Annotation of rpl/lapack/lapack/dtrti2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DTRTI2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTRTI2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrti2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrti2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrti2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTRTI2( 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: *> DTRTI2 computes the inverse of a real upper or lower triangular
! 38: *> matrix.
! 39: *>
! 40: *> This is the Level 2 BLAS version of the algorithm.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] UPLO
! 47: *> \verbatim
! 48: *> UPLO is CHARACTER*1
! 49: *> Specifies whether the matrix A is upper or lower triangular.
! 50: *> = 'U': Upper triangular
! 51: *> = 'L': Lower triangular
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] DIAG
! 55: *> \verbatim
! 56: *> DIAG is CHARACTER*1
! 57: *> Specifies whether or not the matrix A is unit triangular.
! 58: *> = 'N': Non-unit triangular
! 59: *> = 'U': Unit triangular
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] N
! 63: *> \verbatim
! 64: *> N is INTEGER
! 65: *> The order of the matrix A. N >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in,out] A
! 69: *> \verbatim
! 70: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 71: *> On entry, the triangular matrix A. If UPLO = 'U', the
! 72: *> leading n by n upper triangular part of the array A contains
! 73: *> the upper triangular matrix, and the strictly lower
! 74: *> triangular part of A is not referenced. If UPLO = 'L', the
! 75: *> leading n by n lower triangular part of the array A contains
! 76: *> the lower triangular matrix, and the strictly upper
! 77: *> triangular part of A is not referenced. If DIAG = 'U', the
! 78: *> diagonal elements of A are also not referenced and are
! 79: *> assumed to be 1.
! 80: *>
! 81: *> On exit, the (triangular) inverse of the original matrix, in
! 82: *> the same storage format.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] LDA
! 86: *> \verbatim
! 87: *> LDA is INTEGER
! 88: *> The leading dimension of the array A. LDA >= max(1,N).
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[out] INFO
! 92: *> \verbatim
! 93: *> INFO is INTEGER
! 94: *> = 0: successful exit
! 95: *> < 0: if INFO = -k, the k-th argument had an illegal value
! 96: *> \endverbatim
! 97: *
! 98: * Authors:
! 99: * ========
! 100: *
! 101: *> \author Univ. of Tennessee
! 102: *> \author Univ. of California Berkeley
! 103: *> \author Univ. of Colorado Denver
! 104: *> \author NAG Ltd.
! 105: *
! 106: *> \date November 2011
! 107: *
! 108: *> \ingroup doubleOTHERcomputational
! 109: *
! 110: * =====================================================================
1.1 bertrand 111: SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
112: *
1.8 ! bertrand 113: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 114: * -- LAPACK is a software package provided by Univ. of Tennessee, --
115: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 116: * November 2011
1.1 bertrand 117: *
118: * .. Scalar Arguments ..
119: CHARACTER DIAG, UPLO
120: INTEGER INFO, LDA, N
121: * ..
122: * .. Array Arguments ..
123: DOUBLE PRECISION A( LDA, * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: DOUBLE PRECISION ONE
130: PARAMETER ( ONE = 1.0D+0 )
131: * ..
132: * .. Local Scalars ..
133: LOGICAL NOUNIT, UPPER
134: INTEGER J
135: DOUBLE PRECISION AJJ
136: * ..
137: * .. External Functions ..
138: LOGICAL LSAME
139: EXTERNAL LSAME
140: * ..
141: * .. External Subroutines ..
142: EXTERNAL DSCAL, DTRMV, XERBLA
143: * ..
144: * .. Intrinsic Functions ..
145: INTRINSIC MAX
146: * ..
147: * .. Executable Statements ..
148: *
149: * Test the input parameters.
150: *
151: INFO = 0
152: UPPER = LSAME( UPLO, 'U' )
153: NOUNIT = LSAME( DIAG, 'N' )
154: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
155: INFO = -1
156: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
157: INFO = -2
158: ELSE IF( N.LT.0 ) THEN
159: INFO = -3
160: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
161: INFO = -5
162: END IF
163: IF( INFO.NE.0 ) THEN
164: CALL XERBLA( 'DTRTI2', -INFO )
165: RETURN
166: END IF
167: *
168: IF( UPPER ) THEN
169: *
170: * Compute inverse of upper triangular matrix.
171: *
172: DO 10 J = 1, N
173: IF( NOUNIT ) THEN
174: A( J, J ) = ONE / A( J, J )
175: AJJ = -A( J, J )
176: ELSE
177: AJJ = -ONE
178: END IF
179: *
180: * Compute elements 1:j-1 of j-th column.
181: *
182: CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
183: $ A( 1, J ), 1 )
184: CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
185: 10 CONTINUE
186: ELSE
187: *
188: * Compute inverse of lower triangular matrix.
189: *
190: DO 20 J = N, 1, -1
191: IF( NOUNIT ) THEN
192: A( J, J ) = ONE / A( J, J )
193: AJJ = -A( J, J )
194: ELSE
195: AJJ = -ONE
196: END IF
197: IF( J.LT.N ) THEN
198: *
199: * Compute elements j+1:n of j-th column.
200: *
201: CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
202: $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
203: CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
204: END IF
205: 20 CONTINUE
206: END IF
207: *
208: RETURN
209: *
210: * End of DTRTI2
211: *
212: END
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