Annotation of rpl/lapack/lapack/dtptrs.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DTPTRS
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTPTRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtptrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtptrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtptrs.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER DIAG, TRANS, UPLO
! 25: * INTEGER INFO, LDB, N, NRHS
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION AP( * ), B( LDB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DTPTRS solves a triangular system of the form
! 38: *>
! 39: *> A * X = B or A**T * X = B,
! 40: *>
! 41: *> where A is a triangular matrix of order N stored in packed format,
! 42: *> and B is an N-by-NRHS matrix. A check is made to verify that A is
! 43: *> nonsingular.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] UPLO
! 50: *> \verbatim
! 51: *> UPLO is CHARACTER*1
! 52: *> = 'U': A is upper triangular;
! 53: *> = 'L': A is lower triangular.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] TRANS
! 57: *> \verbatim
! 58: *> TRANS is CHARACTER*1
! 59: *> Specifies the form of the system of equations:
! 60: *> = 'N': A * X = B (No transpose)
! 61: *> = 'T': A**T * X = B (Transpose)
! 62: *> = 'C': A**H * X = B (Conjugate transpose = Transpose)
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] DIAG
! 66: *> \verbatim
! 67: *> DIAG is CHARACTER*1
! 68: *> = 'N': A is non-unit triangular;
! 69: *> = 'U': A is unit triangular.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] N
! 73: *> \verbatim
! 74: *> N is INTEGER
! 75: *> The order of the matrix A. N >= 0.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] NRHS
! 79: *> \verbatim
! 80: *> NRHS is INTEGER
! 81: *> The number of right hand sides, i.e., the number of columns
! 82: *> of the matrix B. NRHS >= 0.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] AP
! 86: *> \verbatim
! 87: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 88: *> The upper or lower triangular matrix A, packed columnwise in
! 89: *> a linear array. The j-th column of A is stored in the array
! 90: *> AP as follows:
! 91: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 92: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in,out] B
! 96: *> \verbatim
! 97: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 98: *> On entry, the right hand side matrix B.
! 99: *> On exit, if INFO = 0, the solution matrix X.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] LDB
! 103: *> \verbatim
! 104: *> LDB is INTEGER
! 105: *> The leading dimension of the array B. LDB >= max(1,N).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] INFO
! 109: *> \verbatim
! 110: *> INFO is INTEGER
! 111: *> = 0: successful exit
! 112: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 113: *> > 0: if INFO = i, the i-th diagonal element of A is zero,
! 114: *> indicating that the matrix is singular and the
! 115: *> solutions X have not been computed.
! 116: *> \endverbatim
! 117: *
! 118: * Authors:
! 119: * ========
! 120: *
! 121: *> \author Univ. of Tennessee
! 122: *> \author Univ. of California Berkeley
! 123: *> \author Univ. of Colorado Denver
! 124: *> \author NAG Ltd.
! 125: *
! 126: *> \date November 2011
! 127: *
! 128: *> \ingroup doubleOTHERcomputational
! 129: *
! 130: * =====================================================================
1.1 bertrand 131: SUBROUTINE DTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
132: *
1.9 ! bertrand 133: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 136: * November 2011
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER DIAG, TRANS, UPLO
140: INTEGER INFO, LDB, N, NRHS
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION AP( * ), B( LDB, * )
144: * ..
145: *
146: * =====================================================================
147: *
148: * .. Parameters ..
149: DOUBLE PRECISION ZERO
150: PARAMETER ( ZERO = 0.0D+0 )
151: * ..
152: * .. Local Scalars ..
153: LOGICAL NOUNIT, UPPER
154: INTEGER J, JC
155: * ..
156: * .. External Functions ..
157: LOGICAL LSAME
158: EXTERNAL LSAME
159: * ..
160: * .. External Subroutines ..
161: EXTERNAL DTPSV, XERBLA
162: * ..
163: * .. Intrinsic Functions ..
164: INTRINSIC MAX
165: * ..
166: * .. Executable Statements ..
167: *
168: * Test the input parameters.
169: *
170: INFO = 0
171: UPPER = LSAME( UPLO, 'U' )
172: NOUNIT = LSAME( DIAG, 'N' )
173: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
174: INFO = -1
175: ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
176: $ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
177: INFO = -2
178: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
179: INFO = -3
180: ELSE IF( N.LT.0 ) THEN
181: INFO = -4
182: ELSE IF( NRHS.LT.0 ) THEN
183: INFO = -5
184: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
185: INFO = -8
186: END IF
187: IF( INFO.NE.0 ) THEN
188: CALL XERBLA( 'DTPTRS', -INFO )
189: RETURN
190: END IF
191: *
192: * Quick return if possible
193: *
194: IF( N.EQ.0 )
195: $ RETURN
196: *
197: * Check for singularity.
198: *
199: IF( NOUNIT ) THEN
200: IF( UPPER ) THEN
201: JC = 1
202: DO 10 INFO = 1, N
203: IF( AP( JC+INFO-1 ).EQ.ZERO )
204: $ RETURN
205: JC = JC + INFO
206: 10 CONTINUE
207: ELSE
208: JC = 1
209: DO 20 INFO = 1, N
210: IF( AP( JC ).EQ.ZERO )
211: $ RETURN
212: JC = JC + N - INFO + 1
213: 20 CONTINUE
214: END IF
215: END IF
216: INFO = 0
217: *
1.8 bertrand 218: * Solve A * x = b or A**T * x = b.
1.1 bertrand 219: *
220: DO 30 J = 1, NRHS
221: CALL DTPSV( UPLO, TRANS, DIAG, N, AP, B( 1, J ), 1 )
222: 30 CONTINUE
223: *
224: RETURN
225: *
226: * End of DTPTRS
227: *
228: END
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