--- rpl/lapack/lapack/ztbrfs.f 2010/01/26 15:22:46 1.1
+++ rpl/lapack/lapack/ztbrfs.f 2023/08/07 08:39:40 1.17
@@ -1,12 +1,194 @@
+*> \brief \b ZTBRFS
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZTBRFS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
+* LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER DIAG, TRANS, UPLO
+* INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
+* COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ),
+* $ X( LDX, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZTBRFS provides error bounds and backward error estimates for the
+*> solution to a system of linear equations with a triangular band
+*> coefficient matrix.
+*>
+*> The solution matrix X must be computed by ZTBTRS or some other
+*> means before entering this routine. ZTBRFS does not do iterative
+*> refinement because doing so cannot improve the backward error.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': A is upper triangular;
+*> = 'L': A is lower triangular.
+*> \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] DIAG
+*> \verbatim
+*> DIAG is CHARACTER*1
+*> = 'N': A is non-unit triangular;
+*> = 'U': A is unit triangular.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] KD
+*> \verbatim
+*> KD is INTEGER
+*> The number of superdiagonals or subdiagonals of the
+*> triangular band matrix A. KD >= 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] AB
+*> \verbatim
+*> AB is COMPLEX*16 array, dimension (LDAB,N)
+*> The upper or lower triangular 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).
+*> If DIAG = 'U', the diagonal elements of A are not referenced
+*> and are assumed to be 1.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KD+1.
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB,NRHS)
+*> The 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[in] X
+*> \verbatim
+*> X is COMPLEX*16 array, dimension (LDX,NRHS)
+*> The 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] 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
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16OTHERcomputational
+*
+* =====================================================================
SUBROUTINE ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
$ LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
-*
-* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
@@ -18,92 +200,6 @@
$ X( LDX, * )
* ..
*
-* Purpose
-* =======
-*
-* ZTBRFS provides error bounds and backward error estimates for the
-* solution to a system of linear equations with a triangular band
-* coefficient matrix.
-*
-* The solution matrix X must be computed by ZTBTRS or some other
-* means before entering this routine. ZTBRFS does not do iterative
-* refinement because doing so cannot improve the backward error.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* = 'U': A is upper triangular;
-* = 'L': A is lower triangular.
-*
-* 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)
-*
-* DIAG (input) CHARACTER*1
-* = 'N': A is non-unit triangular;
-* = 'U': A is unit triangular.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* KD (input) INTEGER
-* The number of superdiagonals or subdiagonals of the
-* triangular band matrix A. KD >= 0.
-*
-* NRHS (input) INTEGER
-* The number of right hand sides, i.e., the number of columns
-* of the matrices B and X. NRHS >= 0.
-*
-* AB (input) COMPLEX*16 array, dimension (LDAB,N)
-* The upper or lower triangular 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).
-* If DIAG = 'U', the diagonal elements of A are not referenced
-* and are assumed to be 1.
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KD+1.
-*
-* B (input) COMPLEX*16 array, dimension (LDB,NRHS)
-* The right hand side matrix B.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* X (input) COMPLEX*16 array, dimension (LDX,NRHS)
-* The solution matrix X.
-*
-* LDX (input) INTEGER
-* The leading dimension of the array X. LDX >= max(1,N).
-*
-* 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
-*
* =====================================================================
*
* .. Parameters ..