Annotation of rpl/lapack/lapack/zlanht.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER NORM
! 10: INTEGER N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION D( * )
! 14: COMPLEX*16 E( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZLANHT returns the value of the one norm, or the Frobenius norm, or
! 21: * the infinity norm, or the element of largest absolute value of a
! 22: * complex Hermitian tridiagonal matrix A.
! 23: *
! 24: * Description
! 25: * ===========
! 26: *
! 27: * ZLANHT returns the value
! 28: *
! 29: * ZLANHT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 30: * (
! 31: * ( norm1(A), NORM = '1', 'O' or 'o'
! 32: * (
! 33: * ( normI(A), NORM = 'I' or 'i'
! 34: * (
! 35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 36: *
! 37: * where norm1 denotes the one norm of a matrix (maximum column sum),
! 38: * normI denotes the infinity norm of a matrix (maximum row sum) and
! 39: * normF denotes the Frobenius norm of a matrix (square root of sum of
! 40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 41: *
! 42: * Arguments
! 43: * =========
! 44: *
! 45: * NORM (input) CHARACTER*1
! 46: * Specifies the value to be returned in ZLANHT as described
! 47: * above.
! 48: *
! 49: * N (input) INTEGER
! 50: * The order of the matrix A. N >= 0. When N = 0, ZLANHT is
! 51: * set to zero.
! 52: *
! 53: * D (input) DOUBLE PRECISION array, dimension (N)
! 54: * The diagonal elements of A.
! 55: *
! 56: * E (input) COMPLEX*16 array, dimension (N-1)
! 57: * The (n-1) sub-diagonal or super-diagonal elements of A.
! 58: *
! 59: * =====================================================================
! 60: *
! 61: * .. Parameters ..
! 62: DOUBLE PRECISION ONE, ZERO
! 63: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 64: * ..
! 65: * .. Local Scalars ..
! 66: INTEGER I
! 67: DOUBLE PRECISION ANORM, SCALE, SUM
! 68: * ..
! 69: * .. External Functions ..
! 70: LOGICAL LSAME
! 71: EXTERNAL LSAME
! 72: * ..
! 73: * .. External Subroutines ..
! 74: EXTERNAL DLASSQ, ZLASSQ
! 75: * ..
! 76: * .. Intrinsic Functions ..
! 77: INTRINSIC ABS, MAX, SQRT
! 78: * ..
! 79: * .. Executable Statements ..
! 80: *
! 81: IF( N.LE.0 ) THEN
! 82: ANORM = ZERO
! 83: ELSE IF( LSAME( NORM, 'M' ) ) THEN
! 84: *
! 85: * Find max(abs(A(i,j))).
! 86: *
! 87: ANORM = ABS( D( N ) )
! 88: DO 10 I = 1, N - 1
! 89: ANORM = MAX( ANORM, ABS( D( I ) ) )
! 90: ANORM = MAX( ANORM, ABS( E( I ) ) )
! 91: 10 CONTINUE
! 92: ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
! 93: $ LSAME( NORM, 'I' ) ) THEN
! 94: *
! 95: * Find norm1(A).
! 96: *
! 97: IF( N.EQ.1 ) THEN
! 98: ANORM = ABS( D( 1 ) )
! 99: ELSE
! 100: ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
! 101: $ ABS( E( N-1 ) )+ABS( D( N ) ) )
! 102: DO 20 I = 2, N - 1
! 103: ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
! 104: $ ABS( E( I-1 ) ) )
! 105: 20 CONTINUE
! 106: END IF
! 107: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
! 108: *
! 109: * Find normF(A).
! 110: *
! 111: SCALE = ZERO
! 112: SUM = ONE
! 113: IF( N.GT.1 ) THEN
! 114: CALL ZLASSQ( N-1, E, 1, SCALE, SUM )
! 115: SUM = 2*SUM
! 116: END IF
! 117: CALL DLASSQ( N, D, 1, SCALE, SUM )
! 118: ANORM = SCALE*SQRT( SUM )
! 119: END IF
! 120: *
! 121: ZLANHT = ANORM
! 122: RETURN
! 123: *
! 124: * End of ZLANHT
! 125: *
! 126: END
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