Annotation of rpl/lapack/lapack/dpftrs.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b DPFTRS
1.1 bertrand 2: *
1.7 ! bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.7 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.7 ! bertrand 8: *> \htmlonly
! 9: *> Download DPFTRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftrs.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER TRANSR, UPLO
! 25: * INTEGER INFO, LDB, N, NRHS
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION A( 0: * ), B( LDB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DPFTRS solves a system of linear equations A*X = B with a symmetric
! 38: *> positive definite matrix A using the Cholesky factorization
! 39: *> A = U**T*U or A = L*L**T computed by DPFTRF.
! 40: *> \endverbatim
! 41: *
! 42: * Arguments:
! 43: * ==========
! 44: *
! 45: *> \param[in] TRANSR
! 46: *> \verbatim
! 47: *> TRANSR is CHARACTER*1
! 48: *> = 'N': The Normal TRANSR of RFP A is stored;
! 49: *> = 'T': The Transpose TRANSR of RFP A is stored.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] UPLO
! 53: *> \verbatim
! 54: *> UPLO is CHARACTER*1
! 55: *> = 'U': Upper triangle of RFP A is stored;
! 56: *> = 'L': Lower triangle of RFP A is stored.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in] N
! 60: *> \verbatim
! 61: *> N is INTEGER
! 62: *> The order of the matrix A. N >= 0.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] NRHS
! 66: *> \verbatim
! 67: *> NRHS is INTEGER
! 68: *> The number of right hand sides, i.e., the number of columns
! 69: *> of the matrix B. NRHS >= 0.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] A
! 73: *> \verbatim
! 74: *> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
! 75: *> The triangular factor U or L from the Cholesky factorization
! 76: *> of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
! 77: *> See note below for more details about RFP A.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in,out] B
! 81: *> \verbatim
! 82: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 83: *> On entry, the right hand side matrix B.
! 84: *> On exit, the solution matrix X.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] LDB
! 88: *> \verbatim
! 89: *> LDB is INTEGER
! 90: *> The leading dimension of the array B. LDB >= max(1,N).
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[out] INFO
! 94: *> \verbatim
! 95: *> INFO is INTEGER
! 96: *> = 0: successful exit
! 97: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 98: *> \endverbatim
! 99: *
! 100: * Authors:
! 101: * ========
! 102: *
! 103: *> \author Univ. of Tennessee
! 104: *> \author Univ. of California Berkeley
! 105: *> \author Univ. of Colorado Denver
! 106: *> \author NAG Ltd.
! 107: *
! 108: *> \date November 2011
! 109: *
! 110: *> \ingroup doubleOTHERcomputational
! 111: *
! 112: *> \par Further Details:
! 113: * =====================
! 114: *>
! 115: *> \verbatim
! 116: *>
! 117: *> We first consider Rectangular Full Packed (RFP) Format when N is
! 118: *> even. We give an example where N = 6.
! 119: *>
! 120: *> AP is Upper AP is Lower
! 121: *>
! 122: *> 00 01 02 03 04 05 00
! 123: *> 11 12 13 14 15 10 11
! 124: *> 22 23 24 25 20 21 22
! 125: *> 33 34 35 30 31 32 33
! 126: *> 44 45 40 41 42 43 44
! 127: *> 55 50 51 52 53 54 55
! 128: *>
! 129: *>
! 130: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 131: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
! 132: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
! 133: *> the transpose of the first three columns of AP upper.
! 134: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
! 135: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
! 136: *> the transpose of the last three columns of AP lower.
! 137: *> This covers the case N even and TRANSR = 'N'.
! 138: *>
! 139: *> RFP A RFP A
! 140: *>
! 141: *> 03 04 05 33 43 53
! 142: *> 13 14 15 00 44 54
! 143: *> 23 24 25 10 11 55
! 144: *> 33 34 35 20 21 22
! 145: *> 00 44 45 30 31 32
! 146: *> 01 11 55 40 41 42
! 147: *> 02 12 22 50 51 52
! 148: *>
! 149: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 150: *> transpose of RFP A above. One therefore gets:
! 151: *>
! 152: *>
! 153: *> RFP A RFP A
! 154: *>
! 155: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
! 156: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
! 157: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
! 158: *>
! 159: *>
! 160: *> We then consider Rectangular Full Packed (RFP) Format when N is
! 161: *> odd. We give an example where N = 5.
! 162: *>
! 163: *> AP is Upper AP is Lower
! 164: *>
! 165: *> 00 01 02 03 04 00
! 166: *> 11 12 13 14 10 11
! 167: *> 22 23 24 20 21 22
! 168: *> 33 34 30 31 32 33
! 169: *> 44 40 41 42 43 44
! 170: *>
! 171: *>
! 172: *> Let TRANSR = 'N'. RFP holds AP as follows:
! 173: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
! 174: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
! 175: *> the transpose of the first two columns of AP upper.
! 176: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
! 177: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
! 178: *> the transpose of the last two columns of AP lower.
! 179: *> This covers the case N odd and TRANSR = 'N'.
! 180: *>
! 181: *> RFP A RFP A
! 182: *>
! 183: *> 02 03 04 00 33 43
! 184: *> 12 13 14 10 11 44
! 185: *> 22 23 24 20 21 22
! 186: *> 00 33 34 30 31 32
! 187: *> 01 11 44 40 41 42
! 188: *>
! 189: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
! 190: *> transpose of RFP A above. One therefore gets:
! 191: *>
! 192: *> RFP A RFP A
! 193: *>
! 194: *> 02 12 22 00 01 00 10 20 30 40 50
! 195: *> 03 13 23 33 11 33 11 21 31 41 51
! 196: *> 04 14 24 34 44 43 44 22 32 42 52
! 197: *> \endverbatim
! 198: *>
! 199: * =====================================================================
! 200: SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
! 201: *
! 202: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 203: * -- LAPACK is a software package provided by Univ. of Tennessee, --
204: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 205: * November 2011
1.1 bertrand 206: *
207: * .. Scalar Arguments ..
208: CHARACTER TRANSR, UPLO
209: INTEGER INFO, LDB, N, NRHS
210: * ..
211: * .. Array Arguments ..
212: DOUBLE PRECISION A( 0: * ), B( LDB, * )
213: * ..
214: *
215: * =====================================================================
216: *
217: * .. Parameters ..
218: DOUBLE PRECISION ONE
219: PARAMETER ( ONE = 1.0D+0 )
220: * ..
221: * .. Local Scalars ..
222: LOGICAL LOWER, NORMALTRANSR
223: * ..
224: * .. External Functions ..
225: LOGICAL LSAME
226: EXTERNAL LSAME
227: * ..
228: * .. External Subroutines ..
229: EXTERNAL XERBLA, DTFSM
230: * ..
231: * .. Intrinsic Functions ..
232: INTRINSIC MAX
233: * ..
234: * .. Executable Statements ..
235: *
236: * Test the input parameters.
237: *
238: INFO = 0
239: NORMALTRANSR = LSAME( TRANSR, 'N' )
240: LOWER = LSAME( UPLO, 'L' )
241: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
242: INFO = -1
243: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
244: INFO = -2
245: ELSE IF( N.LT.0 ) THEN
246: INFO = -3
247: ELSE IF( NRHS.LT.0 ) THEN
248: INFO = -4
249: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
250: INFO = -7
251: END IF
252: IF( INFO.NE.0 ) THEN
253: CALL XERBLA( 'DPFTRS', -INFO )
254: RETURN
255: END IF
256: *
257: * Quick return if possible
258: *
259: IF( N.EQ.0 .OR. NRHS.EQ.0 )
1.6 bertrand 260: $ RETURN
1.1 bertrand 261: *
262: * start execution: there are two triangular solves
263: *
264: IF( LOWER ) THEN
265: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 266: $ LDB )
1.1 bertrand 267: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 268: $ LDB )
1.1 bertrand 269: ELSE
270: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 271: $ LDB )
1.1 bertrand 272: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 273: $ LDB )
1.1 bertrand 274: END IF
275: *
276: RETURN
277: *
278: * End of DPFTRS
279: *
280: END
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