Annotation of rpl/lapack/lapack/zgtsv.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZGTSV
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGTSV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtsv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtsv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtsv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDB, N, NRHS
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> ZGTSV solves the equation
! 37: *>
! 38: *> A*X = B,
! 39: *>
! 40: *> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
! 41: *> partial pivoting.
! 42: *>
! 43: *> Note that the equation A**T *X = B may be solved by interchanging the
! 44: *> order of the arguments DU and DL.
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] N
! 51: *> \verbatim
! 52: *> N is INTEGER
! 53: *> The order of the matrix A. N >= 0.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] NRHS
! 57: *> \verbatim
! 58: *> NRHS is INTEGER
! 59: *> The number of right hand sides, i.e., the number of columns
! 60: *> of the matrix B. NRHS >= 0.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in,out] DL
! 64: *> \verbatim
! 65: *> DL is COMPLEX*16 array, dimension (N-1)
! 66: *> On entry, DL must contain the (n-1) subdiagonal elements of
! 67: *> A.
! 68: *> On exit, DL is overwritten by the (n-2) elements of the
! 69: *> second superdiagonal of the upper triangular matrix U from
! 70: *> the LU factorization of A, in DL(1), ..., DL(n-2).
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in,out] D
! 74: *> \verbatim
! 75: *> D is COMPLEX*16 array, dimension (N)
! 76: *> On entry, D must contain the diagonal elements of A.
! 77: *> On exit, D is overwritten by the n diagonal elements of U.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in,out] DU
! 81: *> \verbatim
! 82: *> DU is COMPLEX*16 array, dimension (N-1)
! 83: *> On entry, DU must contain the (n-1) superdiagonal elements
! 84: *> of A.
! 85: *> On exit, DU is overwritten by the (n-1) elements of the first
! 86: *> superdiagonal of U.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in,out] B
! 90: *> \verbatim
! 91: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 92: *> On entry, the N-by-NRHS right hand side matrix B.
! 93: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] LDB
! 97: *> \verbatim
! 98: *> LDB is INTEGER
! 99: *> The leading dimension of the array B. LDB >= max(1,N).
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[out] INFO
! 103: *> \verbatim
! 104: *> INFO is INTEGER
! 105: *> = 0: successful exit
! 106: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 107: *> > 0: if INFO = i, U(i,i) is exactly zero, and the solution
! 108: *> has not been computed. The factorization has not been
! 109: *> completed unless i = N.
! 110: *> \endverbatim
! 111: *
! 112: * Authors:
! 113: * ========
! 114: *
! 115: *> \author Univ. of Tennessee
! 116: *> \author Univ. of California Berkeley
! 117: *> \author Univ. of Colorado Denver
! 118: *> \author NAG Ltd.
! 119: *
! 120: *> \date November 2011
! 121: *
! 122: *> \ingroup complex16OTHERcomputational
! 123: *
! 124: * =====================================================================
1.1 bertrand 125: SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
126: *
1.9 ! bertrand 127: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 130: * November 2011
1.1 bertrand 131: *
132: * .. Scalar Arguments ..
133: INTEGER INFO, LDB, N, NRHS
134: * ..
135: * .. Array Arguments ..
136: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: COMPLEX*16 ZERO
143: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
144: * ..
145: * .. Local Scalars ..
146: INTEGER J, K
147: COMPLEX*16 MULT, TEMP, ZDUM
148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC ABS, DBLE, DIMAG, MAX
151: * ..
152: * .. External Subroutines ..
153: EXTERNAL XERBLA
154: * ..
155: * .. Statement Functions ..
156: DOUBLE PRECISION CABS1
157: * ..
158: * .. Statement Function definitions ..
159: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
160: * ..
161: * .. Executable Statements ..
162: *
163: INFO = 0
164: IF( N.LT.0 ) THEN
165: INFO = -1
166: ELSE IF( NRHS.LT.0 ) THEN
167: INFO = -2
168: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
169: INFO = -7
170: END IF
171: IF( INFO.NE.0 ) THEN
172: CALL XERBLA( 'ZGTSV ', -INFO )
173: RETURN
174: END IF
175: *
176: IF( N.EQ.0 )
177: $ RETURN
178: *
179: DO 30 K = 1, N - 1
180: IF( DL( K ).EQ.ZERO ) THEN
181: *
182: * Subdiagonal is zero, no elimination is required.
183: *
184: IF( D( K ).EQ.ZERO ) THEN
185: *
186: * Diagonal is zero: set INFO = K and return; a unique
187: * solution can not be found.
188: *
189: INFO = K
190: RETURN
191: END IF
192: ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
193: *
194: * No row interchange required
195: *
196: MULT = DL( K ) / D( K )
197: D( K+1 ) = D( K+1 ) - MULT*DU( K )
198: DO 10 J = 1, NRHS
199: B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
200: 10 CONTINUE
201: IF( K.LT.( N-1 ) )
202: $ DL( K ) = ZERO
203: ELSE
204: *
205: * Interchange rows K and K+1
206: *
207: MULT = D( K ) / DL( K )
208: D( K ) = DL( K )
209: TEMP = D( K+1 )
210: D( K+1 ) = DU( K ) - MULT*TEMP
211: IF( K.LT.( N-1 ) ) THEN
212: DL( K ) = DU( K+1 )
213: DU( K+1 ) = -MULT*DL( K )
214: END IF
215: DU( K ) = TEMP
216: DO 20 J = 1, NRHS
217: TEMP = B( K, J )
218: B( K, J ) = B( K+1, J )
219: B( K+1, J ) = TEMP - MULT*B( K+1, J )
220: 20 CONTINUE
221: END IF
222: 30 CONTINUE
223: IF( D( N ).EQ.ZERO ) THEN
224: INFO = N
225: RETURN
226: END IF
227: *
228: * Back solve with the matrix U from the factorization.
229: *
230: DO 50 J = 1, NRHS
231: B( N, J ) = B( N, J ) / D( N )
232: IF( N.GT.1 )
233: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
234: DO 40 K = N - 2, 1, -1
235: B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
236: $ B( K+2, J ) ) / D( K )
237: 40 CONTINUE
238: 50 CONTINUE
239: *
240: RETURN
241: *
242: * End of ZGTSV
243: *
244: END
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