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Functions
FLA_Tridiag_UT_l_unb_var2.c File Reference

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Functions

FLA_Error FLA_Tridiag_UT_l_unb_var2 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Tridiag_UT_l_step_unb_var2 (FLA_Obj A, FLA_Obj T)
 

Function Documentation

◆ FLA_Tridiag_UT_l_step_unb_var2()

FLA_Error FLA_Tridiag_UT_l_step_unb_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dotc(), FLA_Gemv(), FLA_Hemv(), FLA_Her2(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, 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_var2().

19 {
20  FLA_Obj ATL, ATR, A00, a01, A02,
21  ABL, ABR, a10t, alpha11, a12t,
22  A20, a21, A22;
23  FLA_Obj TTL, TTR, T00, t01, T02,
24  TBL, TBR, t10t, tau11, t12t,
25  T20, t21, T22;
26  FLA_Obj uT, u01,
27  uB, upsilon11,
28  u21;
29  FLA_Obj zT, z01,
30  zB, zeta11,
31  z21;
32  FLA_Obj wT, w01,
33  wB, omega11,
34  w21;
35  FLA_Obj u, z, w;
36 
37  FLA_Obj inv_tau11;
38  FLA_Obj minus_inv_tau11;
39  FLA_Obj first_elem;
40  FLA_Obj beta;
41  FLA_Obj minus_upsilon11;
42  FLA_Obj minus_conj_upsilon11;
43  FLA_Obj minus_zeta11;
44  FLA_Obj minus_conj_zeta11;
45 
46  FLA_Obj a21_t,
47  a21_b;
48 
49  FLA_Datatype datatype_A;
50  dim_t m_A;
51  dim_t b_alg;
52 
53 
54  b_alg = FLA_Obj_length( T );
55 
56  datatype_A = FLA_Obj_datatype( A );
57  m_A = FLA_Obj_length( A );
58 
59  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
60  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
61  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
62  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
63  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_upsilon11 );
64  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_upsilon11 );
65  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_zeta11 );
66  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_zeta11 );
67  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
68  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
69  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
70 
71  FLA_Part_2x2( A, &ATL, &ATR,
72  &ABL, &ABR, 0, 0, FLA_TL );
73  FLA_Part_2x2( T, &TTL, &TTR,
74  &TBL, &TBR, 0, 0, FLA_TL );
75  FLA_Part_2x1( u, &uT,
76  &uB, 0, FLA_TOP );
77  FLA_Part_2x1( z, &zT,
78  &zB, 0, FLA_TOP );
79  FLA_Part_2x1( w, &wT,
80  &wB, 0, FLA_TOP );
81 
82  while ( FLA_Obj_length( ATL ) < b_alg )
83  {
84  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
85  /* ************* */ /* ************************** */
86  &a10t, /**/ &alpha11, &a12t,
87  ABL, /**/ ABR, &A20, /**/ &a21, &A22,
88  1, 1, FLA_BR );
89  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
90  /* ************* */ /* ************************ */
91  &t10t, /**/ &tau11, &t12t,
92  TBL, /**/ TBR, &T20, /**/ &t21, &T22,
93  1, 1, FLA_BR );
94  FLA_Repart_2x1_to_3x1( uT, &u01,
95  /* ** */ /* ********* */
96  &upsilon11,
97  uB, &u21, 1, FLA_BOTTOM );
98  FLA_Repart_2x1_to_3x1( zT, &z01,
99  /* ** */ /* ****** */
100  &zeta11,
101  zB, &z21, 1, FLA_BOTTOM );
102  FLA_Repart_2x1_to_3x1( wT, &w01,
103  /* ** */ /* ******* */
104  &omega11,
105  wB, &w21, 1, FLA_BOTTOM );
106 
107  /*------------------------------------------------------------*/
108 
109  if ( FLA_Obj_length( ATL ) > 0 )
110  {
111  FLA_Copy( upsilon11, minus_upsilon11 );
112  FLA_Scal( FLA_MINUS_ONE, minus_upsilon11 );
113  FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon11, minus_conj_upsilon11 );
114 
115  FLA_Copy( zeta11, minus_zeta11 );
116  FLA_Scal( FLA_MINUS_ONE, minus_zeta11 );
117  FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta11, minus_conj_zeta11 );
118 
119  // alpha11 = alpha11 - upsilon11 * conj(zeta11) - zeta11 * conj(upsilon11);
120  FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon11, zeta11, alpha11 );
121  FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta11, upsilon11, alpha11 );
122 
123  // a21 = a21 - conj(zeta11) * u21 - conj(upsilon11) * z21;
124  FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_zeta11, u21, a21 );
125  FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon11, z21, a21 );
126  }
127 
128  if ( FLA_Obj_length( A22 ) > 0 )
129  {
130  FLA_Part_2x1( a21, &a21_t,
131  &a21_b, 1, FLA_TOP );
132 
133  // [ x21, tau11, a21 ] = House( a21 );
134  FLA_Househ2_UT( FLA_LEFT,
135  a21_t,
136  a21_b, tau11 );
137 
138  // inv_tau11 = 1 / tau11;
139  // minus_inv_tau11 = -1 / tau11;
140  FLA_Set( FLA_ONE, inv_tau11 );
141  FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
142  FLA_Copy( inv_tau11, minus_inv_tau11 );
143  FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
144 
145  // Save first element of a21_t and set it to one so we can use a21 as
146  // u21 in subsequent computations. We will restore a21_t later on.
147  FLA_Copy( a21_t, first_elem );
148  FLA_Set( FLA_ONE, a21_t );
149  }
150 
151  if ( FLA_Obj_length( ATL ) > 0 )
152  {
153  // A22 = A22 - u21 * z21' - z21 * u21';
154  FLA_Her2( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, u21, z21, A22 );
155  }
156 
157  if ( FLA_Obj_length( A22 ) > 0 )
158  {
159  // w21 = A22 * x21;
160  FLA_Hemv( FLA_LOWER_TRIANGULAR, FLA_ONE, A22, a21, FLA_ZERO, w21 );
161 
162  // u21 = x21;
163  // z21 = w21;
164  FLA_Copy( a21, u21 );
165  FLA_Copy( w21, z21 );
166 
167  // beta = u21' * z21 / 2;
168  FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
169  FLA_Inv_scal( FLA_TWO, beta );
170 
171  // z21 = ( z21 - beta / tau * u21 ) / tau;
172  FLA_Scal( minus_inv_tau11, beta );
173  FLA_Axpy( beta, a21, z21 );
174  FLA_Scal( inv_tau11, z21 );
175 
176  // t01 = U20' * u21;
177  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
178 
179  // Restore first element of a21.
180  FLA_Copy( first_elem, a21_t );
181  }
182 
183  // Update A22 if this is the last iteration; this is needed when we're
184  // being called from the blocked routine so A22 is left in a valid state.
185  if ( FLA_Obj_length( ATL ) + 1 == b_alg &&
186  FLA_Obj_length( A22 ) > 0 )
187  {
188  // A22 = A22 - u21 * y21' - z21 * u21';
189  FLA_Her2( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, u21, z21, A22 );
190  }
191 
192  /*------------------------------------------------------------*/
193 
194  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
195  a10t, alpha11, /**/ a12t,
196  /* ************** */ /* ************************ */
197  &ABL, /**/ &ABR, A20, a21, /**/ A22,
198  FLA_TL );
199  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
200  t10t, tau11, /**/ t12t,
201  /* ************** */ /* ********************** */
202  &TBL, /**/ &TBR, T20, t21, /**/ T22,
203  FLA_TL );
204  FLA_Cont_with_3x1_to_2x1( &uT, u01,
205  upsilon11,
206  /* ** */ /* ********* */
207  &uB, u21, FLA_TOP );
208  FLA_Cont_with_3x1_to_2x1( &zT, z01,
209  zeta11,
210  /* ** */ /* ****** */
211  &zB, z21, FLA_TOP );
212  FLA_Cont_with_3x1_to_2x1( &wT, w01,
213  omega11,
214  /* ** */ /* ******* */
215  &wB, w21, FLA_TOP );
216  }
217 
218  FLA_Obj_free( &inv_tau11 );
219  FLA_Obj_free( &minus_inv_tau11 );
220  FLA_Obj_free( &first_elem );
221  FLA_Obj_free( &beta );
222  FLA_Obj_free( &minus_upsilon11 );
223  FLA_Obj_free( &minus_conj_upsilon11 );
224  FLA_Obj_free( &minus_zeta11 );
225  FLA_Obj_free( &minus_conj_zeta11 );
226  FLA_Obj_free( &u );
227  FLA_Obj_free( &z );
228  FLA_Obj_free( &w );
229 
230  return FLA_SUCCESS;
231 }
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_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_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition: FLA_Househ2_UT.c:16
unsigned long dim_t
Definition: FLA_type_defs.h:71
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition: FLA_Obj.c:588
FLA_Error FLA_Axpyt(FLA_Trans trans, FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition: FLA_Axpyt.c:15
FLA_Obj FLA_MINUS_ONE
Definition: FLA_Init.c:22
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_Copy(FLA_Obj A, FLA_Obj B)
Definition: FLA_Copy.c:15
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_Inv_scalc(FLA_Conj conjalpha, FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scalc.c:13
FLA_Error FLA_Copyt(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition: FLA_Copyt.c:15
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_Her2(FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj A)
Definition: FLA_Her2.c:13
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_Obj FLA_ONE
Definition: FLA_Init.c:18
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_Datatype FLA_Obj_datatype(FLA_Obj obj)
Definition: FLA_Query.c:13
Definition: FLA_type_defs.h:158
FLA_Error FLA_Set(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Set.c:13
FLA_Error FLA_Scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Scal.c:15
FLA_Error FLA_Inv_scal(FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scal.c:13
FLA_Error FLA_Axpy(FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition: FLA_Axpy.c:15
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
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
int FLA_Datatype
Definition: FLA_type_defs.h:49
dim_t FLA_Obj_length(FLA_Obj obj)
Definition: FLA_Query.c:116
FLA_Obj FLA_TWO
Definition: FLA_Init.c:17
FLA_Obj FLA_ZERO
Definition: FLA_Init.c:20
FLA_Error FLA_Dotc(FLA_Conj conj, FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition: FLA_Dotc.c:13

◆ FLA_Tridiag_UT_l_unb_var2()

FLA_Error FLA_Tridiag_UT_l_unb_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Tridiag_UT_l_step_unb_var2().

Referenced by FLA_Tridiag_UT_l().

14 {
15  return FLA_Tridiag_UT_l_step_unb_var2( A, T );
16 }
FLA_Error FLA_Tridiag_UT_l_step_unb_var2(FLA_Obj A, FLA_Obj T)
Definition: FLA_Tridiag_UT_l_unb_var2.c:18