142 lines
4.0 KiB
FortranFixed
142 lines
4.0 KiB
FortranFixed
DOUBLE PRECISION FUNCTION ZLANGT( NORM, N, DL, D, DU )
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER NORM
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INTEGER N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 D( * ), DL( * ), DU( * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZLANGT returns the value of the one norm, or the Frobenius norm, or
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* the infinity norm, or the element of largest absolute value of a
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* complex tridiagonal matrix A.
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*
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* Description
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* ===========
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*
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* ZLANGT returns the value
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*
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* ZLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
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* (
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* ( norm1(A), NORM = '1', 'O' or 'o'
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* (
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* ( normI(A), NORM = 'I' or 'i'
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* (
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* ( normF(A), NORM = 'F', 'f', 'E' or 'e'
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*
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* where norm1 denotes the one norm of a matrix (maximum column sum),
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* normI denotes the infinity norm of a matrix (maximum row sum) and
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* normF denotes the Frobenius norm of a matrix (square root of sum of
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* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
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*
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* Arguments
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* =========
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*
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* NORM (input) CHARACTER*1
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* Specifies the value to be returned in ZLANGT as described
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* above.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0. When N = 0, ZLANGT is
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* set to zero.
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*
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* DL (input) COMPLEX*16 array, dimension (N-1)
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* The (n-1) sub-diagonal elements of A.
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*
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* D (input) COMPLEX*16 array, dimension (N)
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* The diagonal elements of A.
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*
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* DU (input) COMPLEX*16 array, dimension (N-1)
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* The (n-1) super-diagonal elements of A.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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DOUBLE PRECISION ANORM, SCALE, SUM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL ZLASSQ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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IF( N.LE.0 ) THEN
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ANORM = ZERO
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ELSE IF( LSAME( NORM, 'M' ) ) THEN
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*
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* Find max(abs(A(i,j))).
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*
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ANORM = ABS( D( N ) )
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DO 10 I = 1, N - 1
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ANORM = MAX( ANORM, ABS( DL( I ) ) )
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ANORM = MAX( ANORM, ABS( D( I ) ) )
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ANORM = MAX( ANORM, ABS( DU( I ) ) )
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10 CONTINUE
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ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN
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*
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* Find norm1(A).
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*
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IF( N.EQ.1 ) THEN
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ANORM = ABS( D( 1 ) )
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ELSE
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ANORM = MAX( ABS( D( 1 ) )+ABS( DL( 1 ) ),
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$ ABS( D( N ) )+ABS( DU( N-1 ) ) )
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DO 20 I = 2, N - 1
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ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DL( I ) )+
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$ ABS( DU( I-1 ) ) )
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20 CONTINUE
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END IF
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ELSE IF( LSAME( NORM, 'I' ) ) THEN
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*
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* Find normI(A).
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*
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IF( N.EQ.1 ) THEN
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ANORM = ABS( D( 1 ) )
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ELSE
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ANORM = MAX( ABS( D( 1 ) )+ABS( DU( 1 ) ),
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$ ABS( D( N ) )+ABS( DL( N-1 ) ) )
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DO 30 I = 2, N - 1
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ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DU( I ) )+
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$ ABS( DL( I-1 ) ) )
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30 CONTINUE
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END IF
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ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
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*
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* Find normF(A).
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*
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SCALE = ZERO
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SUM = ONE
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CALL ZLASSQ( N, D, 1, SCALE, SUM )
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IF( N.GT.1 ) THEN
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CALL ZLASSQ( N-1, DL, 1, SCALE, SUM )
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CALL ZLASSQ( N-1, DU, 1, SCALE, SUM )
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END IF
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ANORM = SCALE*SQRT( SUM )
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END IF
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*
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ZLANGT = ANORM
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RETURN
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*
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* End of ZLANGT
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*
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END
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