Annotation of rpl/lapack/lapack/dgetrs.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DGETRS
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGETRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrs.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER TRANS
! 25: * INTEGER INFO, LDA, LDB, N, NRHS
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DGETRS solves a system of linear equations
! 39: *> A * X = B or A**T * X = B
! 40: *> with a general N-by-N matrix A using the LU factorization computed
! 41: *> by DGETRF.
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] TRANS
! 48: *> \verbatim
! 49: *> TRANS is CHARACTER*1
! 50: *> Specifies the form of the system of equations:
! 51: *> = 'N': A * X = B (No transpose)
! 52: *> = 'T': A**T* X = B (Transpose)
! 53: *> = 'C': A**T* X = B (Conjugate transpose = Transpose)
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] N
! 57: *> \verbatim
! 58: *> N is INTEGER
! 59: *> The order of the matrix A. N >= 0.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] NRHS
! 63: *> \verbatim
! 64: *> NRHS is INTEGER
! 65: *> The number of right hand sides, i.e., the number of columns
! 66: *> of the matrix B. NRHS >= 0.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] A
! 70: *> \verbatim
! 71: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 72: *> The factors L and U from the factorization A = P*L*U
! 73: *> as computed by DGETRF.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] LDA
! 77: *> \verbatim
! 78: *> LDA is INTEGER
! 79: *> The leading dimension of the array A. LDA >= max(1,N).
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] IPIV
! 83: *> \verbatim
! 84: *> IPIV is INTEGER array, dimension (N)
! 85: *> The pivot indices from DGETRF; for 1<=i<=N, row i of the
! 86: *> matrix was interchanged with row IPIV(i).
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in,out] B
! 90: *> \verbatim
! 91: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 92: *> On entry, the right hand side matrix B.
! 93: *> On exit, the 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: *> \endverbatim
! 108: *
! 109: * Authors:
! 110: * ========
! 111: *
! 112: *> \author Univ. of Tennessee
! 113: *> \author Univ. of California Berkeley
! 114: *> \author Univ. of Colorado Denver
! 115: *> \author NAG Ltd.
! 116: *
! 117: *> \date November 2011
! 118: *
! 119: *> \ingroup doubleGEcomputational
! 120: *
! 121: * =====================================================================
1.1 bertrand 122: SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
123: *
1.9 ! bertrand 124: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 127: * November 2011
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: CHARACTER TRANS
131: INTEGER INFO, LDA, LDB, N, NRHS
132: * ..
133: * .. Array Arguments ..
134: INTEGER IPIV( * )
135: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
136: * ..
137: *
138: * =====================================================================
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ONE
142: PARAMETER ( ONE = 1.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: LOGICAL NOTRAN
146: * ..
147: * .. External Functions ..
148: LOGICAL LSAME
149: EXTERNAL LSAME
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL DLASWP, DTRSM, XERBLA
153: * ..
154: * .. Intrinsic Functions ..
155: INTRINSIC MAX
156: * ..
157: * .. Executable Statements ..
158: *
159: * Test the input parameters.
160: *
161: INFO = 0
162: NOTRAN = LSAME( TRANS, 'N' )
163: IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
164: $ LSAME( TRANS, 'C' ) ) THEN
165: INFO = -1
166: ELSE IF( N.LT.0 ) THEN
167: INFO = -2
168: ELSE IF( NRHS.LT.0 ) THEN
169: INFO = -3
170: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
171: INFO = -5
172: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
173: INFO = -8
174: END IF
175: IF( INFO.NE.0 ) THEN
176: CALL XERBLA( 'DGETRS', -INFO )
177: RETURN
178: END IF
179: *
180: * Quick return if possible
181: *
182: IF( N.EQ.0 .OR. NRHS.EQ.0 )
183: $ RETURN
184: *
185: IF( NOTRAN ) THEN
186: *
187: * Solve A * X = B.
188: *
189: * Apply row interchanges to the right hand sides.
190: *
191: CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 )
192: *
193: * Solve L*X = B, overwriting B with X.
194: *
195: CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS,
196: $ ONE, A, LDA, B, LDB )
197: *
198: * Solve U*X = B, overwriting B with X.
199: *
200: CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
201: $ NRHS, ONE, A, LDA, B, LDB )
202: ELSE
203: *
1.8 bertrand 204: * Solve A**T * X = B.
1.1 bertrand 205: *
1.8 bertrand 206: * Solve U**T *X = B, overwriting B with X.
1.1 bertrand 207: *
208: CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
209: $ ONE, A, LDA, B, LDB )
210: *
1.8 bertrand 211: * Solve L**T *X = B, overwriting B with X.
1.1 bertrand 212: *
213: CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE,
214: $ A, LDA, B, LDB )
215: *
216: * Apply row interchanges to the solution vectors.
217: *
218: CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 )
219: END IF
220: *
221: RETURN
222: *
223: * End of DGETRS
224: *
225: END
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