From e1d39294aee16fa6db9ba079b14442358217db71 Mon Sep 17 00:00:00 2001 From: julie Date: Thu, 6 Oct 2011 06:53:11 +0000 Subject: Integrating Doxygen in comments --- SRC/spbsv.f | 242 +++++++++++++++++++++++++++++++++++++++--------------------- 1 file changed, 157 insertions(+), 85 deletions(-) (limited to 'SRC/spbsv.f') diff --git a/SRC/spbsv.f b/SRC/spbsv.f index 8c046420..cbc1794b 100644 --- a/SRC/spbsv.f +++ b/SRC/spbsv.f @@ -1,104 +1,176 @@ - SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) -* -* -- LAPACK driver routine (version 3.3.1) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, KD, LDAB, LDB, N, NRHS -* .. -* .. Array Arguments .. - REAL AB( LDAB, * ), B( LDB, * ) -* .. -* +*> \brief SPBSV 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/ +* +* Definition +* ========== +* +* SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, KD, LDAB, LDB, N, NRHS +* .. +* .. Array Arguments .. +* REAL AB( LDAB, * ), B( LDB, * ) +* .. +* * Purpose * ======= * -* SPBSV 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. +*>\details \b Purpose: +*>\verbatim +*> +*> SPBSV 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 * ========= * -* 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) REAL 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. +*> \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 REAL 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. +*> \endverbatim +*> \verbatim +*> 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 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 +* ======= * -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= KD+1. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* B (input/output) 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. +*> \date November 2011 * -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,N). +*> \ingroup realOTHERsolve * -* 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 * =============== +*>\details \b Further \b 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 SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) * -* 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 * * +* -- LAPACK solve routine (version 3.3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* Array elements marked * are not used by the routine. +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, KD, LDAB, LDB, N, NRHS +* .. +* .. Array Arguments .. + REAL AB( LDAB, * ), B( LDB, * ) +* .. * * ===================================================================== * -- cgit v1.2.3