DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) ! ! -- LAPACK auxiliary routine (version 3.1) -- ! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. ! November 2006 ! ! .. Scalar Arguments .. CHARACTER NORM, UPLO INTEGER LDA, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), WORK( * ) ! .. ! ! Purpose ! ======= ! ! DLANSY 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. ! ! Description ! =========== ! ! DLANSY returns the value ! ! DLANSY = ( 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 DLANSY 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, DLANSY is ! set to zero. ! ! A (input) DOUBLE PRECISION 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 .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. INTEGER I, J DOUBLE PRECISION ABSA, SCALE, SUM, VALUE ! .. ! .. External Subroutines .. ! EXTERNAL DLASSQ ! .. ! .. External Functions .. ! LOGICAL LSAME ! EXTERNAL LSAME ! .. ! .. Intrinsic Functions .. INTRINSIC ABS, MAX, 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 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J, N VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 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 VALUE = MAX( VALUE, WORK( I ) ) 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 VALUE = MAX( VALUE, SUM ) 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN ! ! Find normF(A). ! SCALE = ZERO SUM = ONE IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) 110 CONTINUE ELSE DO 120 J = 1, N - 1 CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) 120 CONTINUE END IF SUM = 2*SUM CALL DLASSQ( N, A, LDA+1, SCALE, SUM ) VALUE = SCALE*SQRT( SUM ) END IF ! DLANSY = VALUE RETURN ! ! End of DLANSY ! END FUNCTION DLANSY