*> \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 December 2016 * *> \ingroup doubleOTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER NORM, UPLO INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION AP( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, K DOUBLE PRECISION ABSA, SCALE, SUM, VALUE * .. * .. External Subroutines .. EXTERNAL DLASSQ * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. 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 K = 1 DO 20 J = 1, N DO 10 I = K, K + J - 1 SUM = ABS( AP( I ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE K = K + J 20 CONTINUE ELSE K = 1 DO 40 J = 1, N DO 30 I = K, K + N - J SUM = ABS( AP( I ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE K = K + N - J + 1 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 K = 1 IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N SUM = ZERO DO 50 I = 1, J - 1 ABSA = ABS( AP( K ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA K = K + 1 50 CONTINUE WORK( J ) = SUM + ABS( AP( K ) ) K = K + 1 60 CONTINUE DO 70 I = 1, N SUM = WORK( I ) IF( VALUE .LT. SUM .OR. DISNAN( 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( AP( K ) ) K = K + 1 DO 90 I = J + 1, N ABSA = ABS( AP( K ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA K = K + 1 90 CONTINUE IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE K = 2 IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM ) K = K + J 110 CONTINUE ELSE DO 120 J = 1, N - 1 CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM ) K = K + N - J + 1 120 CONTINUE END IF SUM = 2*SUM K = 1 DO 130 I = 1, N IF( AP( K ).NE.ZERO ) THEN ABSA = ABS( AP( K ) ) IF( SCALE.LT.ABSA ) THEN SUM = ONE + SUM*( SCALE / ABSA )**2 SCALE = ABSA ELSE SUM = SUM + ( ABSA / SCALE )**2 END IF END IF IF( LSAME( UPLO, 'U' ) ) THEN K = K + I + 1 ELSE K = K + N - I + 1 END IF 130 CONTINUE VALUE = SCALE*SQRT( SUM ) END IF * DLANSP = VALUE RETURN * * End of DLANSP * END