Annotation of rpl/lapack/lapack/dppsv.f, revision 1.9
1.9 ! bertrand 1: *> \brief <b> DPPSV computes the solution to system of linear equations A * X = B for OTHER 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 DPPSV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppsv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dppsv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dppsv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPPSV( 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: *> DPPSV 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 stored in
! 40: *> packed format and X and B 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] AP
! 75: *> \verbatim
! 76: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 77: *> On entry, the upper or lower triangle of the symmetric matrix
! 78: *> A, packed columnwise in a linear array. The j-th column of A
! 79: *> is stored in the array AP as follows:
! 80: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 81: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 82: *> See below for further details.
! 83: *>
! 84: *> On exit, if INFO = 0, the factor U or L from the Cholesky
! 85: *> factorization A = U**T*U or A = L*L**T, in the same storage
! 86: *> format as A.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in,out] B
! 90: *> \verbatim
! 91: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 92: *> On entry, the N-by-NRHS right hand side matrix B.
! 93: *> On exit, if INFO = 0, the N-by-NRHS 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: *> > 0: if INFO = i, the leading minor of order i of A is not
! 108: *> positive definite, so the factorization could not be
! 109: *> completed, and the solution has not been computed.
! 110: *> \endverbatim
! 111: *
! 112: * Authors:
! 113: * ========
! 114: *
! 115: *> \author Univ. of Tennessee
! 116: *> \author Univ. of California Berkeley
! 117: *> \author Univ. of Colorado Denver
! 118: *> \author NAG Ltd.
! 119: *
! 120: *> \date November 2011
! 121: *
! 122: *> \ingroup doubleOTHERsolve
! 123: *
! 124: *> \par Further Details:
! 125: * =====================
! 126: *>
! 127: *> \verbatim
! 128: *>
! 129: *> The packed storage scheme is illustrated by the following example
! 130: *> when N = 4, UPLO = 'U':
! 131: *>
! 132: *> Two-dimensional storage of the symmetric matrix A:
! 133: *>
! 134: *> a11 a12 a13 a14
! 135: *> a22 a23 a24
! 136: *> a33 a34 (aij = conjg(aji))
! 137: *> a44
! 138: *>
! 139: *> Packed storage of the upper triangle of A:
! 140: *>
! 141: *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
! 142: *> \endverbatim
! 143: *>
! 144: * =====================================================================
1.1 bertrand 145: SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
146: *
1.9 ! bertrand 147: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 148: * -- LAPACK is a software package provided by Univ. of Tennessee, --
149: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 150: * November 2011
1.1 bertrand 151: *
152: * .. Scalar Arguments ..
153: CHARACTER UPLO
154: INTEGER INFO, LDB, N, NRHS
155: * ..
156: * .. Array Arguments ..
157: DOUBLE PRECISION AP( * ), B( LDB, * )
158: * ..
159: *
160: * =====================================================================
161: *
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL DPPTRF, DPPTRS, XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC MAX
171: * ..
172: * .. Executable Statements ..
173: *
174: * Test the input parameters.
175: *
176: INFO = 0
177: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
178: INFO = -1
179: ELSE IF( N.LT.0 ) THEN
180: INFO = -2
181: ELSE IF( NRHS.LT.0 ) THEN
182: INFO = -3
183: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
184: INFO = -6
185: END IF
186: IF( INFO.NE.0 ) THEN
187: CALL XERBLA( 'DPPSV ', -INFO )
188: RETURN
189: END IF
190: *
1.8 bertrand 191: * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
1.1 bertrand 192: *
193: CALL DPPTRF( UPLO, N, AP, INFO )
194: IF( INFO.EQ.0 ) THEN
195: *
196: * Solve the system A*X = B, overwriting B with X.
197: *
198: CALL DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
199: *
200: END IF
201: RETURN
202: *
203: * End of DPPSV
204: *
205: END
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