Annotation of rpl/lapack/lapack/dpttrf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DPTTRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DPTTRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpttrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpttrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpttrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPTTRF( N, D, E, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION D( * ), E( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DPTTRF computes the L*D*L**T factorization of a real symmetric
! 37: *> positive definite tridiagonal matrix A. The factorization may also
! 38: *> be regarded as having the form A = U**T*D*U.
! 39: *> \endverbatim
! 40: *
! 41: * Arguments:
! 42: * ==========
! 43: *
! 44: *> \param[in] N
! 45: *> \verbatim
! 46: *> N is INTEGER
! 47: *> The order of the matrix A. N >= 0.
! 48: *> \endverbatim
! 49: *>
! 50: *> \param[in,out] D
! 51: *> \verbatim
! 52: *> D is DOUBLE PRECISION array, dimension (N)
! 53: *> On entry, the n diagonal elements of the tridiagonal matrix
! 54: *> A. On exit, the n diagonal elements of the diagonal matrix
! 55: *> D from the L*D*L**T factorization of A.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in,out] E
! 59: *> \verbatim
! 60: *> E is DOUBLE PRECISION array, dimension (N-1)
! 61: *> On entry, the (n-1) subdiagonal elements of the tridiagonal
! 62: *> matrix A. On exit, the (n-1) subdiagonal elements of the
! 63: *> unit bidiagonal factor L from the L*D*L**T factorization of A.
! 64: *> E can also be regarded as the superdiagonal of the unit
! 65: *> bidiagonal factor U from the U**T*D*U factorization of A.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[out] INFO
! 69: *> \verbatim
! 70: *> INFO is INTEGER
! 71: *> = 0: successful exit
! 72: *> < 0: if INFO = -k, the k-th argument had an illegal value
! 73: *> > 0: if INFO = k, the leading minor of order k is not
! 74: *> positive definite; if k < N, the factorization could not
! 75: *> be completed, while if k = N, the factorization was
! 76: *> completed, but D(N) <= 0.
! 77: *> \endverbatim
! 78: *
! 79: * Authors:
! 80: * ========
! 81: *
! 82: *> \author Univ. of Tennessee
! 83: *> \author Univ. of California Berkeley
! 84: *> \author Univ. of Colorado Denver
! 85: *> \author NAG Ltd.
! 86: *
! 87: *> \date November 2011
! 88: *
! 89: *> \ingroup auxOTHERcomputational
! 90: *
! 91: * =====================================================================
1.1 bertrand 92: SUBROUTINE DPTTRF( N, D, E, INFO )
93: *
1.9 ! bertrand 94: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 95: * -- LAPACK is a software package provided by Univ. of Tennessee, --
96: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 97: * November 2011
1.1 bertrand 98: *
99: * .. Scalar Arguments ..
100: INTEGER INFO, N
101: * ..
102: * .. Array Arguments ..
103: DOUBLE PRECISION D( * ), E( * )
104: * ..
105: *
106: * =====================================================================
107: *
108: * .. Parameters ..
109: DOUBLE PRECISION ZERO
110: PARAMETER ( ZERO = 0.0D+0 )
111: * ..
112: * .. Local Scalars ..
113: INTEGER I, I4
114: DOUBLE PRECISION EI
115: * ..
116: * .. External Subroutines ..
117: EXTERNAL XERBLA
118: * ..
119: * .. Intrinsic Functions ..
120: INTRINSIC MOD
121: * ..
122: * .. Executable Statements ..
123: *
124: * Test the input parameters.
125: *
126: INFO = 0
127: IF( N.LT.0 ) THEN
128: INFO = -1
129: CALL XERBLA( 'DPTTRF', -INFO )
130: RETURN
131: END IF
132: *
133: * Quick return if possible
134: *
135: IF( N.EQ.0 )
136: $ RETURN
137: *
1.8 bertrand 138: * Compute the L*D*L**T (or U**T*D*U) factorization of A.
1.1 bertrand 139: *
140: I4 = MOD( N-1, 4 )
141: DO 10 I = 1, I4
142: IF( D( I ).LE.ZERO ) THEN
143: INFO = I
144: GO TO 30
145: END IF
146: EI = E( I )
147: E( I ) = EI / D( I )
148: D( I+1 ) = D( I+1 ) - E( I )*EI
149: 10 CONTINUE
150: *
151: DO 20 I = I4 + 1, N - 4, 4
152: *
153: * Drop out of the loop if d(i) <= 0: the matrix is not positive
154: * definite.
155: *
156: IF( D( I ).LE.ZERO ) THEN
157: INFO = I
158: GO TO 30
159: END IF
160: *
161: * Solve for e(i) and d(i+1).
162: *
163: EI = E( I )
164: E( I ) = EI / D( I )
165: D( I+1 ) = D( I+1 ) - E( I )*EI
166: *
167: IF( D( I+1 ).LE.ZERO ) THEN
168: INFO = I + 1
169: GO TO 30
170: END IF
171: *
172: * Solve for e(i+1) and d(i+2).
173: *
174: EI = E( I+1 )
175: E( I+1 ) = EI / D( I+1 )
176: D( I+2 ) = D( I+2 ) - E( I+1 )*EI
177: *
178: IF( D( I+2 ).LE.ZERO ) THEN
179: INFO = I + 2
180: GO TO 30
181: END IF
182: *
183: * Solve for e(i+2) and d(i+3).
184: *
185: EI = E( I+2 )
186: E( I+2 ) = EI / D( I+2 )
187: D( I+3 ) = D( I+3 ) - E( I+2 )*EI
188: *
189: IF( D( I+3 ).LE.ZERO ) THEN
190: INFO = I + 3
191: GO TO 30
192: END IF
193: *
194: * Solve for e(i+3) and d(i+4).
195: *
196: EI = E( I+3 )
197: E( I+3 ) = EI / D( I+3 )
198: D( I+4 ) = D( I+4 ) - E( I+3 )*EI
199: 20 CONTINUE
200: *
201: * Check d(n) for positive definiteness.
202: *
203: IF( D( N ).LE.ZERO )
204: $ INFO = N
205: *
206: 30 CONTINUE
207: RETURN
208: *
209: * End of DPTTRF
210: *
211: END
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