Annotation of rpl/lapack/lapack/dpptrs.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DPPTRS
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DPPTRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrs.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER 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: *> DPPTRS solves a system of linear equations A*X = B with a symmetric
! 38: *> positive definite matrix A in packed storage using the Cholesky
! 39: *> factorization A = U**T*U or A = L*L**T computed by DPPTRF.
! 40: *> \endverbatim
! 41: *
! 42: * Arguments:
! 43: * ==========
! 44: *
! 45: *> \param[in] UPLO
! 46: *> \verbatim
! 47: *> UPLO is CHARACTER*1
! 48: *> = 'U': Upper triangle of A is stored;
! 49: *> = 'L': Lower triangle of A is stored.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] N
! 53: *> \verbatim
! 54: *> N is INTEGER
! 55: *> The order of the matrix A. N >= 0.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] NRHS
! 59: *> \verbatim
! 60: *> NRHS is INTEGER
! 61: *> The number of right hand sides, i.e., the number of columns
! 62: *> of the matrix B. NRHS >= 0.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] AP
! 66: *> \verbatim
! 67: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 68: *> The triangular factor U or L from the Cholesky factorization
! 69: *> A = U**T*U or A = L*L**T, packed columnwise in a linear
! 70: *> array. The j-th column of U or L is stored in the array AP
! 71: *> as follows:
! 72: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
! 73: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in,out] B
! 77: *> \verbatim
! 78: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 79: *> On entry, the right hand side matrix B.
! 80: *> On exit, the solution matrix X.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] LDB
! 84: *> \verbatim
! 85: *> LDB is INTEGER
! 86: *> The leading dimension of the array B. LDB >= max(1,N).
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[out] INFO
! 90: *> \verbatim
! 91: *> INFO is INTEGER
! 92: *> = 0: successful exit
! 93: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 94: *> \endverbatim
! 95: *
! 96: * Authors:
! 97: * ========
! 98: *
! 99: *> \author Univ. of Tennessee
! 100: *> \author Univ. of California Berkeley
! 101: *> \author Univ. of Colorado Denver
! 102: *> \author NAG Ltd.
! 103: *
! 104: *> \date November 2011
! 105: *
! 106: *> \ingroup doubleOTHERcomputational
! 107: *
! 108: * =====================================================================
1.1 bertrand 109: SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
110: *
1.9 ! bertrand 111: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 112: * -- LAPACK is a software package provided by Univ. of Tennessee, --
113: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 114: * November 2011
1.1 bertrand 115: *
116: * .. Scalar Arguments ..
117: CHARACTER UPLO
118: INTEGER INFO, LDB, N, NRHS
119: * ..
120: * .. Array Arguments ..
121: DOUBLE PRECISION AP( * ), B( LDB, * )
122: * ..
123: *
124: * =====================================================================
125: *
126: * .. Local Scalars ..
127: LOGICAL UPPER
128: INTEGER I
129: * ..
130: * .. External Functions ..
131: LOGICAL LSAME
132: EXTERNAL LSAME
133: * ..
134: * .. External Subroutines ..
135: EXTERNAL DTPSV, XERBLA
136: * ..
137: * .. Intrinsic Functions ..
138: INTRINSIC MAX
139: * ..
140: * .. Executable Statements ..
141: *
142: * Test the input parameters.
143: *
144: INFO = 0
145: UPPER = LSAME( UPLO, 'U' )
146: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
147: INFO = -1
148: ELSE IF( N.LT.0 ) THEN
149: INFO = -2
150: ELSE IF( NRHS.LT.0 ) THEN
151: INFO = -3
152: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
153: INFO = -6
154: END IF
155: IF( INFO.NE.0 ) THEN
156: CALL XERBLA( 'DPPTRS', -INFO )
157: RETURN
158: END IF
159: *
160: * Quick return if possible
161: *
162: IF( N.EQ.0 .OR. NRHS.EQ.0 )
163: $ RETURN
164: *
165: IF( UPPER ) THEN
166: *
1.8 bertrand 167: * Solve A*X = B where A = U**T * U.
1.1 bertrand 168: *
169: DO 10 I = 1, NRHS
170: *
1.8 bertrand 171: * Solve U**T *X = B, overwriting B with X.
1.1 bertrand 172: *
173: CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', N, AP,
174: $ B( 1, I ), 1 )
175: *
176: * Solve U*X = B, overwriting B with X.
177: *
178: CALL DTPSV( 'Upper', 'No transpose', 'Non-unit', N, AP,
179: $ B( 1, I ), 1 )
180: 10 CONTINUE
181: ELSE
182: *
1.8 bertrand 183: * Solve A*X = B where A = L * L**T.
1.1 bertrand 184: *
185: DO 20 I = 1, NRHS
186: *
187: * Solve L*Y = B, overwriting B with X.
188: *
189: CALL DTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
190: $ B( 1, I ), 1 )
191: *
1.8 bertrand 192: * Solve L**T *X = Y, overwriting B with X.
1.1 bertrand 193: *
194: CALL DTPSV( 'Lower', 'Transpose', 'Non-unit', N, AP,
195: $ B( 1, I ), 1 )
196: 20 CONTINUE
197: END IF
198: *
199: RETURN
200: *
201: * End of DPPTRS
202: *
203: END
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