Added (S,D,C,Z) (SY,HE) routines, drivers for new rook code

Close #82

Added routines for new factorization code for symmetric indefinite
( or Hermitian indefinite ) matrices with bounded Bunch-Kaufman
( rook ) pivoting algorithm.

New more efficient storage format for factors U ( or L ),
block-diagonal matrix D, and pivoting information stored in IPIV:

factor L is stored explicitly in lower triangle of A;
diagonal of D is stored on the diagonal of A;
subdiagonal elements of D are stored in array E;
IPIV format is the same as in *_ROOK routines, but differs
from SY Bunch-Kaufman routines (e.g. *SYTRF).
The factorization output of these new rook _RK routines is not
compatible
with the existing _ROOK routines and vice versa. This new factorization
format is designed in such a way, that there is a possibility in the
future
to write new Bunch-Kaufman routines that conform to this new
factorization format.
Then the future Bunch-Kaufman routines could share solver
*TRS_3,inversion *TRI_3
and condition estimator *CON_3.

To convert between the factorization formats in both ways the following
routines
are developed:

CONVERSION ROUTINES BETWEEN FACTORIZATION FORMATS

DOUBLE PRECISION (symmetric indefinite matrices):

new file:   SRC/dsyconvf.f
new file:   SRC/dsyconvf_rook.f
REAL (symmetric indefinite matrices):

new file:   SRC/csyconvf.f
new file:   SRC/csyconvf_rook.f
COMPLEX*16 (symmetric indefinite and Hermitian indefinite matrices):

new file:   SRC/zsyconvf.f
new file:   SRC/zsyconvf_rook.f
COMPLEX (symmetric indefinite and Hermitian indefinite matrices):

new file:   SRC/ssyconvf.f
new file:   SRC/ssyconvf_rook.f
*SYCONVF routine converts between old Bunch-Kaufman storage format (
denote (L1,D1,IPIV1) )
that is used by *SYTRF and new rook storage format ( denote (L2,D2,
IPIV2))
that is used by *SYTRF_RK

*SYCONVF_ROOK routine between old rook storage format ( denote
(L1,D1,IPIV2) )
that is used by *SYTRF_ROOK and new rook storage format ( denote
(L2,D2, IPIV2))
that is used by *SYTRF_RK

ROUTINES AND DRIVERS

DOUBLE PRECISION (symmetric indefinite matrices):

new file:   SRC/dsytf2_rk.f BLAS2 unblocked factorization
new file:   SRC/dlasyf_rk.f BLAS3 auxiliary blocked partial
factorization
new file:   SRC/dsytrf_rk.f BLAS3 blocked factorization
new file:   SRC/dsytrs_3.f BLAS3 solver
new file:   SRC/dsycon_3.f BLAS3 condition number estimator
new file:   SRC/dsytri_3.f BLAS3 inversion, sets the size of work array
and calls *sytri_3x
new file:   SRC/dsytri_3x.f BLAS3 auxiliary inversion, actually
computes blocked inversion
new file:   SRC/dsysv_rk.f BLAS3 solver driver
REAL (symmetric indefinite matrices):

new file:   SRC/ssytf2_rk.f BLAS2 unblocked factorization
new file:   SRC/slasyf_rk.f BLAS3 auxiliary blocked partial
factorization
new file:   SRC/ssytrf_rk.f BLAS3 blocked factorization
new file:   SRC/ssytrs_3.f BLAS3 solver
new file:   SRC/ssycon_3.f BLAS3 condition number estimator
new file:   SRC/ssytri_3.f BLAS3 inversion, sets the size of work array
and calls *sytri_3x
new file:   SRC/ssytri_3x.f BLAS3 auxiliary inversion, actually
computes blocked inversion
new file:   SRC/ssysv_rk.f BLAS3 solver driver
COMPLEX*16 (symmetric indefinite matrices):

new file:   SRC/zsytf2_rk.f BLAS2 unblocked factorization
new file:   SRC/zlasyf_rk.f BLAS3 auxiliary blocked partial
factorization
new file:   SRC/zsytrf_rk.f BLAS3 blocked factorization
new file:   SRC/zsytrs_3.f BLAS3 solver
new file:   SRC/zsycon_3.f BLAS3 condition number estimator
new file:   SRC/zsytri_3.f BLAS3 inversion, sets the size of work array
and calls *sytri_3x
new file:   SRC/zsytri_3x.f BLAS3 auxiliary inversion, actually
computes blocked inversion
new file:   SRC/zsysv_rk.f BLAS3 solver driver
COMPLEX*16 (Hermitian indefinite matrices):

new file:   SRC/zhetf2_rk.f BLAS2 unblocked factorization
new file:   SRC/zlahef_rk.f BLAS3 auxiliary blocked partial
factorization
new file:   SRC/zhetrf_rk.f BLAS3 blocked factorization
new file:   SRC/zhetrs_3.f BLAS3 solver
new file:   SRC/zhecon_3.f BLAS3 condition number estimator
new file:   SRC/zhetri_3.f BLAS3 inversion, sets the size of work array
and calls *sytri_3x
new file:   SRC/zhetri_3x.f BLAS3 auxiliary inversion, actually
computes blocked inversion
new file:   SRC/zhesv_rk.f BLAS3 solver driver
COMPLEX (symmetric indefinite matrices):

new file:   SRC/csytf2_rk.f BLAS2 unblocked factorization
new file:   SRC/clasyf_rk.f BLAS3 auxiliary blocked partial
factorization
new file:   SRC/csytrf_rk.f BLAS3 blocked factorization
new file:   SRC/csytrs_3.f BLAS3 solver
new file:   SRC/csycon_3.f BLAS3 condition number estimator
new file:   SRC/csytri_3.f BLAS3 inversion, sets the size of work array
and calls *sytri_3x
new file:   SRC/csytri_3x.f BLAS3 auxiliary inversion, actually
computes blocked inversion
new file:   SRC/csysv_rk.f BLAS3 solver driver
COMPLEX (Hermitian indefinite matrices):

new file:   SRC/chetf2_rk.f BLAS2 unblocked factorization
new file:   SRC/clahef_rk.f BLAS3 auxiliary blocked partial
factorization
new file:   SRC/chetrf_rk.f BLAS3 blocked factorization
new file:   SRC/chetrs_3.f BLAS3 solver
new file:   SRC/checon_3.f BLAS3 condition number estimator
new file:   SRC/chetri_3.f BLAS3 inversion, sets the size of work array
and calls *sytri_3x
new file:   SRC/chetri_3x.f BLAS3 auxiliary inversion, actually
computes blocked inversion
new file:   SRC/chesv_rk.f BLAS3 solver driver
MISC

modified:   SRC/CMakeLists.txt
modified:   SRC/Makefile
TEST CODE

modified:   TESTING/LIN/CMakeLists.txt
modified:   TESTING/LIN/Makefile

modified:   TESTING/LIN/aladhd.f
modified:   TESTING/LIN/alaerh.f
modified:   TESTING/LIN/alahd.f
DOUBLE PRECISION (symmetric indefinite matrices):

modified:   TESTING/LIN/dchkaa.f
modified:   TESTING/LIN/derrsy.f
modified:   TESTING/LIN/derrsyx.f
modified:   TESTING/LIN/derrvx.f
modified:   TESTING/LIN/derrvxx.f

modified:   TESTING/dtest.in

new file:   TESTING/LIN/dchksy_rk.f
new file:   TESTING/LIN/ddrvsy_rk.f
new file:   TESTING/LIN/dsyt01_3.f
REAL (symmetric indefinite matrices):

modified:   TESTING/LIN/schkaa.f
modified:   TESTING/LIN/serrsy.f
modified:   TESTING/LIN/serrsyx.f
modified:   TESTING/LIN/serrvx.f
modified:   TESTING/LIN/serrvxx.f

modified:   TESTING/stest.in

new file:   TESTING/LIN/schksy_rk.f
new file:   TESTING/LIN/sdrvsy_rk.f
new file:   TESTING/LIN/ssyt01_3.f
COMPLEX*16 (symmetric indefinite and Hermitian indefinite matrices):

modified:   TESTING/LIN/zchkaa.f
modified:   TESTING/LIN/zerrsy.f
modified:   TESTING/LIN/zerrsyx.f
modified:   TESTING/LIN/zerrhe.f
modified:   TESTING/LIN/zerrhex.f
modified:   TESTING/LIN/zerrvx.f
modified:   TESTING/LIN/zerrvxx.f

modified:   TESTING/ztest.in

new file:   TESTING/LIN/zchksy_rk.f
new file:   TESTING/LIN/zdrvsy_rk.f
new file:   TESTING/LIN/zsyt01_3.f
new file:   TESTING/LIN/zchkhe_rk.f
new file:   TESTING/LIN/zdrvhe_rk.f
new file:   TESTING/LIN/zhet01_3.f
COMPLEX (symmetric indefinite and Hermitian indefinite matrices):

modified:   TESTING/LIN/cchkaa.f
modified:   TESTING/LIN/cerrsy.f
modified:   TESTING/LIN/cerrsyx.f
modified:   TESTING/LIN/cerrhe.f
modified:   TESTING/LIN/cerrhex.f
modified:   TESTING/LIN/cerrvx.f
modified:   TESTING/LIN/cerrvxx.f

modified:   TESTING/ctest.in

new file:   TESTING/LIN/cchksy_rk.f
new file:   TESTING/LIN/cdrvsy_rk.f
new file:   TESTING/LIN/csyt01_3.f
new file:   TESTING/LIN/cchkhe_rk.f
new file:   TESTING/LIN/cdrvhe_rk.f
new file:   TESTING/LIN/chet01_3.f

1 files changed, 85 insertions, 11 deletions

diff --git a/TESTING/LIN/derrvxx.f b/TESTING/LIN/derrvxx.f
index b28e01cb..d29797b4 100644
--- a/TESTING/LIN/derrvxx.f
+++ b/TESTING/LIN/derrvxx.f
@@ -82,9 +82,10 @@
 *     .. Local Arrays ..
       INTEGER            IP( NMAX ), IW( NMAX )
       DOUBLE PRECISION   A( NMAX, NMAX ), AF( NMAX, NMAX ), B( NMAX ),
-     $                   C( NMAX ), R( NMAX ), R1( NMAX ), R2( NMAX ),
-     $                   W( 2*NMAX ), X( NMAX ), ERR_BNDS_N( NMAX, 3 ),
-     $                   ERR_BNDS_C( NMAX, 3 ), PARAMS( 1 )
+     $                   C( NMAX ), E( NMAX ), R( NMAX ), R1( NMAX ),
+     $                   R2( NMAX ), W( 2*NMAX ), X( NMAX ),
+     $                   ERR_BNDS_N( NMAX, 3 ), ERR_BNDS_C( NMAX, 3 ),
+     $                   PARAMS( 1 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -94,7 +95,8 @@
       EXTERNAL           CHKXER, DGBSV, DGBSVX, DGESV, DGESVX, DGTSV,
      $                   DGTSVX, DPBSV, DPBSVX, DPOSV, DPOSVX, DPPSV,
      $                   DPPSVX, DPTSV, DPTSVX, DSPSV, DSPSVX, DSYSV,
-     $                   DSYSVX, DGESVXX, DSYSVXX, DPOSVXX, DGBSVXX
+     $                   DSYSV_RK, DSYSV_ROOK, DSYSVX, DGESVXX, DSYSVXX,
+     $                   DPOSVXX, DGBSVXX
 *     ..
 *     .. Scalars in Common ..
       LOGICAL            LERR, OK
@@ -121,13 +123,14 @@
             A( I, J ) = 1.D0 / DBLE( I+J )
             AF( I, J ) = 1.D0 / DBLE( I+J )
    10    CONTINUE
-         B( J ) = 0.D0
-         R1( J ) = 0.D0
-         R2( J ) = 0.D0
-         W( J ) = 0.D0
-         X( J ) = 0.D0
-         C( J ) = 0.D0
-         R( J ) = 0.D0
+         B( J ) = 0.D+0
+         E( J ) = 0.D+0
+         R1( J ) = 0.D+0
+         R2( J ) = 0.D+0
+         W( J ) = 0.D+0
+         X( J ) = 0.D+0
+         C( J ) = 0.D+0
+         R( J ) = 0.D+0
          IP( J ) = J
    20 CONTINUE
       EQ = ' '
@@ -795,9 +798,18 @@
          INFOT = 3
          CALL DSYSV( 'U', 0, -1, A, 1, IP, B, 1, W, 1, INFO )
          CALL CHKXER( 'DSYSV ', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL DSYSV( 'U', 2, 0, A, 1, IP, B, 2, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
          INFOT = 8
          CALL DSYSV( 'U', 2, 0, A, 2, IP, B, 1, W, 1, INFO )
          CALL CHKXER( 'DSYSV ', INFOT, NOUT, LERR, OK )
+         INFOT = 10
+         CALL DSYSV( 'U', 0, 0, A, 1, IP, B, 1, W, 0, INFO )
+         CALL CHKXER( 'DSYSV ', INFOT, NOUT, LERR, OK )
+         INFOT = 10
+         CALL DSYSV( 'U', 0, 0, A, 1, IP, B, 1, W, -2, INFO )
+         CALL CHKXER( 'DSYSV ', INFOT, NOUT, LERR, OK )
 *
 *        DSYSVX
 *
@@ -907,6 +919,68 @@
      $        ERR_BNDS_C, NPARAMS, PARAMS, W, IW, INFO )
          CALL CHKXER( 'DSYSVXX', INFOT, NOUT, LERR, OK )
 *
+      ELSE IF( LSAMEN( 2, C2, 'SR' ) ) THEN
+*
+*        DSYSV_ROOK
+*
+         SRNAMT = 'DSYSV_ROOK'
+         INFOT = 1
+         CALL DSYSV_ROOK( '/', 0, 0, A, 1, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL DSYSV_ROOK( 'U', -1, 0, A, 1, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL DSYSV_ROOK( 'U', 0, -1, A, 1, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL DSYSV_ROOK( 'U', 2, 0, A, 1, IP, B, 2, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 8
+         CALL DSYSV_ROOK( 'U', 2, 0, A, 2, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 10
+         CALL DSYSV_ROOK( 'U', 0, 0, A, 1, IP, B, 1, W, 0, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 10
+         CALL DSYSV_ROOK( 'U', 0, 0, A, 1, IP, B, 1, W, -2, INFO )
+         CALL CHKXER( 'DSYSV_ROOK', INFOT, NOUT, LERR, OK )
+*
+      ELSE IF( LSAMEN( 2, C2, 'SK' ) ) THEN
+*
+*        DSYSV_RK
+*
+*        Test error exits of the driver that uses factorization
+*        of a symmetric indefinite matrix with rook
+*        (bounded Bunch-Kaufman) pivoting with the new storage
+*        format for factors L ( or U) and D.
+*
+*        L (or U) is stored in A, diagonal of D is stored on the
+*        diagonal of A, subdiagonal of D is stored in a separate array E.
+*
+         SRNAMT = 'DSYSV_RK'
+         INFOT = 1
+         CALL DSYSV_RK( '/', 0, 0, A, 1, E, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL DSYSV_RK( 'U', -1, 0, A, 1, E, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL DSYSV_RK( 'U', 0, -1, A, 1, E, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL DSYSV_RK( 'U', 2, 0, A, 1, E, IP, B, 2, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 9
+         CALL DSYSV_RK( 'U', 2, 0, A, 2, E, IP, B, 1, W, 1, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 11
+         CALL DSYSV_RK( 'U', 0, 0, A, 1, E, IP, B, 1, W, 0, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 11
+         CALL DSYSV_RK( 'U', 0, 0, A, 1, E, IP, B, 1, W, -2, INFO )
+         CALL CHKXER( 'DSYSV_RK', INFOT, NOUT, LERR, OK )
+*
       ELSE IF( LSAMEN( 2, C2, 'SP' ) ) THEN
 *
 *        DSPSV