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Functions
FLA_Bidiag_UT_u_unb_var2.c File Reference

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Functions

FLA_Error FLA_Bidiag_UT_u_unb_var2 (FLA_Obj A, FLA_Obj TU, FLA_Obj TV)
 
FLA_Error FLA_Bidiag_UT_u_step_unb_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj S)
 

Function Documentation

◆ FLA_Bidiag_UT_u_step_unb_var2()

FLA_Error FLA_Bidiag_UT_u_step_unb_var2 ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  S 
)
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 STL, STR, S00, s01, S02,
27  SBL, SBR, s10t, sigma11, s12t,
28  S20, s21, S22;
29  FLA_Obj yT, y01,
30  yB, psi11,
31  y21;
32  FLA_Obj zT, z01,
33  zB, zeta11,
34  z21;
35  FLA_Obj vT, v01,
36  vB, nu11,
37  v21;
38  FLA_Obj v, y, z;
39 
40  FLA_Obj beta;
41 
42  FLA_Obj a12t_l, a12t_r;
43  FLA_Obj v21_t,
44  v21_b;
45 
46  FLA_Datatype datatype_A;
47  dim_t m_A, n_A;
48  dim_t b_alg;
49 
50 
51  b_alg = FLA_Obj_length( T );
52 
53  datatype_A = FLA_Obj_datatype( A );
54  m_A = FLA_Obj_length( A );
55  n_A = FLA_Obj_width( A );
56 
57  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
58  FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &v );
59  FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &y );
60  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
61 
62  FLA_Part_2x2( A, &ATL, &ATR,
63  &ABL, &ABR, 0, 0, FLA_TL );
64  FLA_Part_2x2( T, &TTL, &TTR,
65  &TBL, &TBR, 0, 0, FLA_TL );
66  FLA_Part_2x2( S, &STL, &STR,
67  &SBL, &SBR, 0, 0, FLA_TL );
68  FLA_Part_2x1( v, &vT,
69  &vB, 0, FLA_TOP );
70  FLA_Part_2x1( y, &yT,
71  &yB, 0, FLA_TOP );
72  FLA_Part_2x1( z, &zT,
73  &zB, 0, FLA_TOP );
74 
75  while ( FLA_Obj_length( ATL ) < b_alg )
76  {
77  FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
78  /* ************* */ /* ************************** */
79  &a10t, /**/ &alpha11, &a12t,
80  ABL, /**/ ABR, &A20, /**/ &a21, &A22,
81  1, 1, FLA_BR );
82  FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
83  /* ************* */ /* ************************** */
84  &t10t, /**/ &tau11, &t12t,
85  TBL, /**/ TBR, &T20, /**/ &t21, &T22,
86  1, 1, FLA_BR );
87  FLA_Repart_2x2_to_3x3( STL, /**/ STR, &S00, /**/ &s01, &S02,
88  /* ************* */ /* ************************** */
89  &s10t, /**/ &sigma11, &s12t,
90  SBL, /**/ SBR, &S20, /**/ &s21, &S22,
91  1, 1, FLA_BR );
92  FLA_Repart_2x1_to_3x1( vT, &v01,
93  /* ** */ /* ***** */
94  &nu11,
95  vB, &v21, 1, FLA_BOTTOM );
96  FLA_Repart_2x1_to_3x1( yT, &y01,
97  /* ** */ /* ***** */
98  &psi11,
99  yB, &y21, 1, FLA_BOTTOM );
100  FLA_Repart_2x1_to_3x1( zT, &z01,
101  /* ** */ /* ***** */
102  &zeta11,
103  zB, &z21, 1, FLA_BOTTOM );
104 
105  /*------------------------------------------------------------*/
106 
107  // [ alpha11_new, u21, tau11 ] = House2( alpha11, a21 );
108  FLA_Househ2_UT( FLA_LEFT,
109  alpha11,
110  a21, tau11 );
111 
112  if ( FLA_Obj_width( A22 ) > 0 )
113  {
114  // y21' = a12t + u21' * A22;
115  // y21 = conj(a12t) + A22' * u21;
116  FLA_Copyt( FLA_CONJ_TRANSPOSE, a12t, y21 );
117  FLA_Gemvc( FLA_CONJ_TRANSPOSE, FLA_NO_CONJUGATE, FLA_ONE, A22, a21, FLA_ONE, y21 );
118 
119  // y21 = y21 / tau11;
120  FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, y21 );
121 
122  // a12t = a12t - conj(y21)^T;
123  FLA_Axpyt( FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, y21, a12t );
124 
125  FLA_Part_1x2( a12t, &a12t_l, &a12t_r, 1, FLA_LEFT );
126  FLA_Part_2x1( v21, &v21_t,
127  &v21_b, 1, FLA_TOP );
128 
129  // [ a12t_l, v12t_b, sigma11 ] = House2( a12t_l, a12t_r );
130  FLA_Househ2_UT( FLA_RIGHT, a12t_l, a12t_r, sigma11 );
131 
132  // v21_t = 1;
133  // v21_b = a12t_r^T;
134  FLA_Set( FLA_ONE, v21_t );
135  FLA_Copyt( FLA_TRANSPOSE, a12t_r, v21_b );
136 
137  // beta = - y21' * v21;
138  FLA_Dotc( FLA_CONJUGATE, y21, v21, beta );
139  FLA_Scal( FLA_MINUS_ONE, beta );
140 
141  // z21 = ( A22 - u21 * y21' ) * v21 / sigma11;
142  // = ( A22 * v21 - u21 * y21' * v21 ) / sigma11;
143  // = ( A22 * v21 + beta * u21 ) / sigma11;
144  FLA_Copy( a21, z21 );
145  FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_NO_CONJUGATE, FLA_ONE, A22, v21, beta, z21 );
146  FLA_Inv_scalc( FLA_NO_CONJUGATE, sigma11, z21 );
147 
148  // A22 = A22 - u21 * y21' - z21 * v21';
149  FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y21, A22 );
150  FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z21, v21, A22 );
151 
152  // s01 = conj(V02) * v21;
153  FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_ONE, A02, v21, FLA_ZERO, s01 );
154  }
155 
156  // t01 = a10t' + U20' * u21;
157  FLA_Copyt( FLA_CONJ_TRANSPOSE, a10t, t01 );
158  FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
159 
160  /*------------------------------------------------------------*/
161 
162  FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
163  a10t, alpha11, /**/ a12t,
164  /* ************** */ /* ************************ */
165  &ABL, /**/ &ABR, A20, a21, /**/ A22,
166  FLA_TL );
167  FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
168  t10t, tau11, /**/ t12t,
169  /* ************** */ /* ************************ */
170  &TBL, /**/ &TBR, T20, t21, /**/ T22,
171  FLA_TL );
172  FLA_Cont_with_3x3_to_2x2( &STL, /**/ &STR, S00, s01, /**/ S02,
173  s10t, sigma11, /**/ s12t,
174  /* ************** */ /* ************************ */
175  &SBL, /**/ &SBR, S20, s21, /**/ S22,
176  FLA_TL );
177  FLA_Cont_with_3x1_to_2x1( &vT, v01,
178  nu11,
179  /* ** */ /* ***** */
180  &vB, v21, FLA_TOP );
181  FLA_Cont_with_3x1_to_2x1( &yT, y01,
182  psi11,
183  /* ** */ /* ***** */
184  &yB, y21, FLA_TOP );
185  FLA_Cont_with_3x1_to_2x1( &zT, z01,
186  zeta11,
187  /* ** */ /* ***** */
188  &zB, z21, FLA_TOP );
189  }
190 
191  FLA_Obj_free( &beta );
192  FLA_Obj_free( &v );
193  FLA_Obj_free( &y );
194  FLA_Obj_free( &z );
195 
196  return FLA_SUCCESS;
197 }
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_Axpyt(FLA_Trans trans, FLA_Obj alpha, FLA_Obj A, FLA_Obj B)
Definition: FLA_Axpyt.c:15
FLA_Error FLA_Copyt(FLA_Trans trans, FLA_Obj A, FLA_Obj B)
Definition: FLA_Copyt.c:15
FLA_Error FLA_Inv_scalc(FLA_Conj conjalpha, FLA_Obj alpha, FLA_Obj A)
Definition: FLA_Inv_scalc.c:13
FLA_Error FLA_Gerc(FLA_Conj conjx, FLA_Conj conjy, FLA_Obj alpha, FLA_Obj x, FLA_Obj y, FLA_Obj A)
Definition: FLA_Gerc.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_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
dim_t FLA_Obj_width(FLA_Obj obj)
Definition: FLA_Query.c:123
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_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_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dotc(), FLA_Gemv(), FLA_Gemvc(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_width(), 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(), and FLA_ZERO.

Referenced by FLA_Bidiag_UT_u_unb_var2().

◆ FLA_Bidiag_UT_u_unb_var2()

FLA_Error FLA_Bidiag_UT_u_unb_var2 ( FLA_Obj  A,
FLA_Obj  TU,
FLA_Obj  TV 
)
14 {
15  return FLA_Bidiag_UT_u_step_unb_var2( A, TU, TV );
16 }
FLA_Error FLA_Bidiag_UT_u_step_unb_var2(FLA_Obj A, FLA_Obj T, FLA_Obj S)
Definition: FLA_Bidiag_UT_u_unb_var2.c:18

References FLA_Bidiag_UT_u_step_unb_var2().

Referenced by FLA_Bidiag_UT_u().