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