--- rpl/lapack/lapack/zgbsv.f 2010/12/21 13:53:42 1.7
+++ rpl/lapack/lapack/zgbsv.f 2011/11/21 20:43:08 1.8
@@ -1,9 +1,171 @@
+*> \brief ZGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGBSV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGBSV computes the solution to a complex system of linear equations
+*> A * X = B, where A is a band matrix of order N with KL subdiagonals
+*> and KU superdiagonals, and X and B are N-by-NRHS matrices.
+*>
+*> The LU decomposition with partial pivoting and row interchanges is
+*> used to factor A as A = L * U, where L is a product of permutation
+*> and unit lower triangular matrices with KL subdiagonals, and U is
+*> upper triangular with KL+KU superdiagonals. The factored form of A
+*> is then used to solve the system of equations A * X = B.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \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] KL
+*> \verbatim
+*> KL is INTEGER
+*> The number of subdiagonals within the band of A. KL >= 0.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*> KU is INTEGER
+*> The number of superdiagonals within the band of A. KU >= 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 COMPLEX*16 array, dimension (LDAB,N)
+*> On entry, the matrix A in band storage, in rows KL+1 to
+*> 2*KL+KU+1; rows 1 to KL of the array need not be set.
+*> The j-th column of A is stored in the j-th column of the
+*> array AB as follows:
+*> AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
+*> On exit, details of the factorization: U is stored as an
+*> upper triangular band matrix with KL+KU superdiagonals in
+*> rows 1 to KL+KU+1, and the multipliers used during the
+*> factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
+*> See below for further details.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> The pivot indices that define the permutation matrix P;
+*> row i of the matrix was interchanged with row IPIV(i).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 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, U(i,i) is exactly zero. The factorization
+*> has been completed, but the factor U is exactly
+*> singular, 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 complex16GBsolve
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The band storage scheme is illustrated by the following example, when
+*> M = N = 6, KL = 2, KU = 1:
+*>
+*> On entry: On exit:
+*>
+*> * * * + + + * * * u14 u25 u36
+*> * * + + + + * * 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
+*> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
+*> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
+*>
+*> Array elements marked * are not used by the routine; elements marked
+*> + need not be set on entry, but are required by the routine to store
+*> elements of U because of fill-in resulting from the row interchanges.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- 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..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
@@ -13,88 +175,6 @@
COMPLEX*16 AB( LDAB, * ), B( LDB, * )
* ..
*
-* Purpose
-* =======
-*
-* ZGBSV computes the solution to a complex system of linear equations
-* A * X = B, where A is a band matrix of order N with KL subdiagonals
-* and KU superdiagonals, and X and B are N-by-NRHS matrices.
-*
-* The LU decomposition with partial pivoting and row interchanges is
-* used to factor A as A = L * U, where L is a product of permutation
-* and unit lower triangular matrices with KL subdiagonals, and U is
-* upper triangular with KL+KU superdiagonals. The factored form of A
-* is then used to solve the system of equations A * X = B.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The number of linear equations, i.e., the order of the
-* matrix A. N >= 0.
-*
-* KL (input) INTEGER
-* The number of subdiagonals within the band of A. KL >= 0.
-*
-* KU (input) INTEGER
-* The number of superdiagonals within the band of A. KU >= 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) COMPLEX*16 array, dimension (LDAB,N)
-* On entry, the matrix A in band storage, in rows KL+1 to
-* 2*KL+KU+1; rows 1 to KL of the array need not be set.
-* The j-th column of A is stored in the j-th column of the
-* array AB as follows:
-* AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
-* On exit, details of the factorization: U is stored as an
-* upper triangular band matrix with KL+KU superdiagonals in
-* rows 1 to KL+KU+1, and the multipliers used during the
-* factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
-* See below for further details.
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
-*
-* IPIV (output) INTEGER array, dimension (N)
-* The pivot indices that define the permutation matrix P;
-* row i of the matrix was interchanged with row IPIV(i).
-*
-* B (input/output) COMPLEX*16 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, U(i,i) is exactly zero. The factorization
-* has been completed, but the factor U is exactly
-* singular, and the solution has not been computed.
-*
-* Further Details
-* ===============
-*
-* The band storage scheme is illustrated by the following example, when
-* M = N = 6, KL = 2, KU = 1:
-*
-* On entry: On exit:
-*
-* * * * + + + * * * u14 u25 u36
-* * * + + + + * * 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
-* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
-* a31 a42 a53 a64 * * m31 m42 m53 m64 * *
-*
-* Array elements marked * are not used by the routine; elements marked
-* + need not be set on entry, but are required by the routine to store
-* elements of U because of fill-in resulting from the row interchanges.
-*
* =====================================================================
*
* .. External Subroutines ..