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Functions
FLA_Tridiag_UT_l_unb_var3.c File Reference

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Functions

FLA_Error FLA_Tridiag_UT_l_unb_var3 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Tridiag_UT_l_step_unb_var3 (FLA_Obj A, FLA_Obj Z, FLA_Obj T)
 

Function Documentation

◆ FLA_Tridiag_UT_l_step_unb_var3()

FLA_Error FLA_Tridiag_UT_l_step_unb_var3 ( FLA_Obj  A,
FLA_Obj  Z,
FLA_Obj  T 
)
30 {
31  FLA_Obj ATL, ATR, A00, a01, A02,
32  ABL, ABR, a10t, alpha11, a12t,
33  A20, a21, A22;
34  FLA_Obj ZTL, ZTR, Z00, z011, Z02,
35  ZBL, ZBR, z10t, zeta11, z12t,
36  Z20, z21, Z22;
37  FLA_Obj TTL, TTR, T00, t01, T02,
38  TBL, TBR, t10t, tau11, t12t,
39  T20, t21, T22;
40  FLA_Obj dT, d01,
41  dB, delta11,
42  d21;
43  FLA_Obj fT, f01,
44  fB, phi11,
45  f21;
46  FLA_Obj d, f;
47 
48  FLA_Obj inv_tau11;
49  FLA_Obj minus_inv_tau11;
50  FLA_Obj beta;
51  FLA_Obj first_elem;
52  FLA_Obj last_elem;
53 
54  FLA_Obj a10t_l, a10t_r;
55  FLA_Obj a21_t,
56  a21_b;
57  FLA_Obj a2;
58 
59  FLA_Datatype datatype_A;
60  dim_t m_A;
61  dim_t b_alg;
62 
63 
64  b_alg = FLA_Obj_length( T );
65 
66  datatype_A = FLA_Obj_datatype( A );
67  m_A = FLA_Obj_length( A );
68 
69  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
70  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
71  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
72  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
73  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &last_elem );
74  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
75  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
76 
77  FLA_Set( FLA_ZERO, Z );
78 
79  FLA_Part_2x2( A, &ATL, &ATR,
80  &ABL, &ABR, 0, 0, FLA_TL );
81  FLA_Part_2x2( Z, &ZTL, &ZTR,
82  &ZBL, &ZBR, 0, 0, FLA_TL );
83  FLA_Part_2x2( T, &TTL, &TTR,
84  &TBL, &TBR, 0, 0, FLA_TL );
85  FLA_Part_2x1( d, &dT,
86  &dB, 0, FLA_TOP );
87  FLA_Part_2x1( f, &fT,
88  &fB, 0, FLA_TOP );
89 
90  while ( FLA_Obj_length( ATL ) < b_alg )
91  {
92  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
93  /* ************* */ /* ************************** */
94  &a10t, /**/ &alpha11, &a12t,
95  ABL, /**/ ABR, &A20, /**/ &a21, &A22,
96  1, 1, FLA_BR );
97  FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR, &Z00, /**/ &z011, &Z02,
98  /* ************* */ /* ************************* */
99  &z10t, /**/ &zeta11, &z12t,
100  ZBL, /**/ ZBR, &Z20, /**/ &z21, &Z22,
101  1, 1, FLA_BR );
102  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
103  /* ************* */ /* ************************ */
104  &t10t, /**/ &tau11, &t12t,
105  TBL, /**/ TBR, &T20, /**/ &t21, &T22,
106  1, 1, FLA_BR );
107  FLA_Repart_2x1_to_3x1( dT, &d01,
108  /* ** */ /* ******* */
109  &delta11,
110  dB, &d21, 1, FLA_BOTTOM );
111  FLA_Repart_2x1_to_3x1( fT, &f01,
112  /* ** */ /* ***** */
113  &phi11,
114  fB, &f21, 1, FLA_BOTTOM );
115 
116  /*------------------------------------------------------------*/
117 
118  // Save first element of a10_r and set it to one so we can use a10t as
119  // u10t in subsequent computations. We will restore a10_r later on.
120  if ( FLA_Obj_length( ATL ) > 0 )
121  {
122  FLA_Part_1x2( a10t, &a10t_l, &a10t_r, 1, FLA_RIGHT );
123  FLA_Copy( a10t_r, last_elem );
124  FLA_Set( FLA_ONE, a10t_r );
125  }
126 
127  FLA_Merge_2x1( alpha11,
128  a21, &a2 );
129 
130  // alpha11 = alpha11 - u10t * z10t' - z10t * u10t';
131  // a21 = a21 - U20 * z10t' - Z20 * u10t';
132  FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, z10t, FLA_ONE, a2 );
133  FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
134 
135  // Restore last element of a10t.
136  if ( FLA_Obj_length( ATL ) > 0 )
137  {
138  FLA_Copy( last_elem, a10t_r );
139  }
140 
141  if ( FLA_Obj_length( A22 ) > 0 )
142  {
143  FLA_Part_2x1( a21, &a21_t,
144  &a21_b, 1, FLA_TOP );
145 
146  // [ u21, tau11, a21 ] = House( a21 );
147  FLA_Househ2_UT( FLA_LEFT,
148  a21_t,
149  a21_b, tau11 );
150 
151  // inv_tau11 = 1 / tau11;
152  // minus_inv_tau11 = -1 / tau11;
153  FLA_Set( FLA_ONE, inv_tau11 );
154  FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
155  FLA_Copy( inv_tau11, minus_inv_tau11 );
156  FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
157 
158  // Save first element of a21_t and set it to one.
159  FLA_Copy( a21_t, first_elem );
160  FLA_Set( FLA_ONE, a21_t );
161 
162  // z21 = A22 * u21;
163  FLA_Hemv( FLA_LOWER_TRIANGULAR, FLA_ONE, A22, a21, FLA_ZERO, z21 );
164 
165  // z21 = z21 - U20 * ( Z20' * u21 ) - Z20 * ( U20' * u21 );
166  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d01 );
167  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f01 );
168 
169  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f01, FLA_ONE, z21 );
170  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d01, FLA_ONE, z21 );
171 
172  // t01 = U20' * u21;
173  FLA_Copy( d01, t01 );
174 
175  // beta = u21' * z21 / 2;
176  FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
177  FLA_Inv_scal( FLA_TWO, beta );
178 
179  // z21 = ( z21 - beta / tau * u21 ) / tau;
180  FLA_Scal( minus_inv_tau11, beta );
181  FLA_Axpy( beta, a21, z21 );
182  FLA_Scal( inv_tau11, z21 );
183 
184  // Restore first element of a21.
185  FLA_Copy( first_elem, a21_t );
186  }
187 
188  /*------------------------------------------------------------*/
189 
190  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
191  a10t, alpha11, /**/ a12t,
192  /* ************** */ /* ************************ */
193  &ABL, /**/ &ABR, A20, a21, /**/ A22,
194  FLA_TL );
195  FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR, Z00, z011, /**/ Z02,
196  z10t, zeta11, /**/ z12t,
197  /* ************** */ /* *********************** */
198  &ZBL, /**/ &ZBR, Z20, z21, /**/ Z22,
199  FLA_TL );
200  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
201  t10t, tau11, /**/ t12t,
202  /* ************** */ /* ********************** */
203  &TBL, /**/ &TBR, T20, t21, /**/ T22,
204  FLA_TL );
205  FLA_Cont_with_3x1_to_2x1( &dT, d01,
206  delta11,
207  /* ** */ /* ******* */
208  &dB, d21, FLA_TOP );
209  FLA_Cont_with_3x1_to_2x1( &fT, f01,
210  phi11,
211  /* ** */ /* ***** */
212  &fB, f21, FLA_TOP );
213  }
214 
215  FLA_Obj_free( &inv_tau11 );
216  FLA_Obj_free( &minus_inv_tau11 );
217  FLA_Obj_free( &beta );
218  FLA_Obj_free( &first_elem );
219  FLA_Obj_free( &last_elem );
220  FLA_Obj_free( &d );
221  FLA_Obj_free( &f );
222 
223  return FLA_SUCCESS;
224 }
FLA_Error FLA_Copy(FLA_Obj A, FLA_Obj B)
Definition: FLA_Copy.c:15
FLA_Error FLA_Scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Scal.c:15
FLA_Error FLA_Dotc(FLA_Conj conj, FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition: FLA_Dotc.c:13
FLA_Error FLA_Axpy(FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition: FLA_Axpy.c:15
FLA_Error FLA_Inv_scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scal.c:13
FLA_Error FLA_Inv_scalc(FLA_Conj conjalpha, FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scalc.c:13
FLA_Error FLA_Hemv(FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Hemv.c:13
FLA_Error FLA_Gemvc(FLA_Trans transa, FLA_Conj conjx, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Gemvc.c:13
FLA_Error FLA_Gemv(FLA_Trans transa, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Gemv.c:15
FLA_Obj FLA_TWO
Definition: FLA_Init.c:17
FLA_Obj FLA_MINUS_ONE
Definition: FLA_Init.c:22
FLA_Obj FLA_ZERO
Definition: FLA_Init.c:20
FLA_Obj FLA_ONE
Definition: FLA_Init.c:18
FLA_Error FLA_Cont_with_3x3_to_2x2(FLA_Obj *ATL, FLA_Obj *ATR, FLA_Obj A00, FLA_Obj A01, FLA_Obj A02, FLA_Obj A10, FLA_Obj A11, FLA_Obj A12, FLA_Obj *ABL, FLA_Obj *ABR, FLA_Obj A20, FLA_Obj A21, FLA_Obj A22, FLA_Quadrant quadrant)
Definition: FLA_View.c:304
FLA_Error FLA_Part_2x2(FLA_Obj A, FLA_Obj *A11, FLA_Obj *A12, FLA_Obj *A21, FLA_Obj *A22, dim_t mb, dim_t nb, FLA_Quadrant quadrant)
Definition: FLA_View.c:17
FLA_Error FLA_Cont_with_3x1_to_2x1(FLA_Obj *AT, FLA_Obj A0, FLA_Obj A1, FLA_Obj *AB, FLA_Obj A2, FLA_Side side)
Definition: FLA_View.c:428
FLA_Error FLA_Repart_2x1_to_3x1(FLA_Obj AT, FLA_Obj *A0, FLA_Obj *A1, FLA_Obj AB, FLA_Obj *A2, dim_t mb, FLA_Side side)
Definition: FLA_View.c:226
FLA_Error FLA_Obj_create(FLA_Datatype datatype, dim_t m, dim_t n, dim_t rs, dim_t cs, FLA_Obj *obj)
Definition: FLA_Obj.c:55
FLA_Error FLA_Part_1x2(FLA_Obj A, FLA_Obj *A1, FLA_Obj *A2, dim_t nb, FLA_Side side)
Definition: FLA_View.c:110
FLA_Error FLA_Part_2x1(FLA_Obj A, FLA_Obj *A1, FLA_Obj *A2, dim_t mb, FLA_Side side)
Definition: FLA_View.c:76
dim_t FLA_Obj_length(FLA_Obj obj)
Definition: FLA_Query.c:116
FLA_Error FLA_Repart_2x2_to_3x3(FLA_Obj ATL, FLA_Obj ATR, FLA_Obj *A00, FLA_Obj *A01, FLA_Obj *A02, FLA_Obj *A10, FLA_Obj *A11, FLA_Obj *A12, FLA_Obj ABL, FLA_Obj ABR, FLA_Obj *A20, FLA_Obj *A21, FLA_Obj *A22, dim_t mb, dim_t nb, FLA_Quadrant quadrant)
Definition: FLA_View.c:142
FLA_Error FLA_Merge_2x1(FLA_Obj AT, FLA_Obj AB, FLA_Obj *A)
Definition: FLA_View.c:541
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition: FLA_Obj.c:588
FLA_Datatype FLA_Obj_datatype(FLA_Obj obj)
Definition: FLA_Query.c:13
int FLA_Datatype
Definition: FLA_type_defs.h:49
unsigned long dim_t
Definition: FLA_type_defs.h:71
FLA_Error FLA_Set(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Set.c:13
FLA_Error FLA_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition: FLA_Househ2_UT.c:16
Definition: FLA_type_defs.h:159

References FLA_Axpy(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Dotc(), FLA_Gemv(), FLA_Gemvc(), FLA_Hemv(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Set(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Tridiag_UT_l_unb_var3().

◆ FLA_Tridiag_UT_l_unb_var3()

FLA_Error FLA_Tridiag_UT_l_unb_var3 ( FLA_Obj  A,
FLA_Obj  T 
)
14 {
15  FLA_Error r_val;
16  FLA_Obj Z;
17 
18  //FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Y );
19  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );
20 
21  r_val = FLA_Tridiag_UT_l_step_unb_var3( A, Z, T );
22 
23  //FLA_Obj_free( &Y );
24  FLA_Obj_free( &Z );
25 
26  return r_val;
27 }
FLA_Error FLA_Tridiag_UT_l_step_unb_var3(FLA_Obj A, FLA_Obj Z, FLA_Obj T)
Definition: FLA_Tridiag_UT_l_unb_var3.c:29
FLA_Error FLA_Obj_create_conf_to(FLA_Trans trans, FLA_Obj old, FLA_Obj *obj)
Definition: FLA_Obj.c:286
int FLA_Error
Definition: FLA_type_defs.h:47

References FLA_Obj_create_conf_to(), FLA_Obj_free(), and FLA_Tridiag_UT_l_step_unb_var3().

Referenced by FLA_Tridiag_UT_l().