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, 159 insertions, 24 deletions

diff --git a/TESTING/LIN/cerrhex.f b/TESTING/LIN/cerrhex.f
index a6ee9fa9..662892e3 100644
--- a/TESTING/LIN/cerrhex.f
+++ b/TESTING/LIN/cerrhex.f
@@ -51,17 +51,17 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date November 2015
+*> \date November 2016
 *
 *> \ingroup complex_lin
 *
 *  =====================================================================
       SUBROUTINE CERRHE( PATH, NUNIT )
 *
-*  -- LAPACK test routine (version 3.6.0) --
+*  -- LAPACK test routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2015
+*     November 2016
 *
 *     .. Scalar Arguments ..
       CHARACTER*3        PATH
@@ -87,18 +87,19 @@
      $                   S( NMAX ), ERR_BNDS_N( NMAX, 3 ),
      $                   ERR_BNDS_C( NMAX, 3 ), PARAMS( 1 )
       COMPLEX            A( NMAX, NMAX ), AF( NMAX, NMAX ), B( NMAX ),
-     $                   W( 2*NMAX ), X( NMAX )
+     $                   E( NMAX ), W( 2*NMAX ), X( NMAX )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
       EXTERNAL           LSAMEN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ALAESM, CHECON,  CHECON_ROOK, CHERFS, CHETF2,
-     $                   CHETF2_ROOK, CHETRF, CHETRF_ROOK, CHETRI,
-     $                   CHETRI_ROOK, CHETRI2, CHETRS,  CHETRS_ROOK,
-     $                   CHKXER, CHPCON, CHPRFS, CHPTRF, CHPTRI, CHPTRS,
-     $                   CHERFSX
+      EXTERNAL           ALAESM, CHECON, CHECON_3, CHECON_ROOK, CHERFS,
+     $                   CHETF2, CHETF2_RK, CHETF2_ROOK, CHETRF,
+     $                   CHETRF_RK, CHETRF_ROOK, CHETRI, CHETRI_3,
+     $                   CHETRI_3X, CHETRI_ROOK, CHETRI2, CHETRI2X,
+     $                   CHETRS, CHETRS_3, CHETRS_ROOK, CHKXER, CHPCON,
+     $                   CHPRFS, CHPTRF, CHPTRI, CHPTRS, CHERFSX
 *     ..
 *     .. Scalars in Common ..
       LOGICAL            LERR, OK
@@ -125,23 +126,23 @@
             A( I, J ) = CMPLX( 1. / REAL( I+J ), -1. / REAL( I+J ) )
             AF( I, J ) = CMPLX( 1. / REAL( I+J ), -1. / REAL( I+J ) )
    10    CONTINUE
-         B( J ) = 0.
-         R1( J ) = 0.
-         R2( J ) = 0.
-         W( J ) = 0.
-         X( J ) = 0.
-         S( J ) = 0.
+         B( J ) = 0.E+0
+         E( J ) = 0.E+0
+         R1( J ) = 0.E+0
+         R2( J ) = 0.E+0
+         W( J ) = 0.E+0
+         X( J ) = 0.E+0
          IP( J ) = J
    20 CONTINUE
       ANRM = 1.0
       OK = .TRUE.
 *
-*     Test error exits of the routines that use factorization
-*     of a Hermitian indefinite matrix with patrial
-*     (Bunch-Kaufman) diagonal pivoting method.
-*
       IF( LSAMEN( 2, C2, 'HE' ) ) THEN
 *
+*        Test error exits of the routines that use factorization
+*        of a Hermitian indefinite matrix with patrial
+*        (Bunch-Kaufman) diagonal pivoting method.
+*
 *        CHETRF
 *
          SRNAMT = 'CHETRF'
@@ -154,6 +155,12 @@
          INFOT = 4
          CALL CHETRF( 'U', 2, A, 1, IP, W, 4, INFO )
          CALL CHKXER( 'CHETRF', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL CHETRF( 'U', 0, A, 1, IP, W, 0, INFO )
+         CALL CHKXER( 'CHETRF', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL CHETRF( 'U', 0, A, 1, IP, W, -2, INFO )
+         CALL CHKXER( 'CHETRF', INFOT, NOUT, LERR, OK )
 *
 *        CHETF2
 *
@@ -194,6 +201,19 @@
          CALL CHETRI2( 'U', 2, A, 1, IP, W, 1, INFO )
          CALL CHKXER( 'CHETRI2', INFOT, NOUT, LERR, OK )
 *
+*        CHETRI2X
+*
+         SRNAMT = 'CHETRI2X'
+         INFOT = 1
+         CALL CHETRI2X( '/', 0, A, 1, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI2X', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHETRI2X( 'U', -1, A, 1, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI2X', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CHETRI2X( 'U', 2, A, 1, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI2X', INFOT, NOUT, LERR, OK )
+*
 *        CHETRS
 *
          SRNAMT = 'CHETRS'
@@ -308,12 +328,12 @@
      $        PARAMS, W, R, INFO )
          CALL CHKXER( 'CHERFSX', INFOT, NOUT, LERR, OK )
 *
+      ELSE IF( LSAMEN( 2, C2, 'HR' ) ) THEN
+*
 *        Test error exits of the routines that use factorization
-*        of a Hermitian indefinite matrix with "rook"
+*        of a Hermitian indefinite matrix with rook
 *        (bounded Bunch-Kaufman) diagonal pivoting method.
 *
-      ELSE IF( LSAMEN( 2, C2, 'HR' ) ) THEN
-*
 *        CHETRF_ROOK
 *
          SRNAMT = 'CHETRF_ROOK'
@@ -326,6 +346,12 @@
          INFOT = 4
          CALL CHETRF_ROOK( 'U', 2, A, 1, IP, W, 4, INFO )
          CALL CHKXER( 'CHETRF_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL CHETRF_ROOK( 'U', 0, A, 1, IP, W, 0, INFO )
+         CALL CHKXER( 'CHETRF_ROOK', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL CHETRF_ROOK( 'U', 0, A, 1, IP, W, -2, INFO )
+         CALL CHKXER( 'CHETRF_ROOK', INFOT, NOUT, LERR, OK )
 *
 *        CHETF2_ROOK
 *
@@ -388,12 +414,121 @@
          CALL CHECON_ROOK( 'U', 1, A, 1, IP, -ANRM, RCOND, W, INFO )
          CALL CHKXER( 'CHECON_ROOK', INFOT, NOUT, LERR, OK )
 *
+      ELSE IF( LSAMEN( 2, C2, 'HK' ) ) THEN
+*
+*        Test error exits of the routines that use factorization
+*        of a Hermitian 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.
+*
+*        CHETRF_RK
+*
+         SRNAMT = 'CHETRF_RK'
+         INFOT = 1
+         CALL CHETRF_RK( '/', 0, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRF_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHETRF_RK( 'U', -1, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRF_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CHETRF_RK( 'U', 2, A, 1, E, IP, W, 4, INFO )
+         CALL CHKXER( 'CHETRF_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 8
+         CALL CHETRF_RK( 'U', 0, A, 1, E, IP, W, 0, INFO )
+         CALL CHKXER( 'CHETRF_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 8
+         CALL CHETRF_RK( 'U', 0, A, 1, E, IP, W, -2, INFO )
+         CALL CHKXER( 'CHETRF_RK', INFOT, NOUT, LERR, OK )
+*
+*        CHETF2_RK
+*
+         SRNAMT = 'CHETF2_RK'
+         INFOT = 1
+         CALL CHETF2_RK( '/', 0, A, 1, E, IP, INFO )
+         CALL CHKXER( 'CHETF2_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHETF2_RK( 'U', -1, A, 1, E, IP, INFO )
+         CALL CHKXER( 'CHETF2_RK', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CHETF2_RK( 'U', 2, A, 1, E, IP, INFO )
+         CALL CHKXER( 'CHETF2_RK', INFOT, NOUT, LERR, OK )
+*
+*        CHETRI_3
+*
+         SRNAMT = 'CHETRI_3'
+         INFOT = 1
+         CALL CHETRI_3( '/', 0, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI_3', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHETRI_3( 'U', -1, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI_3', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CHETRI_3( 'U', 2, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI_3', INFOT, NOUT, LERR, OK )
+         INFOT = 8
+         CALL CHETRI_3( 'U', 0, A, 1, E, IP, W, 0, INFO )
+         CALL CHKXER( 'CHETRI_3', INFOT, NOUT, LERR, OK )
+         INFOT = 8
+         CALL CHETRI_3( 'U', 0, A, 1, E, IP, W, -2, INFO )
+         CALL CHKXER( 'CHETRI_3', INFOT, NOUT, LERR, OK )
+*
+*        CHETRI_3X
+*
+         SRNAMT = 'CHETRI_3X'
+         INFOT = 1
+         CALL CHETRI_3X( '/', 0, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI_3X', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHETRI_3X( 'U', -1, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI_3X', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CHETRI_3X( 'U', 2, A, 1, E, IP, W, 1, INFO )
+         CALL CHKXER( 'CHETRI_3X', INFOT, NOUT, LERR, OK )
+*
+*        CHETRS_3
+*
+         SRNAMT = 'CHETRS_3'
+         INFOT = 1
+         CALL CHETRS_3( '/', 0, 0, A, 1, E, IP, B, 1, INFO )
+         CALL CHKXER( 'CHETRS_3', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHETRS_3( 'U', -1, 0, A, 1, E, IP, B, 1, INFO )
+         CALL CHKXER( 'CHETRS_3', INFOT, NOUT, LERR, OK )
+         INFOT = 3
+         CALL CHETRS_3( 'U', 0, -1, A, 1, E, IP, B, 1, INFO )
+         CALL CHKXER( 'CHETRS_3', INFOT, NOUT, LERR, OK )
+         INFOT = 5
+         CALL CHETRS_3( 'U', 2, 1, A, 1, E, IP, B, 2, INFO )
+         CALL CHKXER( 'CHETRS_3', INFOT, NOUT, LERR, OK )
+         INFOT = 9
+         CALL CHETRS_3( 'U', 2, 1, A, 2, E, IP, B, 1, INFO )
+         CALL CHKXER( 'CHETRS_3', INFOT, NOUT, LERR, OK )
+*
+*        CHECON_3
+*
+         SRNAMT = 'CHECON_3'
+         INFOT = 1
+         CALL CHECON_3( '/', 0, A, 1,  E, IP, ANRM, RCOND, W, INFO )
+         CALL CHKXER( 'CHECON_3', INFOT, NOUT, LERR, OK )
+         INFOT = 2
+         CALL CHECON_3( 'U', -1, A, 1, E, IP, ANRM, RCOND, W, INFO )
+         CALL CHKXER( 'CHECON_3', INFOT, NOUT, LERR, OK )
+         INFOT = 4
+         CALL CHECON_3( 'U', 2, A, 1, E, IP, ANRM, RCOND, W, INFO )
+         CALL CHKXER( 'CHECON_3', INFOT, NOUT, LERR, OK )
+         INFOT = 7
+         CALL CHECON_3( 'U', 1, A, 1, E, IP, -1.0E0, RCOND, W, INFO)
+         CALL CHKXER( 'CHECON_3', INFOT, NOUT, LERR, OK )
+*
+      ELSE IF( LSAMEN( 2, C2, 'HP' ) ) THEN
+*
 *     Test error exits of the routines that use factorization
 *     of a Hermitian indefinite packed matrix with patrial
 *     (Bunch-Kaufman) diagonal pivoting method.
 *
-      ELSE IF( LSAMEN( 2, C2, 'HP' ) ) THEN
-*
 *        CHPTRF
 *
          SRNAMT = 'CHPTRF'