Annotation of rpl/lapack/lapack/dposv.f, revision 1.9
1.9 ! bertrand 1: *> \brief <b> DPOSV computes the solution to system of linear equations A * X = B for PO matrices</b>
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DPOSV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dposv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dposv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dposv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDA, LDB, N, NRHS
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DPOSV computes the solution to a real system of linear equations
! 38: *> A * X = B,
! 39: *> where A is an N-by-N symmetric positive definite matrix and X and B
! 40: *> are N-by-NRHS matrices.
! 41: *>
! 42: *> The Cholesky decomposition is used to factor A as
! 43: *> A = U**T* U, if UPLO = 'U', or
! 44: *> A = L * L**T, if UPLO = 'L',
! 45: *> where U is an upper triangular matrix and L is a lower triangular
! 46: *> matrix. The factored form of A is then used to solve the system of
! 47: *> equations A * X = B.
! 48: *> \endverbatim
! 49: *
! 50: * Arguments:
! 51: * ==========
! 52: *
! 53: *> \param[in] UPLO
! 54: *> \verbatim
! 55: *> UPLO is CHARACTER*1
! 56: *> = 'U': Upper triangle of A is stored;
! 57: *> = 'L': Lower triangle of A is stored.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] N
! 61: *> \verbatim
! 62: *> N is INTEGER
! 63: *> The number of linear equations, i.e., the order of the
! 64: *> matrix A. N >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] NRHS
! 68: *> \verbatim
! 69: *> NRHS is INTEGER
! 70: *> The number of right hand sides, i.e., the number of columns
! 71: *> of the matrix B. NRHS >= 0.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in,out] A
! 75: *> \verbatim
! 76: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 77: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 78: *> N-by-N upper triangular part of A contains the upper
! 79: *> triangular part of the matrix A, and the strictly lower
! 80: *> triangular part of A is not referenced. If UPLO = 'L', the
! 81: *> leading N-by-N lower triangular part of A contains the lower
! 82: *> triangular part of the matrix A, and the strictly upper
! 83: *> triangular part of A is not referenced.
! 84: *>
! 85: *> On exit, if INFO = 0, the factor U or L from the Cholesky
! 86: *> factorization A = U**T*U or A = L*L**T.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] LDA
! 90: *> \verbatim
! 91: *> LDA is INTEGER
! 92: *> The leading dimension of the array A. LDA >= max(1,N).
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in,out] B
! 96: *> \verbatim
! 97: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 98: *> On entry, the N-by-NRHS right hand side matrix B.
! 99: *> On exit, if INFO = 0, the N-by-NRHS 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 leading minor of order i of A is not
! 114: *> positive definite, so the factorization could not be
! 115: *> completed, and the solution has 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 doublePOsolve
! 129: *
! 130: * =====================================================================
1.1 bertrand 131: SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
132: *
1.9 ! bertrand 133: * -- LAPACK driver 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 UPLO
140: INTEGER INFO, LDA, LDB, N, NRHS
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
144: * ..
145: *
146: * =====================================================================
147: *
148: * .. External Functions ..
149: LOGICAL LSAME
150: EXTERNAL LSAME
151: * ..
152: * .. External Subroutines ..
153: EXTERNAL DPOTRF, DPOTRS, XERBLA
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC MAX
157: * ..
158: * .. Executable Statements ..
159: *
160: * Test the input parameters.
161: *
162: INFO = 0
163: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
164: INFO = -1
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -2
167: ELSE IF( NRHS.LT.0 ) THEN
168: INFO = -3
169: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
170: INFO = -5
171: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
172: INFO = -7
173: END IF
174: IF( INFO.NE.0 ) THEN
175: CALL XERBLA( 'DPOSV ', -INFO )
176: RETURN
177: END IF
178: *
1.8 bertrand 179: * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
1.1 bertrand 180: *
181: CALL DPOTRF( UPLO, N, A, LDA, INFO )
182: IF( INFO.EQ.0 ) THEN
183: *
184: * Solve the system A*X = B, overwriting B with X.
185: *
186: CALL DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
187: *
188: END IF
189: RETURN
190: *
191: * End of DPOSV
192: *
193: END
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