--- rpl/lapack/lapack/dpftri.f	2010/08/07 13:21:05	1.1
+++ rpl/lapack/lapack/dpftri.f	2012/08/22 09:48:22	1.9
@@ -1,12 +1,200 @@
-      SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
+*> \brief \b DPFTRI
+*
+*  =========== DOCUMENTATION ===========
 *
-*  -- LAPACK routine (version 3.2.2)                                    --
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
 *
-*  -- Contributed by Fred Gustavson of the IBM Watson Research Center --
-*  -- June 2010                                                       --
+*> \htmlonly
+*> Download DPFTRI + dependencies 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftri.f"> 
+*> [TGZ]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftri.f"> 
+*> [ZIP]</a> 
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftri.f"> 
+*> [TXT]</a>
+*> \endhtmlonly 
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          TRANSR, UPLO
+*       INTEGER            INFO, N
+*       .. Array Arguments ..
+*       DOUBLE PRECISION         A( 0: * )
+*       ..
+*  
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DPFTRI computes the inverse of a (real) symmetric positive definite
+*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
+*> computed by DPFTRF.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] TRANSR
+*> \verbatim
+*>          TRANSR is CHARACTER*1
+*>          = 'N':  The Normal TRANSR of RFP A is stored;
+*>          = 'T':  The Transpose TRANSR of RFP A is stored.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 )
+*>          On entry, the symmetric matrix A in RFP format. RFP format is
+*>          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
+*>          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
+*>          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
+*>          the transpose of RFP A as defined when
+*>          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
+*>          follows: If UPLO = 'U' the RFP A contains the nt elements of
+*>          upper packed A. If UPLO = 'L' the RFP A contains the elements
+*>          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
+*>          'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N
+*>          is odd. See the Note below for more details.
+*>
+*>          On exit, the symmetric inverse of the original matrix, in the
+*>          same storage format.
+*> \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, the (i,i) element of the factor U or L is
+*>                zero, and the inverse could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  We first consider Rectangular Full Packed (RFP) Format when N is
+*>  even. We give an example where N = 6.
+*>
+*>      AP is Upper             AP is Lower
+*>
+*>   00 01 02 03 04 05       00
+*>      11 12 13 14 15       10 11
+*>         22 23 24 25       20 21 22
+*>            33 34 35       30 31 32 33
+*>               44 45       40 41 42 43 44
+*>                  55       50 51 52 53 54 55
+*>
+*>
+*>  Let TRANSR = 'N'. RFP holds AP as follows:
+*>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
+*>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
+*>  the transpose of the first three columns of AP upper.
+*>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
+*>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
+*>  the transpose of the last three columns of AP lower.
+*>  This covers the case N even and TRANSR = 'N'.
+*>
+*>         RFP A                   RFP A
+*>
+*>        03 04 05                33 43 53
+*>        13 14 15                00 44 54
+*>        23 24 25                10 11 55
+*>        33 34 35                20 21 22
+*>        00 44 45                30 31 32
+*>        01 11 55                40 41 42
+*>        02 12 22                50 51 52
+*>
+*>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
+*>  transpose of RFP A above. One therefore gets:
+*>
+*>
+*>           RFP A                   RFP A
+*>
+*>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
+*>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
+*>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
+*>
+*>
+*>  We then consider Rectangular Full Packed (RFP) Format when N is
+*>  odd. We give an example where N = 5.
+*>
+*>     AP is Upper                 AP is Lower
+*>
+*>   00 01 02 03 04              00
+*>      11 12 13 14              10 11
+*>         22 23 24              20 21 22
+*>            33 34              30 31 32 33
+*>               44              40 41 42 43 44
+*>
+*>
+*>  Let TRANSR = 'N'. RFP holds AP as follows:
+*>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
+*>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
+*>  the transpose of the first two columns of AP upper.
+*>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
+*>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
+*>  the transpose of the last two columns of AP lower.
+*>  This covers the case N odd and TRANSR = 'N'.
+*>
+*>         RFP A                   RFP A
+*>
+*>        02 03 04                00 33 43
+*>        12 13 14                10 11 44
+*>        22 23 24                20 21 22
+*>        00 33 34                30 31 32
+*>        01 11 44                40 41 42
+*>
+*>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
+*>  transpose of RFP A above. One therefore gets:
+*>
+*>           RFP A                   RFP A
+*>
+*>     02 12 22 00 01             00 10 20 30 40 50
+*>     03 13 23 33 11             33 11 21 31 41 51
+*>     04 14 24 34 44             43 44 22 32 42 52
+*> \endverbatim
+*>
+*  =====================================================================
+      SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
 *
+*  -- 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 2011
 *
 *     .. Scalar Arguments ..
       CHARACTER          TRANSR, UPLO
@@ -15,133 +203,6 @@
       DOUBLE PRECISION         A( 0: * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  DPFTRI computes the inverse of a (real) symmetric positive definite
-*  matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
-*  computed by DPFTRF.
-*
-*  Arguments
-*  =========
-*
-*  TRANSR  (input) CHARACTER
-*          = 'N':  The Normal TRANSR of RFP A is stored;
-*          = 'T':  The Transpose TRANSR of RFP A is stored.
-*
-*  UPLO    (input) CHARACTER
-*          = 'U':  Upper triangle of A is stored;
-*          = 'L':  Lower triangle of A is stored.
-*
-*  N       (input) INTEGER
-*          The order of the matrix A.  N >= 0.
-*
-*  A       (input/output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 )
-*          On entry, the symmetric matrix A in RFP format. RFP format is
-*          described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
-*          then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
-*          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
-*          the transpose of RFP A as defined when
-*          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
-*          follows: If UPLO = 'U' the RFP A contains the nt elements of
-*          upper packed A. If UPLO = 'L' the RFP A contains the elements
-*          of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
-*          'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N
-*          is odd. See the Note below for more details.
-*
-*          On exit, the symmetric inverse of the original matrix, in the
-*          same storage format.
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit
-*          < 0:  if INFO = -i, the i-th argument had an illegal value
-*          > 0:  if INFO = i, the (i,i) element of the factor U or L is
-*                zero, and the inverse could not be computed.
-*
-*  Further Details
-*  ===============
-*
-*  We first consider Rectangular Full Packed (RFP) Format when N is
-*  even. We give an example where N = 6.
-*
-*      AP is Upper             AP is Lower
-*
-*   00 01 02 03 04 05       00
-*      11 12 13 14 15       10 11
-*         22 23 24 25       20 21 22
-*            33 34 35       30 31 32 33
-*               44 45       40 41 42 43 44
-*                  55       50 51 52 53 54 55
-*
-*
-*  Let TRANSR = 'N'. RFP holds AP as follows:
-*  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
-*  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
-*  the transpose of the first three columns of AP upper.
-*  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
-*  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
-*  the transpose of the last three columns of AP lower.
-*  This covers the case N even and TRANSR = 'N'.
-*
-*         RFP A                   RFP A
-*
-*        03 04 05                33 43 53
-*        13 14 15                00 44 54
-*        23 24 25                10 11 55
-*        33 34 35                20 21 22
-*        00 44 45                30 31 32
-*        01 11 55                40 41 42
-*        02 12 22                50 51 52
-*
-*  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
-*  transpose of RFP A above. One therefore gets:
-*
-*
-*           RFP A                   RFP A
-*
-*     03 13 23 33 00 01 02    33 00 10 20 30 40 50
-*     04 14 24 34 44 11 12    43 44 11 21 31 41 51
-*     05 15 25 35 45 55 22    53 54 55 22 32 42 52
-*
-*
-*  We then consider Rectangular Full Packed (RFP) Format when N is
-*  odd. We give an example where N = 5.
-*
-*     AP is Upper                 AP is Lower
-*
-*   00 01 02 03 04              00
-*      11 12 13 14              10 11
-*         22 23 24              20 21 22
-*            33 34              30 31 32 33
-*               44              40 41 42 43 44
-*
-*
-*  Let TRANSR = 'N'. RFP holds AP as follows:
-*  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
-*  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
-*  the transpose of the first two columns of AP upper.
-*  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
-*  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
-*  the transpose of the last two columns of AP lower.
-*  This covers the case N odd and TRANSR = 'N'.
-*
-*         RFP A                   RFP A
-*
-*        02 03 04                00 33 43
-*        12 13 14                10 11 44
-*        22 23 24                20 21 22
-*        00 33 34                30 31 32
-*        01 11 44                40 41 42
-*
-*  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
-*  transpose of RFP A above. One therefore gets:
-*
-*           RFP A                   RFP A
-*
-*     02 12 22 00 01             00 10 20 30 40 50
-*     03 13 23 33 11             33 11 21 31 41 51
-*     04 14 24 34 44             43 44 22 32 42 52
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -184,13 +245,13 @@
 *     Quick return if possible
 *
       IF( N.EQ.0 )
-     +   RETURN
+     $   RETURN
 *
 *     Invert the triangular Cholesky factor U or L.
 *
       CALL DTFTRI( TRANSR, UPLO, 'N', N, A, INFO )
       IF( INFO.GT.0 )
-     +   RETURN
+     $   RETURN
 *
 *     If N is odd, set NISODD = .TRUE.
 *     If N is even, set K = N/2 and NISODD = .FALSE.
@@ -231,9 +292,9 @@
 *
                CALL DLAUUM( 'L', N1, A( 0 ), N, INFO )
                CALL DSYRK( 'L', 'T', N1, N2, ONE, A( N1 ), N, ONE,
-     +                     A( 0 ), N )
+     $                     A( 0 ), N )
                CALL DTRMM( 'L', 'U', 'N', 'N', N2, N1, ONE, A( N ), N,
-     +                     A( N1 ), N )
+     $                     A( N1 ), N )
                CALL DLAUUM( 'U', N2, A( N ), N, INFO )
 *
             ELSE
@@ -244,9 +305,9 @@
 *
                CALL DLAUUM( 'L', N1, A( N2 ), N, INFO )
                CALL DSYRK( 'L', 'N', N1, N2, ONE, A( 0 ), N, ONE,
-     +                     A( N2 ), N )
+     $                     A( N2 ), N )
                CALL DTRMM( 'R', 'U', 'T', 'N', N1, N2, ONE, A( N1 ), N,
-     +                     A( 0 ), N )
+     $                     A( 0 ), N )
                CALL DLAUUM( 'U', N2, A( N1 ), N, INFO )
 *
             END IF
@@ -262,9 +323,9 @@
 *
                CALL DLAUUM( 'U', N1, A( 0 ), N1, INFO )
                CALL DSYRK( 'U', 'N', N1, N2, ONE, A( N1*N1 ), N1, ONE,
-     +                     A( 0 ), N1 )
+     $                     A( 0 ), N1 )
                CALL DTRMM( 'R', 'L', 'N', 'N', N1, N2, ONE, A( 1 ), N1,
-     +                     A( N1*N1 ), N1 )
+     $                     A( N1*N1 ), N1 )
                CALL DLAUUM( 'L', N2, A( 1 ), N1, INFO )
 *
             ELSE
@@ -274,9 +335,9 @@
 *
                CALL DLAUUM( 'U', N1, A( N2*N2 ), N2, INFO )
                CALL DSYRK( 'U', 'T', N1, N2, ONE, A( 0 ), N2, ONE,
-     +                     A( N2*N2 ), N2 )
+     $                     A( N2*N2 ), N2 )
                CALL DTRMM( 'L', 'L', 'T', 'N', N2, N1, ONE, A( N1*N2 ),
-     +                     N2, A( 0 ), N2 )
+     $                     N2, A( 0 ), N2 )
                CALL DLAUUM( 'L', N2, A( N1*N2 ), N2, INFO )
 *
             END IF
@@ -299,9 +360,9 @@
 *
                CALL DLAUUM( 'L', K, A( 1 ), N+1, INFO )
                CALL DSYRK( 'L', 'T', K, K, ONE, A( K+1 ), N+1, ONE,
-     +                     A( 1 ), N+1 )
+     $                     A( 1 ), N+1 )
                CALL DTRMM( 'L', 'U', 'N', 'N', K, K, ONE, A( 0 ), N+1,
-     +                     A( K+1 ), N+1 )
+     $                     A( K+1 ), N+1 )
                CALL DLAUUM( 'U', K, A( 0 ), N+1, INFO )
 *
             ELSE
@@ -312,9 +373,9 @@
 *
                CALL DLAUUM( 'L', K, A( K+1 ), N+1, INFO )
                CALL DSYRK( 'L', 'N', K, K, ONE, A( 0 ), N+1, ONE,
-     +                     A( K+1 ), N+1 )
+     $                     A( K+1 ), N+1 )
                CALL DTRMM( 'R', 'U', 'T', 'N', K, K, ONE, A( K ), N+1,
-     +                     A( 0 ), N+1 )
+     $                     A( 0 ), N+1 )
                CALL DLAUUM( 'U', K, A( K ), N+1, INFO )
 *
             END IF
@@ -331,9 +392,9 @@
 *
                CALL DLAUUM( 'U', K, A( K ), K, INFO )
                CALL DSYRK( 'U', 'N', K, K, ONE, A( K*( K+1 ) ), K, ONE,
-     +                     A( K ), K )
+     $                     A( K ), K )
                CALL DTRMM( 'R', 'L', 'N', 'N', K, K, ONE, A( 0 ), K,
-     +                     A( K*( K+1 ) ), K )
+     $                     A( K*( K+1 ) ), K )
                CALL DLAUUM( 'L', K, A( 0 ), K, INFO )
 *
             ELSE
@@ -344,9 +405,9 @@
 *
                CALL DLAUUM( 'U', K, A( K*( K+1 ) ), K, INFO )
                CALL DSYRK( 'U', 'T', K, K, ONE, A( 0 ), K, ONE,
-     +                     A( K*( K+1 ) ), K )
+     $                     A( K*( K+1 ) ), K )
                CALL DTRMM( 'L', 'L', 'T', 'N', K, K, ONE, A( K*K ), K,
-     +                     A( 0 ), K )
+     $                     A( 0 ), K )
                CALL DLAUUM( 'L', K, A( K*K ), K, INFO )
 *
             END IF