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Functions
FLA_Hess_UT_unb_var5.c File Reference

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Functions

FLA_Error FLA_Hess_UT_unb_var5 (FLA_Obj A, FLA_Obj T)
 
FLA_Error FLA_Hess_UT_step_unb_var5 (FLA_Obj A, FLA_Obj U, FLA_Obj Z, FLA_Obj T)
 

Function Documentation

◆ FLA_Hess_UT_step_unb_var5()

FLA_Error FLA_Hess_UT_step_unb_var5 ( FLA_Obj  A,
FLA_Obj  U,
FLA_Obj  Z,
FLA_Obj  T 
)

References FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dots(), FLA_Gemv(), FLA_Househ2_UT(), 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_Set(), FLA_Trmvsx(), FLA_Trsv(), FLA_ZERO, and omega1.

Referenced by FLA_Hess_UT_unb_var5().

30 {
31  FLA_Obj ATL, ATR, A00, a01, A02,
32  ABL, ABR, a10t, alpha11, a12t,
33  A20, a21, A22;
34  FLA_Obj UTL, UTR, U00, u01, U02,
35  UBL, UBR, u10t, upsilon11, u12t,
36  U20, u21, U22;
37  FLA_Obj ZTL, ZTR, Z00, z01, Z02,
38  ZBL, ZBR, z10t, zeta11, z12t,
39  Z20, z21, Z22;
40  FLA_Obj TTL, TTR, T00, t01, T02,
41  TBL, TBR, t10t, tau11, t12t,
42  T20, t21, T22;
43  FLA_Obj wT, w0,
44  wB, omega1,
45  w2;
46  FLA_Obj w;
47 
48  FLA_Obj a21_t,
49  a21_b;
50  FLA_Obj u21_t,
51  u21_b;
52 
53  FLA_Datatype datatype_A;
54  dim_t m_A;
55  dim_t b_alg;
56 
57 
58  b_alg = FLA_Obj_length( T );
59 
60  datatype_A = FLA_Obj_datatype( A );
61  m_A = FLA_Obj_length( A );
62 
63  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
64 
65  FLA_Set( FLA_ZERO, U );
66  FLA_Set( FLA_ZERO, Z );
67 
68  FLA_Part_2x2( A, &ATL, &ATR,
69  &ABL, &ABR, 0, 0, FLA_TL );
70  FLA_Part_2x2( U, &UTL, &UTR,
71  &UBL, &UBR, 0, 0, FLA_TL );
72  FLA_Part_2x2( Z, &ZTL, &ZTR,
73  &ZBL, &ZBR, 0, 0, FLA_TL );
74  FLA_Part_2x2( T, &TTL, &TTR,
75  &TBL, &TBR, 0, 0, FLA_TL );
76  FLA_Part_2x1( w, &wT,
77  &wB, 0, FLA_TOP );
78 
79  while ( FLA_Obj_length( ATL ) < b_alg )
80  {
81  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
82  /* ************* */ /* ************************** */
83  &a10t, /**/ &alpha11, &a12t,
84  ABL, /**/ ABR, &A20, /**/ &a21, &A22,
85  1, 1, FLA_BR );
86  FLA_Repart_2x2_to_3x3( UTL, /**/ UTR, &U00, /**/ &u01, &U02,
87  /* ************* */ /* **************************** */
88  &u10t, /**/ &upsilon11, &u12t,
89  UBL, /**/ UBR, &U20, /**/ &u21, &U22,
90  1, 1, FLA_BR );
91  FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR, &Z00, /**/ &z01, &Z02,
92  /* ************* */ /* ************************* */
93  &z10t, /**/ &zeta11, &z12t,
94  ZBL, /**/ ZBR, &Z20, /**/ &z21, &Z22,
95  1, 1, FLA_BR );
96  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
97  /* ************* */ /* ************************** */
98  &t10t, /**/ &tau11, &t12t,
99  TBL, /**/ TBR, &T20, /**/ &t21, &T22,
100  1, 1, FLA_BR );
101  FLA_Repart_2x1_to_3x1( wT, &w0,
102  /* ** */ /* ****** */
103  &omega1,
104  wB, &w2, 1, FLA_BOTTOM );
105 
106  /*------------------------------------------------------------*/
107 
108  if ( FLA_Obj_length( ATL ) > 0 )
109  {
110  // w0 = inv( triu( T00 ) ) * u10t';
111  FLA_Copyt( FLA_CONJ_TRANSPOSE, u10t, w0 );
112  FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
113  T00, w0 );
114 
115  // a01 = a01 - Z00 * w0;
116  // alpha11 = alpha11 - z10t * w0;
117  // a21 = a21 - Z20 * w0;
118  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z00, w0, FLA_ONE, a01 );
119  FLA_Dots( FLA_MINUS_ONE, z10t, w0, FLA_ONE, alpha11 );
120  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, w0, FLA_ONE, a21 );
121 
122  // w0 = inv( triu( T00 ) )' * ( U00' * a01 + u10t' * alpha11 + U20' * a21 );
123  FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
124  FLA_ONE, U00, a01, FLA_ZERO, w0 );
125  FLA_Axpyt( FLA_CONJ_TRANSPOSE, alpha11, u10t, w0 );
126  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, a21, FLA_ONE, w0 );
127 
128  FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
129  T00, w0 );
130 
131  // a01 = a01 - U00 * w0;
132  // alpha11 = alpha11 - u10t * w0;
133  // a21 = a21 - U20 * w0;
134  FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
135  FLA_MINUS_ONE, U00, w0, FLA_ONE, a01 );
136  FLA_Dots( FLA_MINUS_ONE, u10t, w0, FLA_ONE, alpha11 );
137  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, U20, w0, FLA_ONE, a21 );
138  }
139 
140  if ( FLA_Obj_length( a21 ) > 0 )
141  {
142  FLA_Part_2x1( a21, &a21_t,
143  &a21_b, 1, FLA_TOP );
144 
145  // [ u21, tau11, a21 ] = House( a21 );
146  FLA_Househ2_UT( FLA_LEFT,
147  a21_t,
148  a21_b, tau11 );
149 
150  // u21 := a21;
151  FLA_Copy( a21, u21 );
152 
153  // Explicitly set the first element of the Householder vector so we
154  // can use it in regular computations.
155  FLA_Part_2x1( u21, &u21_t,
156  &u21_b, 1, FLA_TOP );
157  FLA_Set( FLA_ONE, u21_t );
158 
159  // z01 = A02 * u21;
160  // zeta11 = a12t * u21;
161  // z21 = A22 * u21;
162  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, u21, FLA_ZERO, z01 );
163  FLA_Dot( a12t, u21, zeta11 );
164  FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, u21, FLA_ZERO, z21 );
165 
166  // t01 = U20' * u21;
167  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, u21, FLA_ZERO, t01 );
168  }
169 
170  /*------------------------------------------------------------*/
171 
172  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
173  a10t, alpha11, /**/ a12t,
174  /* ************** */ /* ************************ */
175  &ABL, /**/ &ABR, A20, a21, /**/ A22,
176  FLA_TL );
177  FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR, U00, u01, /**/ U02,
178  u10t, upsilon11, /**/ u12t,
179  /* ************** */ /* ************************** */
180  &UBL, /**/ &UBR, U20, u21, /**/ U22,
181  FLA_TL );
182  FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR, Z00, z01, /**/ Z02,
183  z10t, zeta11, /**/ z12t,
184  /* ************** */ /* *********************** */
185  &ZBL, /**/ &ZBR, Z20, z21, /**/ Z22,
186  FLA_TL );
187  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
188  t10t, tau11, /**/ t12t,
189  /* ************** */ /* ************************ */
190  &TBL, /**/ &TBR, T20, t21, /**/ T22,
191  FLA_TL );
192  FLA_Cont_with_3x1_to_2x1( &wT, w0,
193  omega1,
194  /* ** */ /* ****** */
195  &wB, w2, FLA_TOP );
196  }
197 
198  FLA_Obj_free( &w );
199 
200  return FLA_SUCCESS;
201 }
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_Trsv(FLA_Uplo uplo, FLA_Trans transa, FLA_Diag diag, FLA_Obj A, FLA_Obj x)
Definition: FLA_Trsv.c:15
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_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_Trmvsx(FLA_Uplo uplo, FLA_Trans transa, FLA_Diag diag, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y)
Definition: FLA_Trmvsx.c:13
FLA_Error FLA_Dots(FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj beta, FLA_Obj rho)
Definition: FLA_Dots.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_Dot(FLA_Obj x, FLA_Obj y, FLA_Obj rho)
Definition: FLA_Dot.c:13
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_ZERO
Definition: FLA_Init.c:20
double *restrict omega1
Definition: bl1_axpyv2bdotaxpy.c:200

◆ FLA_Hess_UT_unb_var5()

FLA_Error FLA_Hess_UT_unb_var5 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_unb_var5(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

Referenced by FLA_Hess_UT_internal().

14 {
15  FLA_Error r_val;
16  FLA_Obj U, Z;
17 
18  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &U );
19  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );
20 
21  r_val = FLA_Hess_UT_step_unb_var5( A, U, Z, T );
22 
23  FLA_Obj_free( &U );
24  FLA_Obj_free( &Z );
25 
26  return r_val;
27 }
FLA_Error FLA_Obj_free(FLA_Obj *obj)
Definition: FLA_Obj.c:588
FLA_Error FLA_Hess_UT_step_unb_var5(FLA_Obj A, FLA_Obj U, FLA_Obj Z, FLA_Obj T)
Definition: FLA_Hess_UT_unb_var5.c:29
int FLA_Error
Definition: FLA_type_defs.h:47
Definition: FLA_type_defs.h:158
FLA_Error FLA_Obj_create_conf_to(FLA_Trans trans, FLA_Obj old, FLA_Obj *obj)
Definition: FLA_Obj.c:286