--- rpl/lapack/lapack/dla_gbrpvgrw.f 2010/08/07 13:21:04 1.1
+++ rpl/lapack/lapack/dla_gbrpvgrw.f 2023/08/07 08:38:52 1.15
@@ -1,16 +1,124 @@
+*> \brief \b DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLA_GBRPVGRW + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
+* LDAB, AFB, LDAFB )
+*
+* .. Scalar Arguments ..
+* INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLA_GBRPVGRW computes the reciprocal pivot growth factor
+*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
+*> much less than 1, the stability of the LU factorization of the
+*> (equilibrated) matrix A could be poor. This also means that the
+*> solution X, estimated condition numbers, and error bounds could be
+*> unreliable.
+*> \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] NCOLS
+*> \verbatim
+*> NCOLS is INTEGER
+*> The number of columns of the matrix A. NCOLS >= 0.
+*> \endverbatim
+*>
+*> \param[in] AB
+*> \verbatim
+*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
+*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
+*> The j-th column of A is stored in the j-th column of the
+*> array AB as follows:
+*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KL+KU+1.
+*> \endverbatim
+*>
+*> \param[in] AFB
+*> \verbatim
+*> AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
+*> Details of the LU factorization of the band matrix A, as
+*> computed by DGBTRF. 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.
+*> \endverbatim
+*>
+*> \param[in] LDAFB
+*> \verbatim
+*> LDAFB is INTEGER
+*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleGBcomputational
+*
+* =====================================================================
DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
$ LDAB, AFB, LDAFB )
*
-* -- LAPACK routine (version 3.2.2) --
-* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
-* -- Jason Riedy of Univ. of California Berkeley. --
-* -- June 2010 --
-*
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley and NAG Ltd. --
+* -- LAPACK computational routine --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
- IMPLICIT NONE
-* ..
* .. Scalar Arguments ..
INTEGER N, KL, KU, NCOLS, LDAB, LDAFB
* ..
@@ -18,51 +126,6 @@
DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * )
* ..
*
-* Purpose
-* =======
-*
-* DLA_GBRPVGRW computes the reciprocal pivot growth factor
-* norm(A)/norm(U). The "max absolute element" norm is used. If this is
-* much less than 1, the stability of the LU factorization of the
-* (equilibrated) matrix A could be poor. This also means that the
-* solution X, estimated condition numbers, and error bounds could be
-* unreliable.
-*
-* 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.
-*
-* NCOLS (input) INTEGER
-* The number of columns of the matrix A. NCOLS >= 0.
-*
-* AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
-* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
-* The j-th column of A is stored in the j-th column of the
-* array AB as follows:
-* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KL+KU+1.
-*
-* AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N)
-* Details of the LU factorization of the band matrix A, as
-* computed by DGBTRF. 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.
-*
-* LDAFB (input) INTEGER
-* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
-*
* =====================================================================
*
* .. Local Scalars ..
@@ -91,4 +154,7 @@
END IF
END DO
DLA_GBRPVGRW = RPVGRW
+*
+* End of DLA_GBRPVGRW
+*
END