Annotation of rpl/lapack/lapack/dspsv.f, revision 1.9
1.9 ! bertrand 1: *> \brief <b> DSPSV 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 DSPSV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspsv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspsv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspsv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDB, N, NRHS
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * DOUBLE PRECISION AP( * ), B( LDB, * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DSPSV computes the solution to a real system of linear equations
! 39: *> A * X = B,
! 40: *> where A is an N-by-N symmetric matrix stored in packed format and X
! 41: *> and B are N-by-NRHS matrices.
! 42: *>
! 43: *> The diagonal pivoting method is used to factor A as
! 44: *> A = U * D * U**T, if UPLO = 'U', or
! 45: *> A = L * D * L**T, if UPLO = 'L',
! 46: *> where U (or L) is a product of permutation and unit upper (lower)
! 47: *> triangular matrices, D is symmetric and block diagonal with 1-by-1
! 48: *> and 2-by-2 diagonal blocks. The factored form of A is then used to
! 49: *> solve the system of equations A * X = B.
! 50: *> \endverbatim
! 51: *
! 52: * Arguments:
! 53: * ==========
! 54: *
! 55: *> \param[in] UPLO
! 56: *> \verbatim
! 57: *> UPLO is CHARACTER*1
! 58: *> = 'U': Upper triangle of A is stored;
! 59: *> = 'L': Lower triangle of A is stored.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] N
! 63: *> \verbatim
! 64: *> N is INTEGER
! 65: *> The number of linear equations, i.e., the order of the
! 66: *> matrix A. N >= 0.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] NRHS
! 70: *> \verbatim
! 71: *> NRHS is INTEGER
! 72: *> The number of right hand sides, i.e., the number of columns
! 73: *> of the matrix B. NRHS >= 0.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in,out] AP
! 77: *> \verbatim
! 78: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 79: *> On entry, the upper or lower triangle of the symmetric matrix
! 80: *> A, packed columnwise in a linear array. The j-th column of A
! 81: *> is stored in the array AP as follows:
! 82: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 83: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 84: *> See below for further details.
! 85: *>
! 86: *> On exit, the block diagonal matrix D and the multipliers used
! 87: *> to obtain the factor U or L from the factorization
! 88: *> A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
! 89: *> a packed triangular matrix in the same storage format as A.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] IPIV
! 93: *> \verbatim
! 94: *> IPIV is INTEGER array, dimension (N)
! 95: *> Details of the interchanges and the block structure of D, as
! 96: *> determined by DSPTRF. If IPIV(k) > 0, then rows and columns
! 97: *> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
! 98: *> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
! 99: *> then rows and columns k-1 and -IPIV(k) were interchanged and
! 100: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
! 101: *> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
! 102: *> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
! 103: *> diagonal block.
! 104: *> \endverbatim
! 105: *>
! 106: *> \param[in,out] B
! 107: *> \verbatim
! 108: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 109: *> On entry, the N-by-NRHS right hand side matrix B.
! 110: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] LDB
! 114: *> \verbatim
! 115: *> LDB is INTEGER
! 116: *> The leading dimension of the array B. LDB >= max(1,N).
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[out] INFO
! 120: *> \verbatim
! 121: *> INFO is INTEGER
! 122: *> = 0: successful exit
! 123: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 124: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 125: *> has been completed, but the block diagonal matrix D is
! 126: *> exactly singular, so the solution could not be
! 127: *> computed.
! 128: *> \endverbatim
! 129: *
! 130: * Authors:
! 131: * ========
! 132: *
! 133: *> \author Univ. of Tennessee
! 134: *> \author Univ. of California Berkeley
! 135: *> \author Univ. of Colorado Denver
! 136: *> \author NAG Ltd.
! 137: *
! 138: *> \date November 2011
! 139: *
! 140: *> \ingroup doubleOTHERsolve
! 141: *
! 142: *> \par Further Details:
! 143: * =====================
! 144: *>
! 145: *> \verbatim
! 146: *>
! 147: *> The packed storage scheme is illustrated by the following example
! 148: *> when N = 4, UPLO = 'U':
! 149: *>
! 150: *> Two-dimensional storage of the symmetric matrix A:
! 151: *>
! 152: *> a11 a12 a13 a14
! 153: *> a22 a23 a24
! 154: *> a33 a34 (aij = aji)
! 155: *> a44
! 156: *>
! 157: *> Packed storage of the upper triangle of A:
! 158: *>
! 159: *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
! 160: *> \endverbatim
! 161: *>
! 162: * =====================================================================
1.1 bertrand 163: SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
164: *
1.9 ! bertrand 165: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 166: * -- LAPACK is a software package provided by Univ. of Tennessee, --
167: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 168: * November 2011
1.1 bertrand 169: *
170: * .. Scalar Arguments ..
171: CHARACTER UPLO
172: INTEGER INFO, LDB, N, NRHS
173: * ..
174: * .. Array Arguments ..
175: INTEGER IPIV( * )
176: DOUBLE PRECISION AP( * ), B( LDB, * )
177: * ..
178: *
179: * =====================================================================
180: *
181: * .. External Functions ..
182: LOGICAL LSAME
183: EXTERNAL LSAME
184: * ..
185: * .. External Subroutines ..
186: EXTERNAL DSPTRF, DSPTRS, XERBLA
187: * ..
188: * .. Intrinsic Functions ..
189: INTRINSIC MAX
190: * ..
191: * .. Executable Statements ..
192: *
193: * Test the input parameters.
194: *
195: INFO = 0
196: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
197: INFO = -1
198: ELSE IF( N.LT.0 ) THEN
199: INFO = -2
200: ELSE IF( NRHS.LT.0 ) THEN
201: INFO = -3
202: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
203: INFO = -7
204: END IF
205: IF( INFO.NE.0 ) THEN
206: CALL XERBLA( 'DSPSV ', -INFO )
207: RETURN
208: END IF
209: *
1.8 bertrand 210: * Compute the factorization A = U*D*U**T or A = L*D*L**T.
1.1 bertrand 211: *
212: CALL DSPTRF( UPLO, N, AP, IPIV, INFO )
213: IF( INFO.EQ.0 ) THEN
214: *
215: * Solve the system A*X = B, overwriting B with X.
216: *
217: CALL DSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
218: *
219: END IF
220: RETURN
221: *
222: * End of DSPSV
223: *
224: END
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