-of-squares * For better accuracy, sum each column separately. * SSQ( 1 ) = ZERO SSQ( 2 ) = ONE * * Sum off-diagonals * IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL SLASSQ( J-1, A( 1, J ), 1, COLSSQ(1), COLSSQ(2) ) CALL SCOMBSSQ( SSQ, COLSSQ ) 110 CONTINUE ELSE DO 120 J = 1, N - 1 COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL SLASSQ( N-J, A( J+1, J ), 1, COLSSQ(1), COLSSQ(2) ) CALL SCOMBSSQ( SSQ, COLSSQ ) 120 CONTINUE END IF SSQ( 2 ) = 2*SSQ( 2 ) * * Sum diagonal * COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL SLASSQ( N, A, LDA+1, COLSSQ( 1 ), COLSSQ( 2 ) ) CALL SCOMBSSQ( SSQ, COLSSQ ) VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * SLANSY = VALUE RETURN * * End of SLANSY * END