LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sspsv()

 subroutine sspsv ( character UPLO, integer N, integer NRHS, real, dimension( * ) AP, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB, integer INFO )

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

Purpose:
``` SSPSV 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 REAL 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 SSPTRF, 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 SSPTRF. 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 REAL 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 sspsv.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 REAL AP( * ), B( LDB, * )
174* ..
175*
176* =====================================================================
177*
178* .. External Functions ..
179 LOGICAL LSAME
180 EXTERNAL lsame
181* ..
182* .. External Subroutines ..
183 EXTERNAL ssptrf, ssptrs, 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( 'SSPSV ', -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 ssptrf( 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 ssptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
215*
216 END IF
217 RETURN
218*
219* End of SSPSV
220*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssptrf(UPLO, N, AP, IPIV, INFO)
SSPTRF
Definition: ssptrf.f:157
subroutine ssptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPTRS
Definition: ssptrs.f:115
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