--- rpl/lapack/lapack/dpbsv.f 2011/07/22 07:38:09 1.8
+++ rpl/lapack/lapack/dpbsv.f 2011/11/21 20:43:01 1.9
@@ -1,9 +1,173 @@
+*> \brief DPBSV 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 DPBSV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, KD, LDAB, LDB, N, NRHS
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DPBSV computes the solution to a real system of linear equations
+*> A * X = B,
+*> where A is an N-by-N symmetric positive definite band matrix 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 band matrix, and L is a lower
+*> triangular band matrix, with the same number of superdiagonals or
+*> subdiagonals as A. 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] KD
+*> \verbatim
+*> KD is INTEGER
+*> The number of superdiagonals of the matrix A if UPLO = 'U',
+*> or the number of subdiagonals if UPLO = 'L'. KD >= 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] AB
+*> \verbatim
+*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
+*> On entry, the upper or lower triangle of the symmetric band
+*> matrix A, stored in the first KD+1 rows of the array. The
+*> j-th column of A is stored in the j-th column of the array AB
+*> as follows:
+*> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
+*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
+*> See below for further details.
+*>
+*> On exit, if INFO = 0, the triangular factor U or L from the
+*> Cholesky factorization A = U**T*U or A = L*L**T of the band
+*> matrix A, in the same storage format as A.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KD+1.
+*> \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 band storage scheme is illustrated by the following example, when
+*> N = 6, KD = 2, and UPLO = 'U':
+*>
+*> On entry: On exit:
+*>
+*> * * a13 a24 a35 a46 * * u13 u24 u35 u46
+*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
+*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
+*>
+*> Similarly, if UPLO = 'L' the format of A is as follows:
+*>
+*> On entry: On exit:
+*>
+*> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
+*> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
+*> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
+*>
+*> Array elements marked * are not used by the routine.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, 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
@@ -13,93 +177,6 @@
DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
-*
-* DPBSV computes the solution to a real system of linear equations
-* A * X = B,
-* where A is an N-by-N symmetric positive definite band matrix 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 band matrix, and L is a lower
-* triangular band matrix, with the same number of superdiagonals or
-* subdiagonals as A. 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.
-*
-* KD (input) INTEGER
-* The number of superdiagonals of the matrix A if UPLO = 'U',
-* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
-*
-* NRHS (input) INTEGER
-* The number of right hand sides, i.e., the number of columns
-* of the matrix B. NRHS >= 0.
-*
-* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
-* On entry, the upper or lower triangle of the symmetric band
-* matrix A, stored in the first KD+1 rows of the array. The
-* j-th column of A is stored in the j-th column of the array AB
-* as follows:
-* if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
-* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
-* See below for further details.
-*
-* On exit, if INFO = 0, the triangular factor U or L from the
-* Cholesky factorization A = U**T*U or A = L*L**T of the band
-* matrix A, in the same storage format as A.
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KD+1.
-*
-* 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 band storage scheme is illustrated by the following example, when
-* N = 6, KD = 2, and UPLO = 'U':
-*
-* On entry: On exit:
-*
-* * * a13 a24 a35 a46 * * u13 u24 u35 u46
-* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
-* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
-*
-* Similarly, if UPLO = 'L' the format of A is as follows:
-*
-* On entry: On exit:
-*
-* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
-* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
-* a31 a42 a53 a64 * * l31 l42 l53 l64 * *
-*
-* Array elements marked * are not used by the routine.
-*
* =====================================================================
*
* .. External Functions ..