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REAL FUNCTION SLANGT( NORM, N, DL, D, DU )
* * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER NORM INTEGER N * .. * .. Array Arguments .. REAL D( * ), DL( * ), DU( * ) * .. * * Purpose * ======= * * SLANGT 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 tridiagonal matrix A. * * Description * =========== * * SLANGT returns the value * * SLANGT = ( 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 SLANGT as described * above. * * N (input) INTEGER * The order of the matrix A. N >= 0. When N = 0, SLANGT is * set to zero. * * DL (input) REAL array, dimension (N-1) * The (n-1) sub-diagonal elements of A. * * D (input) REAL array, dimension (N) * The diagonal elements of A. * * DU (input) REAL array, dimension (N-1) * The (n-1) super-diagonal elements of A. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I REAL ANORM, SCALE, SUM * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SLASSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * IF( N.LE.0 ) THEN ANORM = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * ANORM = ABS( D( N ) ) DO 10 I = 1, N - 1 ANORM = MAX( ANORM, ABS( DL( I ) ) ) ANORM = MAX( ANORM, ABS( D( I ) ) ) ANORM = MAX( ANORM, ABS( DU( I ) ) ) 10 CONTINUE ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN * * Find norm1(A). * IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE ANORM = MAX( ABS( D( 1 ) )+ABS( DL( 1 ) ), $ ABS( D( N ) )+ABS( DU( N-1 ) ) ) DO 20 I = 2, N - 1 ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DL( I ) )+ $ ABS( DU( I-1 ) ) ) 20 CONTINUE END IF ELSE IF( LSAME( NORM, 'I' ) ) THEN * * Find normI(A). * IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE ANORM = MAX( ABS( D( 1 ) )+ABS( DU( 1 ) ), $ ABS( D( N ) )+ABS( DL( N-1 ) ) ) DO 30 I = 2, N - 1 ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DU( I ) )+ $ ABS( DL( I-1 ) ) ) 30 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE CALL SLASSQ( N, D, 1, SCALE, SUM ) IF( N.GT.1 ) THEN CALL SLASSQ( N-1, DL, 1, SCALE, SUM ) CALL SLASSQ( N-1, DU, 1, SCALE, SUM ) END IF ANORM = SCALE*SQRT( SUM ) END IF * SLANGT = ANORM RETURN * * End of SLANGT * END |