Annotation of rpl/lapack/lapack/dgtts2.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DGTTS2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGTTS2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgtts2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgtts2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgtts2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER ITRANS, LDB, N, NRHS
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER IPIV( * )
! 28: * DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DGTTS2 solves one of the systems of equations
! 38: *> A*X = B or A**T*X = B,
! 39: *> with a tridiagonal matrix A using the LU factorization computed
! 40: *> by DGTTRF.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] ITRANS
! 47: *> \verbatim
! 48: *> ITRANS is INTEGER
! 49: *> Specifies the form of the system of equations.
! 50: *> = 0: A * X = B (No transpose)
! 51: *> = 1: A**T* X = B (Transpose)
! 52: *> = 2: A**T* X = B (Conjugate transpose = Transpose)
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] N
! 56: *> \verbatim
! 57: *> N is INTEGER
! 58: *> The order of the matrix A.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] NRHS
! 62: *> \verbatim
! 63: *> NRHS is INTEGER
! 64: *> The number of right hand sides, i.e., the number of columns
! 65: *> of the matrix B. NRHS >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] DL
! 69: *> \verbatim
! 70: *> DL is DOUBLE PRECISION array, dimension (N-1)
! 71: *> The (n-1) multipliers that define the matrix L from the
! 72: *> LU factorization of A.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] D
! 76: *> \verbatim
! 77: *> D is DOUBLE PRECISION array, dimension (N)
! 78: *> The n diagonal elements of the upper triangular matrix U from
! 79: *> the LU factorization of A.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] DU
! 83: *> \verbatim
! 84: *> DU is DOUBLE PRECISION array, dimension (N-1)
! 85: *> The (n-1) elements of the first super-diagonal of U.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] DU2
! 89: *> \verbatim
! 90: *> DU2 is DOUBLE PRECISION array, dimension (N-2)
! 91: *> The (n-2) elements of the second super-diagonal of U.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in] IPIV
! 95: *> \verbatim
! 96: *> IPIV is INTEGER array, dimension (N)
! 97: *> The pivot indices; for 1 <= i <= n, row i of the matrix was
! 98: *> interchanged with row IPIV(i). IPIV(i) will always be either
! 99: *> i or i+1; IPIV(i) = i indicates a row interchange was not
! 100: *> required.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in,out] B
! 104: *> \verbatim
! 105: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 106: *> On entry, the matrix of right hand side vectors B.
! 107: *> On exit, B is overwritten by the solution vectors X.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[in] LDB
! 111: *> \verbatim
! 112: *> LDB is INTEGER
! 113: *> The leading dimension of the array B. LDB >= max(1,N).
! 114: *> \endverbatim
! 115: *
! 116: * Authors:
! 117: * ========
! 118: *
! 119: *> \author Univ. of Tennessee
! 120: *> \author Univ. of California Berkeley
! 121: *> \author Univ. of Colorado Denver
! 122: *> \author NAG Ltd.
! 123: *
! 124: *> \date November 2011
! 125: *
! 126: *> \ingroup doubleOTHERauxiliary
! 127: *
! 128: * =====================================================================
1.1 bertrand 129: SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
130: *
1.9 ! bertrand 131: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 134: * November 2011
1.1 bertrand 135: *
136: * .. Scalar Arguments ..
137: INTEGER ITRANS, LDB, N, NRHS
138: * ..
139: * .. Array Arguments ..
140: INTEGER IPIV( * )
141: DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Local Scalars ..
147: INTEGER I, IP, J
148: DOUBLE PRECISION TEMP
149: * ..
150: * .. Executable Statements ..
151: *
152: * Quick return if possible
153: *
154: IF( N.EQ.0 .OR. NRHS.EQ.0 )
155: $ RETURN
156: *
157: IF( ITRANS.EQ.0 ) THEN
158: *
159: * Solve A*X = B using the LU factorization of A,
160: * overwriting each right hand side vector with its solution.
161: *
162: IF( NRHS.LE.1 ) THEN
163: J = 1
164: 10 CONTINUE
165: *
166: * Solve L*x = b.
167: *
168: DO 20 I = 1, N - 1
169: IP = IPIV( I )
170: TEMP = B( I+1-IP+I, J ) - DL( I )*B( IP, J )
171: B( I, J ) = B( IP, J )
172: B( I+1, J ) = TEMP
173: 20 CONTINUE
174: *
175: * Solve U*x = b.
176: *
177: B( N, J ) = B( N, J ) / D( N )
178: IF( N.GT.1 )
179: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
180: $ D( N-1 )
181: DO 30 I = N - 2, 1, -1
182: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
183: $ B( I+2, J ) ) / D( I )
184: 30 CONTINUE
185: IF( J.LT.NRHS ) THEN
186: J = J + 1
187: GO TO 10
188: END IF
189: ELSE
190: DO 60 J = 1, NRHS
191: *
192: * Solve L*x = b.
193: *
194: DO 40 I = 1, N - 1
195: IF( IPIV( I ).EQ.I ) THEN
196: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
197: ELSE
198: TEMP = B( I, J )
199: B( I, J ) = B( I+1, J )
200: B( I+1, J ) = TEMP - DL( I )*B( I, J )
201: END IF
202: 40 CONTINUE
203: *
204: * Solve U*x = b.
205: *
206: B( N, J ) = B( N, J ) / D( N )
207: IF( N.GT.1 )
208: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
209: $ D( N-1 )
210: DO 50 I = N - 2, 1, -1
211: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
212: $ B( I+2, J ) ) / D( I )
213: 50 CONTINUE
214: 60 CONTINUE
215: END IF
216: ELSE
217: *
1.8 bertrand 218: * Solve A**T * X = B.
1.1 bertrand 219: *
220: IF( NRHS.LE.1 ) THEN
221: *
1.8 bertrand 222: * Solve U**T*x = b.
1.1 bertrand 223: *
224: J = 1
225: 70 CONTINUE
226: B( 1, J ) = B( 1, J ) / D( 1 )
227: IF( N.GT.1 )
228: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
229: DO 80 I = 3, N
230: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
231: $ B( I-2, J ) ) / D( I )
232: 80 CONTINUE
233: *
1.8 bertrand 234: * Solve L**T*x = b.
1.1 bertrand 235: *
236: DO 90 I = N - 1, 1, -1
237: IP = IPIV( I )
238: TEMP = B( I, J ) - DL( I )*B( I+1, J )
239: B( I, J ) = B( IP, J )
240: B( IP, J ) = TEMP
241: 90 CONTINUE
242: IF( J.LT.NRHS ) THEN
243: J = J + 1
244: GO TO 70
245: END IF
246: *
247: ELSE
248: DO 120 J = 1, NRHS
249: *
1.8 bertrand 250: * Solve U**T*x = b.
1.1 bertrand 251: *
252: B( 1, J ) = B( 1, J ) / D( 1 )
253: IF( N.GT.1 )
254: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
255: DO 100 I = 3, N
256: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
257: $ DU2( I-2 )*B( I-2, J ) ) / D( I )
258: 100 CONTINUE
259: DO 110 I = N - 1, 1, -1
260: IF( IPIV( I ).EQ.I ) THEN
261: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
262: ELSE
263: TEMP = B( I+1, J )
264: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
265: B( I, J ) = TEMP
266: END IF
267: 110 CONTINUE
268: 120 CONTINUE
269: END IF
270: END IF
271: *
272: * End of DGTTS2
273: *
274: END
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