--- rpl/lapack/lapack/zgtsvx.f 2010/12/21 13:53:45 1.7
+++ rpl/lapack/lapack/zgtsvx.f 2011/11/21 20:43:11 1.8
@@ -1,11 +1,303 @@
+*> \brief \b ZGTSVX
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGTSVX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
+* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
+* WORK, RWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER FACT, TRANS
+* INTEGER INFO, LDB, LDX, N, NRHS
+* DOUBLE PRECISION RCOND
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
+* COMPLEX*16 B( LDB, * ), D( * ), DF( * ), DL( * ),
+* $ DLF( * ), DU( * ), DU2( * ), DUF( * ),
+* $ WORK( * ), X( LDX, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGTSVX uses the LU factorization to compute the solution to a complex
+*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
+*> where A is a tridiagonal matrix of order N and X and B are N-by-NRHS
+*> matrices.
+*>
+*> Error bounds on the solution and a condition estimate are also
+*> provided.
+*> \endverbatim
+*
+*> \par Description:
+* =================
+*>
+*> \verbatim
+*>
+*> The following steps are performed:
+*>
+*> 1. If FACT = 'N', the LU decomposition is used to factor the matrix A
+*> as A = L * U, where L is a product of permutation and unit lower
+*> bidiagonal matrices and U is upper triangular with nonzeros in
+*> only the main diagonal and first two superdiagonals.
+*>
+*> 2. If some U(i,i)=0, so that U is exactly singular, then the routine
+*> returns with INFO = i. Otherwise, the factored form of A is used
+*> to estimate the condition number of the matrix A. If the
+*> reciprocal of the condition number is less than machine precision,
+*> INFO = N+1 is returned as a warning, but the routine still goes on
+*> to solve for X and compute error bounds as described below.
+*>
+*> 3. The system of equations is solved for X using the factored form
+*> of A.
+*>
+*> 4. Iterative refinement is applied to improve the computed solution
+*> matrix and calculate error bounds and backward error estimates
+*> for it.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] FACT
+*> \verbatim
+*> FACT is CHARACTER*1
+*> Specifies whether or not the factored form of A has been
+*> supplied on entry.
+*> = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form
+*> of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not
+*> be modified.
+*> = 'N': The matrix will be copied to DLF, DF, and DUF
+*> and factored.
+*> \endverbatim
+*>
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER*1
+*> Specifies the form of the system of equations:
+*> = 'N': A * X = B (No transpose)
+*> = 'T': A**T * X = B (Transpose)
+*> = 'C': A**H * X = B (Conjugate transpose)
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> 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] DL
+*> \verbatim
+*> DL is COMPLEX*16 array, dimension (N-1)
+*> The (n-1) subdiagonal elements of A.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*> D is COMPLEX*16 array, dimension (N)
+*> The n diagonal elements of A.
+*> \endverbatim
+*>
+*> \param[in] DU
+*> \verbatim
+*> DU is COMPLEX*16 array, dimension (N-1)
+*> The (n-1) superdiagonal elements of A.
+*> \endverbatim
+*>
+*> \param[in,out] DLF
+*> \verbatim
+*> DLF is or output) COMPLEX*16 array, dimension (N-1)
+*> If FACT = 'F', then DLF is an input argument and on entry
+*> contains the (n-1) multipliers that define the matrix L from
+*> the LU factorization of A as computed by ZGTTRF.
+*>
+*> If FACT = 'N', then DLF is an output argument and on exit
+*> contains the (n-1) multipliers that define the matrix L from
+*> the LU factorization of A.
+*> \endverbatim
+*>
+*> \param[in,out] DF
+*> \verbatim
+*> DF is or output) COMPLEX*16 array, dimension (N)
+*> If FACT = 'F', then DF is an input argument and on entry
+*> contains the n diagonal elements of the upper triangular
+*> matrix U from the LU factorization of A.
+*>
+*> If FACT = 'N', then DF is an output argument and on exit
+*> contains the n diagonal elements of the upper triangular
+*> matrix U from the LU factorization of A.
+*> \endverbatim
+*>
+*> \param[in,out] DUF
+*> \verbatim
+*> DUF is or output) COMPLEX*16 array, dimension (N-1)
+*> If FACT = 'F', then DUF is an input argument and on entry
+*> contains the (n-1) elements of the first superdiagonal of U.
+*>
+*> If FACT = 'N', then DUF is an output argument and on exit
+*> contains the (n-1) elements of the first superdiagonal of U.
+*> \endverbatim
+*>
+*> \param[in,out] DU2
+*> \verbatim
+*> DU2 is or output) COMPLEX*16 array, dimension (N-2)
+*> If FACT = 'F', then DU2 is an input argument and on entry
+*> contains the (n-2) elements of the second superdiagonal of
+*> U.
+*>
+*> If FACT = 'N', then DU2 is an output argument and on exit
+*> contains the (n-2) elements of the second superdiagonal of
+*> U.
+*> \endverbatim
+*>
+*> \param[in,out] IPIV
+*> \verbatim
+*> IPIV is or output) INTEGER array, dimension (N)
+*> If FACT = 'F', then IPIV is an input argument and on entry
+*> contains the pivot indices from the LU factorization of A as
+*> computed by ZGTTRF.
+*>
+*> If FACT = 'N', then IPIV is an output argument and on exit
+*> contains the pivot indices from the LU factorization of A;
+*> row i of the matrix was interchanged with row IPIV(i).
+*> IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
+*> a row interchange was not required.
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> The N-by-NRHS right hand side matrix B.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*> X is COMPLEX*16 array, dimension (LDX,NRHS)
+*> If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDX
+*> \verbatim
+*> LDX is INTEGER
+*> The leading dimension of the array X. LDX >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] RCOND
+*> \verbatim
+*> RCOND is DOUBLE PRECISION
+*> The estimate of the reciprocal condition number of the matrix
+*> A. If RCOND is less than the machine precision (in
+*> particular, if RCOND = 0), the matrix is singular to working
+*> precision. This condition is indicated by a return code of
+*> INFO > 0.
+*> \endverbatim
+*>
+*> \param[out] FERR
+*> \verbatim
+*> FERR is DOUBLE PRECISION array, dimension (NRHS)
+*> The estimated forward error bound for each solution vector
+*> X(j) (the j-th column of the solution matrix X).
+*> If XTRUE is the true solution corresponding to X(j), FERR(j)
+*> is an estimated upper bound for the magnitude of the largest
+*> element in (X(j) - XTRUE) divided by the magnitude of the
+*> largest element in X(j). The estimate is as reliable as
+*> the estimate for RCOND, and is almost always a slight
+*> overestimate of the true error.
+*> \endverbatim
+*>
+*> \param[out] BERR
+*> \verbatim
+*> BERR is DOUBLE PRECISION array, dimension (NRHS)
+*> The componentwise relative backward error of each solution
+*> vector X(j) (i.e., the smallest relative change in
+*> any element of A or B that makes X(j) an exact solution).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (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, and i is
+*> <= N: U(i,i) is exactly zero. The factorization
+*> has not been completed unless i = N, but the
+*> factor U is exactly singular, so the solution
+*> and error bounds could not be computed.
+*> RCOND = 0 is returned.
+*> = N+1: U is nonsingular, but RCOND is less than machine
+*> precision, meaning that the matrix is singular
+*> to working precision. Nevertheless, the
+*> solution and error bounds are computed because
+*> there are a number of situations where the
+*> computed solution can be more accurate than the
+*> value of RCOND would suggest.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERcomputational
+*
+* =====================================================================
SUBROUTINE ZGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
$ DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
$ WORK, RWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational 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 ..
CHARACTER FACT, TRANS
@@ -20,175 +312,6 @@
$ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
-*
-* ZGTSVX uses the LU factorization to compute the solution to a complex
-* system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
-* where A is a tridiagonal matrix of order N and X and B are N-by-NRHS
-* matrices.
-*
-* Error bounds on the solution and a condition estimate are also
-* provided.
-*
-* Description
-* ===========
-*
-* The following steps are performed:
-*
-* 1. If FACT = 'N', the LU decomposition is used to factor the matrix A
-* as A = L * U, where L is a product of permutation and unit lower
-* bidiagonal matrices and U is upper triangular with nonzeros in
-* only the main diagonal and first two superdiagonals.
-*
-* 2. If some U(i,i)=0, so that U is exactly singular, then the routine
-* returns with INFO = i. Otherwise, the factored form of A is used
-* to estimate the condition number of the matrix A. If the
-* reciprocal of the condition number is less than machine precision,
-* INFO = N+1 is returned as a warning, but the routine still goes on
-* to solve for X and compute error bounds as described below.
-*
-* 3. The system of equations is solved for X using the factored form
-* of A.
-*
-* 4. Iterative refinement is applied to improve the computed solution
-* matrix and calculate error bounds and backward error estimates
-* for it.
-*
-* Arguments
-* =========
-*
-* FACT (input) CHARACTER*1
-* Specifies whether or not the factored form of A has been
-* supplied on entry.
-* = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form
-* of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not
-* be modified.
-* = 'N': The matrix will be copied to DLF, DF, and DUF
-* and factored.
-*
-* TRANS (input) CHARACTER*1
-* Specifies the form of the system of equations:
-* = 'N': A * X = B (No transpose)
-* = 'T': A**T * X = B (Transpose)
-* = 'C': A**H * X = B (Conjugate transpose)
-*
-* N (input) INTEGER
-* 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.
-*
-* DL (input) COMPLEX*16 array, dimension (N-1)
-* The (n-1) subdiagonal elements of A.
-*
-* D (input) COMPLEX*16 array, dimension (N)
-* The n diagonal elements of A.
-*
-* DU (input) COMPLEX*16 array, dimension (N-1)
-* The (n-1) superdiagonal elements of A.
-*
-* DLF (input or output) COMPLEX*16 array, dimension (N-1)
-* If FACT = 'F', then DLF is an input argument and on entry
-* contains the (n-1) multipliers that define the matrix L from
-* the LU factorization of A as computed by ZGTTRF.
-*
-* If FACT = 'N', then DLF is an output argument and on exit
-* contains the (n-1) multipliers that define the matrix L from
-* the LU factorization of A.
-*
-* DF (input or output) COMPLEX*16 array, dimension (N)
-* If FACT = 'F', then DF is an input argument and on entry
-* contains the n diagonal elements of the upper triangular
-* matrix U from the LU factorization of A.
-*
-* If FACT = 'N', then DF is an output argument and on exit
-* contains the n diagonal elements of the upper triangular
-* matrix U from the LU factorization of A.
-*
-* DUF (input or output) COMPLEX*16 array, dimension (N-1)
-* If FACT = 'F', then DUF is an input argument and on entry
-* contains the (n-1) elements of the first superdiagonal of U.
-*
-* If FACT = 'N', then DUF is an output argument and on exit
-* contains the (n-1) elements of the first superdiagonal of U.
-*
-* DU2 (input or output) COMPLEX*16 array, dimension (N-2)
-* If FACT = 'F', then DU2 is an input argument and on entry
-* contains the (n-2) elements of the second superdiagonal of
-* U.
-*
-* If FACT = 'N', then DU2 is an output argument and on exit
-* contains the (n-2) elements of the second superdiagonal of
-* U.
-*
-* IPIV (input or output) INTEGER array, dimension (N)
-* If FACT = 'F', then IPIV is an input argument and on entry
-* contains the pivot indices from the LU factorization of A as
-* computed by ZGTTRF.
-*
-* If FACT = 'N', then IPIV is an output argument and on exit
-* contains the pivot indices from the LU factorization of A;
-* row i of the matrix was interchanged with row IPIV(i).
-* IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
-* a row interchange was not required.
-*
-* B (input) COMPLEX*16 array, dimension (LDB,NRHS)
-* The N-by-NRHS right hand side matrix B.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* X (output) COMPLEX*16 array, dimension (LDX,NRHS)
-* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
-*
-* LDX (input) INTEGER
-* The leading dimension of the array X. LDX >= max(1,N).
-*
-* RCOND (output) DOUBLE PRECISION
-* The estimate of the reciprocal condition number of the matrix
-* A. If RCOND is less than the machine precision (in
-* particular, if RCOND = 0), the matrix is singular to working
-* precision. This condition is indicated by a return code of
-* INFO > 0.
-*
-* FERR (output) DOUBLE PRECISION array, dimension (NRHS)
-* The estimated forward error bound for each solution vector
-* X(j) (the j-th column of the solution matrix X).
-* If XTRUE is the true solution corresponding to X(j), FERR(j)
-* is an estimated upper bound for the magnitude of the largest
-* element in (X(j) - XTRUE) divided by the magnitude of the
-* largest element in X(j). The estimate is as reliable as
-* the estimate for RCOND, and is almost always a slight
-* overestimate of the true error.
-*
-* BERR (output) DOUBLE PRECISION array, dimension (NRHS)
-* The componentwise relative backward error of each solution
-* vector X(j) (i.e., the smallest relative change in
-* any element of A or B that makes X(j) an exact solution).
-*
-* WORK (workspace) COMPLEX*16 array, dimension (2*N)
-*
-* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, and i is
-* <= N: U(i,i) is exactly zero. The factorization
-* has not been completed unless i = N, but the
-* factor U is exactly singular, so the solution
-* and error bounds could not be computed.
-* RCOND = 0 is returned.
-* = N+1: U is nonsingular, but RCOND is less than machine
-* precision, meaning that the matrix is singular
-* to working precision. Nevertheless, the
-* solution and error bounds are computed because
-* there are a number of situations where the
-* computed solution can be more accurate than the
-* value of RCOND would suggest.
-*
* =====================================================================
*
* .. Parameters ..