Annotation of rpl/lapack/lapack/dtrtri.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DTRTRI
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTRTRI + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrtri.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrtri.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrtri.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER DIAG, UPLO
! 25: * INTEGER INFO, LDA, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION A( LDA, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DTRTRI computes the inverse of a real upper or lower triangular
! 38: *> matrix A.
! 39: *>
! 40: *> This is the Level 3 BLAS version of the algorithm.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] UPLO
! 47: *> \verbatim
! 48: *> UPLO is CHARACTER*1
! 49: *> = 'U': A is upper triangular;
! 50: *> = 'L': A is lower triangular.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] DIAG
! 54: *> \verbatim
! 55: *> DIAG is CHARACTER*1
! 56: *> = 'N': A is non-unit triangular;
! 57: *> = 'U': A is unit triangular.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] N
! 61: *> \verbatim
! 62: *> N is INTEGER
! 63: *> The order of the matrix A. N >= 0.
! 64: *> \endverbatim
! 65: *>
! 66: *> \param[in,out] A
! 67: *> \verbatim
! 68: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 69: *> On entry, the triangular matrix A. If UPLO = 'U', the
! 70: *> leading N-by-N upper triangular part of the array A contains
! 71: *> the upper triangular matrix, and the strictly lower
! 72: *> triangular part of A is not referenced. If UPLO = 'L', the
! 73: *> leading N-by-N lower triangular part of the array A contains
! 74: *> the lower triangular matrix, and the strictly upper
! 75: *> triangular part of A is not referenced. If DIAG = 'U', the
! 76: *> diagonal elements of A are also not referenced and are
! 77: *> assumed to be 1.
! 78: *> On exit, the (triangular) inverse of the original matrix, in
! 79: *> the same storage format.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] LDA
! 83: *> \verbatim
! 84: *> LDA is INTEGER
! 85: *> The leading dimension of the array A. LDA >= max(1,N).
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[out] INFO
! 89: *> \verbatim
! 90: *> INFO is INTEGER
! 91: *> = 0: successful exit
! 92: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 93: *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
! 94: *> matrix is singular and its inverse can not be computed.
! 95: *> \endverbatim
! 96: *
! 97: * Authors:
! 98: * ========
! 99: *
! 100: *> \author Univ. of Tennessee
! 101: *> \author Univ. of California Berkeley
! 102: *> \author Univ. of Colorado Denver
! 103: *> \author NAG Ltd.
! 104: *
! 105: *> \date November 2011
! 106: *
! 107: *> \ingroup doubleOTHERcomputational
! 108: *
! 109: * =====================================================================
1.1 bertrand 110: SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
111: *
1.8 ! bertrand 112: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 113: * -- LAPACK is a software package provided by Univ. of Tennessee, --
114: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 115: * November 2011
1.1 bertrand 116: *
117: * .. Scalar Arguments ..
118: CHARACTER DIAG, UPLO
119: INTEGER INFO, LDA, N
120: * ..
121: * .. Array Arguments ..
122: DOUBLE PRECISION A( LDA, * )
123: * ..
124: *
125: * =====================================================================
126: *
127: * .. Parameters ..
128: DOUBLE PRECISION ONE, ZERO
129: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
130: * ..
131: * .. Local Scalars ..
132: LOGICAL NOUNIT, UPPER
133: INTEGER J, JB, NB, NN
134: * ..
135: * .. External Functions ..
136: LOGICAL LSAME
137: INTEGER ILAENV
138: EXTERNAL LSAME, ILAENV
139: * ..
140: * .. External Subroutines ..
141: EXTERNAL DTRMM, DTRSM, DTRTI2, XERBLA
142: * ..
143: * .. Intrinsic Functions ..
144: INTRINSIC MAX, MIN
145: * ..
146: * .. Executable Statements ..
147: *
148: * Test the input parameters.
149: *
150: INFO = 0
151: UPPER = LSAME( UPLO, 'U' )
152: NOUNIT = LSAME( DIAG, 'N' )
153: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
154: INFO = -1
155: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
156: INFO = -2
157: ELSE IF( N.LT.0 ) THEN
158: INFO = -3
159: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
160: INFO = -5
161: END IF
162: IF( INFO.NE.0 ) THEN
163: CALL XERBLA( 'DTRTRI', -INFO )
164: RETURN
165: END IF
166: *
167: * Quick return if possible
168: *
169: IF( N.EQ.0 )
170: $ RETURN
171: *
172: * Check for singularity if non-unit.
173: *
174: IF( NOUNIT ) THEN
175: DO 10 INFO = 1, N
176: IF( A( INFO, INFO ).EQ.ZERO )
177: $ RETURN
178: 10 CONTINUE
179: INFO = 0
180: END IF
181: *
182: * Determine the block size for this environment.
183: *
184: NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 )
185: IF( NB.LE.1 .OR. NB.GE.N ) THEN
186: *
187: * Use unblocked code
188: *
189: CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
190: ELSE
191: *
192: * Use blocked code
193: *
194: IF( UPPER ) THEN
195: *
196: * Compute inverse of upper triangular matrix
197: *
198: DO 20 J = 1, N, NB
199: JB = MIN( NB, N-J+1 )
200: *
201: * Compute rows 1:j-1 of current block column
202: *
203: CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
204: $ JB, ONE, A, LDA, A( 1, J ), LDA )
205: CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
206: $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
207: *
208: * Compute inverse of current diagonal block
209: *
210: CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
211: 20 CONTINUE
212: ELSE
213: *
214: * Compute inverse of lower triangular matrix
215: *
216: NN = ( ( N-1 ) / NB )*NB + 1
217: DO 30 J = NN, 1, -NB
218: JB = MIN( NB, N-J+1 )
219: IF( J+JB.LE.N ) THEN
220: *
221: * Compute rows j+jb:n of current block column
222: *
223: CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG,
224: $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
225: $ A( J+JB, J ), LDA )
226: CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG,
227: $ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
228: $ A( J+JB, J ), LDA )
229: END IF
230: *
231: * Compute inverse of current diagonal block
232: *
233: CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
234: 30 CONTINUE
235: END IF
236: END IF
237: *
238: RETURN
239: *
240: * End of DTRTRI
241: *
242: END
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