LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dspsv()

subroutine dspsv ( character uplo,
integer n,
integer nrhs,
double precision, dimension( * ) ap,
integer, dimension( * ) ipiv,
double precision, dimension( ldb, * ) b,
integer ldb,
integer info )

DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Download DSPSV + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DSPSV computes the solution to a real system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric matrix stored in packed format and X
!> and B are N-by-NRHS matrices.
!>
!> The diagonal pivoting method is used to factor A as
!>    A = U * D * U**T,  if UPLO = 'U', or
!>    A = L * D * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, D is symmetric and block diagonal with 1-by-1
!> and 2-by-2 diagonal blocks.  The factored form of A is then used to
!> solve the system of equations A * X = B.
!> 
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!> 
[in]N
!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!> 
[in]NRHS
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!> 
[in,out]AP
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          On entry, the upper or lower triangle of the symmetric matrix
!>          A, packed columnwise in a linear array.  The j-th column of A
!>          is stored in the array AP as follows:
!>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
!>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
!>          See below for further details.
!>
!>          On exit, the block diagonal matrix D and the multipliers used
!>          to obtain the factor U or L from the factorization
!>          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
!>          a packed triangular matrix in the same storage format as A.
!> 
[out]IPIV
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D, as
!>          determined by DSPTRF.  If IPIV(k) > 0, then rows and columns
!>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
!>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
!>          then rows and columns k-1 and -IPIV(k) were interchanged and
!>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
!>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
!>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
!>          diagonal block.
!> 
[in,out]B
!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the N-by-NRHS right hand side matrix B.
!>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
!> 
[in]LDB
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!> 
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
!>                has been completed, but the block diagonal matrix D is
!>                exactly singular, so the solution could not be
!>                computed.
!> 
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  The packed storage scheme is illustrated by the following example
!>  when N = 4, UPLO = 'U':
!>
!>  Two-dimensional storage of the symmetric matrix A:
!>
!>     a11 a12 a13 a14
!>         a22 a23 a24
!>             a33 a34     (aij = aji)
!>                 a44
!>
!>  Packed storage of the upper triangle of A:
!>
!>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
!> 

Definition at line 159 of file dspsv.f.

160*
161* -- LAPACK driver routine --
162* -- LAPACK is a software package provided by Univ. of Tennessee, --
163* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164*
165* .. Scalar Arguments ..
166 CHARACTER UPLO
167 INTEGER INFO, LDB, N, NRHS
168* ..
169* .. Array Arguments ..
170 INTEGER IPIV( * )
171 DOUBLE PRECISION AP( * ), B( LDB, * )
172* ..
173*
174* =====================================================================
175*
176* .. External Functions ..
177 LOGICAL LSAME
178 EXTERNAL lsame
179* ..
180* .. External Subroutines ..
181 EXTERNAL dsptrf, dsptrs, xerbla
182* ..
183* .. Intrinsic Functions ..
184 INTRINSIC max
185* ..
186* .. Executable Statements ..
187*
188* Test the input parameters.
189*
190 info = 0
191 IF( .NOT.lsame( uplo, 'U' ) .AND.
192 $ .NOT.lsame( uplo, 'L' ) ) THEN
193 info = -1
194 ELSE IF( n.LT.0 ) THEN
195 info = -2
196 ELSE IF( nrhs.LT.0 ) THEN
197 info = -3
198 ELSE IF( ldb.LT.max( 1, n ) ) THEN
199 info = -7
200 END IF
201 IF( info.NE.0 ) THEN
202 CALL xerbla( 'DSPSV ', -info )
203 RETURN
204 END IF
205*
206* Compute the factorization A = U*D*U**T or A = L*D*L**T.
207*
208 CALL dsptrf( uplo, n, ap, ipiv, info )
209 IF( info.EQ.0 ) THEN
210*
211* Solve the system A*X = B, overwriting B with X.
212*
213 CALL dsptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
214*
215 END IF
216 RETURN
217*
218* End of DSPSV
219*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dsptrf(uplo, n, ap, ipiv, info)
DSPTRF
Definition dsptrf.f:157
subroutine dsptrs(uplo, n, nrhs, ap, ipiv, b, ldb, info)
DSPTRS
Definition dsptrs.f:113
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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