--- rpl/lapack/lapack/zptsvx.f 2010/08/13 21:04:14 1.6
+++ rpl/lapack/lapack/zptsvx.f 2011/11/21 22:19:56 1.10
@@ -1,10 +1,243 @@
+*> \brief \b ZPTSVX
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZPTSVX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
+* RCOND, FERR, BERR, WORK, RWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER FACT
+* INTEGER INFO, LDB, LDX, N, NRHS
+* DOUBLE PRECISION RCOND
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
+* $ RWORK( * )
+* COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ),
+* $ X( LDX, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZPTSVX uses the factorization A = L*D*L**H to compute the solution
+*> to a complex system of linear equations A*X = B, where A is an
+*> N-by-N Hermitian positive definite tridiagonal matrix 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 matrix A is factored as A = L*D*L**H, where L
+*> is a unit lower bidiagonal matrix and D is diagonal. The
+*> factorization can also be regarded as having the form
+*> A = U**H*D*U.
+*>
+*> 2. If the leading i-by-i principal minor is not positive definite,
+*> 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 the matrix
+*> A is supplied on entry.
+*> = 'F': On entry, DF and EF contain the factored form of A.
+*> D, E, DF, and EF will not be modified.
+*> = 'N': The matrix A will be copied to DF and EF and
+*> factored.
+*> \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 matrices B and X. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (N)
+*> The n diagonal elements of the tridiagonal matrix A.
+*> \endverbatim
+*>
+*> \param[in] E
+*> \verbatim
+*> E is COMPLEX*16 array, dimension (N-1)
+*> The (n-1) subdiagonal elements of the tridiagonal matrix A.
+*> \endverbatim
+*>
+*> \param[in,out] DF
+*> \verbatim
+*> DF is or output) DOUBLE PRECISION array, dimension (N)
+*> If FACT = 'F', then DF is an input argument and on entry
+*> contains the n diagonal elements of the diagonal matrix D
+*> from the L*D*L**H factorization of A.
+*> If FACT = 'N', then DF is an output argument and on exit
+*> contains the n diagonal elements of the diagonal matrix D
+*> from the L*D*L**H factorization of A.
+*> \endverbatim
+*>
+*> \param[in,out] EF
+*> \verbatim
+*> EF is or output) COMPLEX*16 array, dimension (N-1)
+*> If FACT = 'F', then EF is an input argument and on entry
+*> contains the (n-1) subdiagonal elements of the unit
+*> bidiagonal factor L from the L*D*L**H factorization of A.
+*> If FACT = 'N', then EF is an output argument and on exit
+*> contains the (n-1) subdiagonal elements of the unit
+*> bidiagonal factor L from the L*D*L**H factorization of A.
+*> \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 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 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).
+*> \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 (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: 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. 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 ZPTSVX( FACT, N, NRHS, D, E, DF, EF, 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
@@ -18,133 +251,6 @@
$ X( LDX, * )
* ..
*
-* Purpose
-* =======
-*
-* ZPTSVX uses the factorization A = L*D*L**H to compute the solution
-* to a complex system of linear equations A*X = B, where A is an
-* N-by-N Hermitian positive definite tridiagonal matrix 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 matrix A is factored as A = L*D*L**H, where L
-* is a unit lower bidiagonal matrix and D is diagonal. The
-* factorization can also be regarded as having the form
-* A = U**H*D*U.
-*
-* 2. If the leading i-by-i principal minor is not positive definite,
-* 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 the matrix
-* A is supplied on entry.
-* = 'F': On entry, DF and EF contain the factored form of A.
-* D, E, DF, and EF will not be modified.
-* = 'N': The matrix A will be copied to DF and EF and
-* factored.
-*
-* 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 matrices B and X. NRHS >= 0.
-*
-* D (input) DOUBLE PRECISION array, dimension (N)
-* The n diagonal elements of the tridiagonal matrix A.
-*
-* E (input) COMPLEX*16 array, dimension (N-1)
-* The (n-1) subdiagonal elements of the tridiagonal matrix A.
-*
-* DF (input or output) DOUBLE PRECISION array, dimension (N)
-* If FACT = 'F', then DF is an input argument and on entry
-* contains the n diagonal elements of the diagonal matrix D
-* from the L*D*L**H factorization of A.
-* If FACT = 'N', then DF is an output argument and on exit
-* contains the n diagonal elements of the diagonal matrix D
-* from the L*D*L**H factorization of A.
-*
-* EF (input or output) COMPLEX*16 array, dimension (N-1)
-* If FACT = 'F', then EF is an input argument and on entry
-* contains the (n-1) subdiagonal elements of the unit
-* bidiagonal factor L from the L*D*L**H factorization of A.
-* If FACT = 'N', then EF is an output argument and on exit
-* contains the (n-1) subdiagonal elements of the unit
-* bidiagonal factor L from the L*D*L**H factorization of A.
-*
-* 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 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 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).
-*
-* 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 (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: 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. 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 ..
@@ -191,7 +297,7 @@
*
IF( NOFACT ) THEN
*
-* Compute the L*D*L' (or U'*D*U) factorization of A.
+* Compute the L*D*L**H (or U**H*D*U) factorization of A.
*
CALL DCOPY( N, D, 1, DF, 1 )
IF( N.GT.1 )