--- rpl/lapack/lapack/dppsv.f 2010/01/26 15:22:45 1.1
+++ rpl/lapack/lapack/dppsv.f 2023/08/07 08:39:04 1.18
@@ -1,9 +1,150 @@
+*> \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.
+*
+*> \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 3.2) --
+* -- LAPACK driver routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -13,79 +154,6 @@
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 ..
@@ -117,7 +185,7 @@
RETURN
END IF
*
-* Compute the Cholesky factorization A = U'*U or A = L*L'.
+* Compute the Cholesky factorization A = U**T*U or A = L*L**T.
*
CALL DPPTRF( UPLO, N, AP, INFO )
IF( INFO.EQ.0 ) THEN