--- rpl/lapack/lapack/dppsv.f 2011/07/22 07:38:10 1.8 +++ rpl/lapack/lapack/dppsv.f 2011/11/21 20:43:02 1.9 @@ -1,9 +1,153 @@ +*> \brief DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DPPSV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDB, N, NRHS +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AP( * ), B( LDB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPPSV 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 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, 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 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. +*> \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 doubleOTHERsolve +* +*> \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 DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) * -* -- LAPACK driver routine (version 3.3.1) -- +* -- 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..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. CHARACTER UPLO @@ -13,79 +157,6 @@ DOUBLE PRECISION AP( * ), B( LDB, * ) * .. * -* Purpose -* ======= -* -* DPPSV 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. -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The number of linear equations, i.e., the order of the -* matrix A. N >= 0. -* -* NRHS (input) INTEGER -* The number of right hand sides, i.e., the number of columns -* of the matrix B. NRHS >= 0. -* -* AP (input/output) 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, 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. -* -* B (input/output) 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. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,N). -* -* INFO (output) 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 ] -* * ===================================================================== * * .. External Functions ..