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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 )
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_Copy
FLA_Error FLA_Copy(FLA_Obj A, FLA_Obj B)
Definition FLA_Copy.c:15
FLA_Scal
FLA_Error FLA_Scal(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Scal.c:15
FLA_Dotc
FLA_Error FLA_Dotc(FLA_Conj conj, FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition FLA_Dotc.c:13
FLA_Axpy
FLA_Error FLA_Axpy(FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition FLA_Axpy.c:15
FLA_Axpyt
FLA_Error FLA_Axpyt(FLA_Trans trans, FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition FLA_Axpyt.c:15
FLA_Inv_scal
FLA_Error FLA_Inv_scal(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Inv_scal.c:13
FLA_Copyt
FLA_Error FLA_Copyt(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition FLA_Copyt.c:15
FLA_Inv_scalc
FLA_Error FLA_Inv_scalc(FLA_Conj conjalpha, FLA_Obj alpha, FLA_Obj A)
Definition FLA_Inv_scalc.c:13
FLA_Her2
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_Hemv
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_Gemv
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_TWO
FLA_Obj FLA_TWO
Definition FLA_Init.c:17
FLA_MINUS_ONE
FLA_Obj FLA_MINUS_ONE
Definition FLA_Init.c:22
FLA_ZERO
FLA_Obj FLA_ZERO
Definition FLA_Init.c:20
FLA_ONE
FLA_Obj FLA_ONE
Definition FLA_Init.c:18
FLA_Cont_with_3x3_to_2x2
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_Part_2x2
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_Cont_with_3x1_to_2x1
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_Repart_2x1_to_3x1
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_Obj_create
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_Part_2x1
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_Obj_length
dim_t FLA_Obj_length(FLA_Obj obj)
Definition FLA_Query.c:116
FLA_Repart_2x2_to_3x3
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_Obj_free
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition FLA_Obj.c:588
FLA_Obj_datatype
FLA_Datatype FLA_Obj_datatype(FLA_Obj obj)
Definition FLA_Query.c:13
FLA_Datatype
int FLA_Datatype
Definition FLA_type_defs.h:49
dim_t
unsigned long dim_t
Definition FLA_type_defs.h:71
FLA_Set
FLA_Error FLA_Set(FLA_Obj alpha, FLA_Obj A)
Definition FLA_Set.c:13
FLA_Househ2_UT
FLA_Error FLA_Househ2_UT(FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
Definition FLA_Househ2_UT.c:16
FLA_Obj_view
Definition FLA_type_defs.h:159

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().

◆ FLA_Tridiag_UT_l_unb_var2()

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

References FLA_Tridiag_UT_l_step_unb_var2().

Referenced by FLA_Tridiag_UT_l().

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