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

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

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

Purpose:
``` SPPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as
A = U**T* U,  if UPLO = 'U', or
A = L * L**T,  if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.  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, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.``` [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, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been 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 = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]```

Definition at line 143 of file sppsv.f.

144*
145* -- LAPACK driver routine --
146* -- LAPACK is a software package provided by Univ. of Tennessee, --
147* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148*
149* .. Scalar Arguments ..
150 CHARACTER UPLO
151 INTEGER INFO, LDB, N, NRHS
152* ..
153* .. Array Arguments ..
154 REAL AP( * ), B( LDB, * )
155* ..
156*
157* =====================================================================
158*
159* .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL lsame
162* ..
163* .. External Subroutines ..
164 EXTERNAL spptrf, spptrs, xerbla
165* ..
166* .. Intrinsic Functions ..
167 INTRINSIC max
168* ..
169* .. Executable Statements ..
170*
171* Test the input parameters.
172*
173 info = 0
174 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
175 info = -1
176 ELSE IF( n.LT.0 ) THEN
177 info = -2
178 ELSE IF( nrhs.LT.0 ) THEN
179 info = -3
180 ELSE IF( ldb.LT.max( 1, n ) ) THEN
181 info = -6
182 END IF
183 IF( info.NE.0 ) THEN
184 CALL xerbla( 'SPPSV ', -info )
185 RETURN
186 END IF
187*
188* Compute the Cholesky factorization A = U**T*U or A = L*L**T.
189*
190 CALL spptrf( uplo, n, ap, info )
191 IF( info.EQ.0 ) THEN
192*
193* Solve the system A*X = B, overwriting B with X.
194*
195 CALL spptrs( uplo, n, nrhs, ap, b, ldb, info )
196*
197 END IF
198 RETURN
199*
200* End of SPPSV
201*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine spptrf(UPLO, N, AP, INFO)
SPPTRF
Definition: spptrf.f:119
subroutine spptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
SPPTRS
Definition: spptrs.f:108
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