 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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

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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.```
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 161 of file dspsv.f.

162 *
163 * -- LAPACK driver routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  CHARACTER UPLO
169  INTEGER INFO, LDB, N, NRHS
170 * ..
171 * .. Array Arguments ..
172  INTEGER IPIV( * )
173  DOUBLE PRECISION AP( * ), B( LDB, * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. External Functions ..
179  LOGICAL LSAME
180  EXTERNAL lsame
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL dsptrf, dsptrs, xerbla
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC max
187 * ..
188 * .. Executable Statements ..
189 *
190 * Test the input parameters.
191 *
192  info = 0
193  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194  info = -1
195  ELSE IF( n.LT.0 ) THEN
196  info = -2
197  ELSE IF( nrhs.LT.0 ) THEN
198  info = -3
199  ELSE IF( ldb.LT.max( 1, n ) ) THEN
200  info = -7
201  END IF
202  IF( info.NE.0 ) THEN
203  CALL xerbla( 'DSPSV ', -info )
204  RETURN
205  END IF
206 *
207 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
208 *
209  CALL dsptrf( uplo, n, ap, ipiv, info )
210  IF( info.EQ.0 ) THEN
211 *
212 * Solve the system A*X = B, overwriting B with X.
213 *
214  CALL dsptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
215 *
216  END IF
217  RETURN
218 *
219 * End of DSPSV
220 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dsptrf(UPLO, N, AP, IPIV, INFO)
DSPTRF
Definition: dsptrf.f:159
subroutine dsptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
DSPTRS
Definition: dsptrs.f:115
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