Annotation of rpl/lapack/lapack/zgttrf.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZGTTRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGTTRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgttrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgttrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgttrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER IPIV( * )
! 28: * COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
! 38: *> using elimination with partial pivoting and row interchanges.
! 39: *>
! 40: *> The factorization has the form
! 41: *> A = L * U
! 42: *> where L is a product of permutation and unit lower bidiagonal
! 43: *> matrices and U is upper triangular with nonzeros in only the main
! 44: *> diagonal and first two superdiagonals.
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] N
! 51: *> \verbatim
! 52: *> N is INTEGER
! 53: *> The order of the matrix A.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in,out] DL
! 57: *> \verbatim
! 58: *> DL is COMPLEX*16 array, dimension (N-1)
! 59: *> On entry, DL must contain the (n-1) sub-diagonal elements of
! 60: *> A.
! 61: *>
! 62: *> On exit, DL is overwritten by the (n-1) multipliers that
! 63: *> define the matrix L from the LU factorization of A.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in,out] D
! 67: *> \verbatim
! 68: *> D is COMPLEX*16 array, dimension (N)
! 69: *> On entry, D must contain the diagonal elements of A.
! 70: *>
! 71: *> On exit, D is overwritten by the n diagonal elements of the
! 72: *> upper triangular matrix U from the LU factorization of A.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in,out] DU
! 76: *> \verbatim
! 77: *> DU is COMPLEX*16 array, dimension (N-1)
! 78: *> On entry, DU must contain the (n-1) super-diagonal elements
! 79: *> of A.
! 80: *>
! 81: *> On exit, DU is overwritten by the (n-1) elements of the first
! 82: *> super-diagonal of U.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[out] DU2
! 86: *> \verbatim
! 87: *> DU2 is COMPLEX*16 array, dimension (N-2)
! 88: *> On exit, DU2 is overwritten by the (n-2) elements of the
! 89: *> second super-diagonal of U.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] IPIV
! 93: *> \verbatim
! 94: *> IPIV is INTEGER array, dimension (N)
! 95: *> The pivot indices; for 1 <= i <= n, row i of the matrix was
! 96: *> interchanged with row IPIV(i). IPIV(i) will always be either
! 97: *> i or i+1; IPIV(i) = i indicates a row interchange was not
! 98: *> required.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[out] INFO
! 102: *> \verbatim
! 103: *> INFO is INTEGER
! 104: *> = 0: successful exit
! 105: *> < 0: if INFO = -k, the k-th argument had an illegal value
! 106: *> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
! 107: *> has been completed, but the factor U is exactly
! 108: *> singular, and division by zero will occur if it is used
! 109: *> to solve a system of equations.
! 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 ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
126: *
1.8 ! 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..--
1.8 ! bertrand 130: * November 2011
1.1 bertrand 131: *
132: * .. Scalar Arguments ..
133: INTEGER INFO, N
134: * ..
135: * .. Array Arguments ..
136: INTEGER IPIV( * )
137: COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
138: * ..
139: *
140: * =====================================================================
141: *
142: * .. Parameters ..
143: DOUBLE PRECISION ZERO
144: PARAMETER ( ZERO = 0.0D+0 )
145: * ..
146: * .. Local Scalars ..
147: INTEGER I
148: COMPLEX*16 FACT, TEMP, ZDUM
149: * ..
150: * .. External Subroutines ..
151: EXTERNAL XERBLA
152: * ..
153: * .. Intrinsic Functions ..
154: INTRINSIC ABS, DBLE, DIMAG
155: * ..
156: * .. Statement Functions ..
157: DOUBLE PRECISION CABS1
158: * ..
159: * .. Statement Function definitions ..
160: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
161: * ..
162: * .. Executable Statements ..
163: *
164: INFO = 0
165: IF( N.LT.0 ) THEN
166: INFO = -1
167: CALL XERBLA( 'ZGTTRF', -INFO )
168: RETURN
169: END IF
170: *
171: * Quick return if possible
172: *
173: IF( N.EQ.0 )
174: $ RETURN
175: *
176: * Initialize IPIV(i) = i and DU2(i) = 0
177: *
178: DO 10 I = 1, N
179: IPIV( I ) = I
180: 10 CONTINUE
181: DO 20 I = 1, N - 2
182: DU2( I ) = ZERO
183: 20 CONTINUE
184: *
185: DO 30 I = 1, N - 2
186: IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
187: *
188: * No row interchange required, eliminate DL(I)
189: *
190: IF( CABS1( D( I ) ).NE.ZERO ) THEN
191: FACT = DL( I ) / D( I )
192: DL( I ) = FACT
193: D( I+1 ) = D( I+1 ) - FACT*DU( I )
194: END IF
195: ELSE
196: *
197: * Interchange rows I and I+1, eliminate DL(I)
198: *
199: FACT = D( I ) / DL( I )
200: D( I ) = DL( I )
201: DL( I ) = FACT
202: TEMP = DU( I )
203: DU( I ) = D( I+1 )
204: D( I+1 ) = TEMP - FACT*D( I+1 )
205: DU2( I ) = DU( I+1 )
206: DU( I+1 ) = -FACT*DU( I+1 )
207: IPIV( I ) = I + 1
208: END IF
209: 30 CONTINUE
210: IF( N.GT.1 ) THEN
211: I = N - 1
212: IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
213: IF( CABS1( D( I ) ).NE.ZERO ) THEN
214: FACT = DL( I ) / D( I )
215: DL( I ) = FACT
216: D( I+1 ) = D( I+1 ) - FACT*DU( I )
217: END IF
218: ELSE
219: FACT = D( I ) / DL( I )
220: D( I ) = DL( I )
221: DL( I ) = FACT
222: TEMP = DU( I )
223: DU( I ) = D( I+1 )
224: D( I+1 ) = TEMP - FACT*D( I+1 )
225: IPIV( I ) = I + 1
226: END IF
227: END IF
228: *
229: * Check for a zero on the diagonal of U.
230: *
231: DO 40 I = 1, N
232: IF( CABS1( D( I ) ).EQ.ZERO ) THEN
233: INFO = I
234: GO TO 50
235: END IF
236: 40 CONTINUE
237: 50 CONTINUE
238: *
239: RETURN
240: *
241: * End of ZGTTRF
242: *
243: END
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