*> \brief \b CPPTRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CPPTRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. * COMPLEX AP( * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CPPTRS solves a system of linear equations A*X = B with a Hermitian *> positive definite matrix A in packed storage using the Cholesky *> factorization A = U**H*U or A = L*L**H computed by CPPTRF. *> \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 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] AP *> \verbatim *> AP is COMPLEX array, dimension (N*(N+1)/2) *> The triangular factor U or L from the Cholesky factorization *> A = U**H*U or A = L*L**H, packed columnwise in a linear *> array. The j-th column of U or L is stored in the array AP *> as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, the 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 *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complexOTHERcomputational * * ===================================================================== SUBROUTINE CPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. COMPLEX AP( * ), B( LDB, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL UPPER INTEGER I * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CTPSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .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( 'CPPTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Solve A*X = B where A = U**H * U. * DO 10 I = 1, NRHS * * Solve U**H *X = B, overwriting B with X. * CALL CTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', N, $ AP, B( 1, I ), 1 ) * * Solve U*X = B, overwriting B with X. * CALL CTPSV( 'Upper', 'No transpose', 'Non-unit', N, AP, $ B( 1, I ), 1 ) 10 CONTINUE ELSE * * Solve A*X = B where A = L * L**H. * DO 20 I = 1, NRHS * * Solve L*Y = B, overwriting B with X. * CALL CTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP, $ B( 1, I ), 1 ) * * Solve L**H *X = Y, overwriting B with X. * CALL CTPSV( 'Lower', 'Conjugate transpose', 'Non-unit', N, $ AP, B( 1, I ), 1 ) 20 CONTINUE END IF * RETURN * * End of CPPTRS * END