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*> \brief <b> SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SPPSV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sppsv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sppsv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sppsv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* REAL AP( * ), B( LDB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order of the
*> matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup realOTHERsolve
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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 ]
*> \endverbatim
*>
* =====================================================================
SUBROUTINE SPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
*
* -- LAPACK driver routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL AP( * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SPPTRF, SPPTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SPPSV ', -INFO )
RETURN
END IF
*
* Compute the Cholesky factorization A = U**T*U or A = L*L**T.
*
CALL SPPTRF( UPLO, N, AP, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
CALL SPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
*
END IF
RETURN
*
* End of SPPSV
*
END
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