Annotation of rpl/lapack/lapack/zlanht.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLANHT
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLANHT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanht.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanht.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanht.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER NORM
! 25: * INTEGER N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION D( * )
! 29: * COMPLEX*16 E( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZLANHT returns the value of the one norm, or the Frobenius norm, or
! 39: *> the infinity norm, or the element of largest absolute value of a
! 40: *> complex Hermitian tridiagonal matrix A.
! 41: *> \endverbatim
! 42: *>
! 43: *> \return ZLANHT
! 44: *> \verbatim
! 45: *>
! 46: *> ZLANHT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 47: *> (
! 48: *> ( norm1(A), NORM = '1', 'O' or 'o'
! 49: *> (
! 50: *> ( normI(A), NORM = 'I' or 'i'
! 51: *> (
! 52: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 53: *>
! 54: *> where norm1 denotes the one norm of a matrix (maximum column sum),
! 55: *> normI denotes the infinity norm of a matrix (maximum row sum) and
! 56: *> normF denotes the Frobenius norm of a matrix (square root of sum of
! 57: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 58: *> \endverbatim
! 59: *
! 60: * Arguments:
! 61: * ==========
! 62: *
! 63: *> \param[in] NORM
! 64: *> \verbatim
! 65: *> NORM is CHARACTER*1
! 66: *> Specifies the value to be returned in ZLANHT as described
! 67: *> above.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] N
! 71: *> \verbatim
! 72: *> N is INTEGER
! 73: *> The order of the matrix A. N >= 0. When N = 0, ZLANHT is
! 74: *> set to zero.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] D
! 78: *> \verbatim
! 79: *> D is DOUBLE PRECISION array, dimension (N)
! 80: *> The diagonal elements of A.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] E
! 84: *> \verbatim
! 85: *> E is COMPLEX*16 array, dimension (N-1)
! 86: *> The (n-1) sub-diagonal or super-diagonal elements of A.
! 87: *> \endverbatim
! 88: *
! 89: * Authors:
! 90: * ========
! 91: *
! 92: *> \author Univ. of Tennessee
! 93: *> \author Univ. of California Berkeley
! 94: *> \author Univ. of Colorado Denver
! 95: *> \author NAG Ltd.
! 96: *
! 97: *> \date November 2011
! 98: *
! 99: *> \ingroup complex16OTHERauxiliary
! 100: *
! 101: * =====================================================================
1.1 bertrand 102: DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E )
103: *
1.8 ! bertrand 104: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 105: * -- LAPACK is a software package provided by Univ. of Tennessee, --
106: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 107: * November 2011
1.1 bertrand 108: *
109: * .. Scalar Arguments ..
110: CHARACTER NORM
111: INTEGER N
112: * ..
113: * .. Array Arguments ..
114: DOUBLE PRECISION D( * )
115: COMPLEX*16 E( * )
116: * ..
117: *
118: * =====================================================================
119: *
120: * .. Parameters ..
121: DOUBLE PRECISION ONE, ZERO
122: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
123: * ..
124: * .. Local Scalars ..
125: INTEGER I
126: DOUBLE PRECISION ANORM, SCALE, SUM
127: * ..
128: * .. External Functions ..
129: LOGICAL LSAME
130: EXTERNAL LSAME
131: * ..
132: * .. External Subroutines ..
133: EXTERNAL DLASSQ, ZLASSQ
134: * ..
135: * .. Intrinsic Functions ..
136: INTRINSIC ABS, MAX, SQRT
137: * ..
138: * .. Executable Statements ..
139: *
140: IF( N.LE.0 ) THEN
141: ANORM = ZERO
142: ELSE IF( LSAME( NORM, 'M' ) ) THEN
143: *
144: * Find max(abs(A(i,j))).
145: *
146: ANORM = ABS( D( N ) )
147: DO 10 I = 1, N - 1
148: ANORM = MAX( ANORM, ABS( D( I ) ) )
149: ANORM = MAX( ANORM, ABS( E( I ) ) )
150: 10 CONTINUE
151: ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
152: $ LSAME( NORM, 'I' ) ) THEN
153: *
154: * Find norm1(A).
155: *
156: IF( N.EQ.1 ) THEN
157: ANORM = ABS( D( 1 ) )
158: ELSE
159: ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
160: $ ABS( E( N-1 ) )+ABS( D( N ) ) )
161: DO 20 I = 2, N - 1
162: ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
163: $ ABS( E( I-1 ) ) )
164: 20 CONTINUE
165: END IF
166: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
167: *
168: * Find normF(A).
169: *
170: SCALE = ZERO
171: SUM = ONE
172: IF( N.GT.1 ) THEN
173: CALL ZLASSQ( N-1, E, 1, SCALE, SUM )
174: SUM = 2*SUM
175: END IF
176: CALL DLASSQ( N, D, 1, SCALE, SUM )
177: ANORM = SCALE*SQRT( SUM )
178: END IF
179: *
180: ZLANHT = ANORM
181: RETURN
182: *
183: * End of ZLANHT
184: *
185: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlanht.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack