File: zsytrf

package info (click to toggle)
ruby-lapack 1.8.2-1
  • links: PTS, VCS
  • area: main
  • in suites: bookworm, forky, sid, trixie
  • size: 28,572 kB
  • sloc: ansic: 191,612; ruby: 3,937; makefile: 6
file content (156 lines) | stat: -rw-r--r-- 6,476 bytes parent folder | download | duplicates (5)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
--- 
:name: zsytrf
:md5sum: 9c93e85cbf5380c2c19fa9764c96cc12
:category: :subroutine
:arguments: 
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublecomplex
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- ipiv: 
    :type: integer
    :intent: output
    :dims: 
    - n
- work: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZSYTRF computes the factorization of a complex symmetric matrix A\n\
  *  using the Bunch-Kaufman diagonal pivoting method.  The form of the\n\
  *  factorization is\n\
  *\n\
  *     A = U*D*U**T  or  A = L*D*L**T\n\
  *\n\
  *  where U (or L) is a product of permutation and unit upper (lower)\n\
  *  triangular matrices, and D is symmetric and block diagonal with\n\
  *  with 1-by-1 and 2-by-2 diagonal blocks.\n\
  *\n\
  *  This is the blocked version of the algorithm, calling Level 3 BLAS.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          = 'U':  Upper triangle of A is stored;\n\
  *          = 'L':  Lower triangle of A is stored.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A.  N >= 0.\n\
  *\n\
  *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)\n\
  *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading\n\
  *          N-by-N upper triangular part of A contains the upper\n\
  *          triangular part of the matrix A, and the strictly lower\n\
  *          triangular part of A is not referenced.  If UPLO = 'L', the\n\
  *          leading N-by-N lower triangular part of A contains the lower\n\
  *          triangular part of the matrix A, and the strictly upper\n\
  *          triangular part of A is not referenced.\n\
  *\n\
  *          On exit, the block diagonal matrix D and the multipliers used\n\
  *          to obtain the factor U or L (see below for further details).\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A.  LDA >= max(1,N).\n\
  *\n\
  *  IPIV    (output) INTEGER array, dimension (N)\n\
  *          Details of the interchanges and the block structure of D.\n\
  *          If IPIV(k) > 0, then rows and columns k and IPIV(k) were\n\
  *          interchanged and D(k,k) is a 1-by-1 diagonal block.\n\
  *          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and\n\
  *          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)\n\
  *          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =\n\
  *          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were\n\
  *          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.\n\
  *\n\
  *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The length of WORK.  LWORK >=1.  For best performance\n\
  *          LWORK >= N*NB, where NB is the block size returned by ILAENV.\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal size of the WORK array, returns\n\
  *          this value as the first entry of the WORK array, and no error\n\
  *          message related to LWORK is issued by XERBLA.\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value\n\
  *          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization\n\
  *                has been completed, but the block diagonal matrix D is\n\
  *                exactly singular, and division by zero will occur if it\n\
  *                is used to solve a system of equations.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  If UPLO = 'U', then A = U*D*U', where\n\
  *     U = P(n)*U(n)* ... *P(k)U(k)* ...,\n\
  *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to\n\
  *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1\n\
  *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as\n\
  *  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such\n\
  *  that if the diagonal block D(k) is of order s (s = 1 or 2), then\n\
  *\n\
  *             (   I    v    0   )   k-s\n\
  *     U(k) =  (   0    I    0   )   s\n\
  *             (   0    0    I   )   n-k\n\
  *                k-s   s   n-k\n\
  *\n\
  *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).\n\
  *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),\n\
  *  and A(k,k), and v overwrites A(1:k-2,k-1:k).\n\
  *\n\
  *  If UPLO = 'L', then A = L*D*L', where\n\
  *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,\n\
  *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to\n\
  *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1\n\
  *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as\n\
  *  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such\n\
  *  that if the diagonal block D(k) is of order s (s = 1 or 2), then\n\
  *\n\
  *             (   I    0     0   )  k-1\n\
  *     L(k) =  (   0    I     0   )  s\n\
  *             (   0    v     I   )  n-k-s+1\n\
  *                k-1   s  n-k-s+1\n\
  *\n\
  *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).\n\
  *  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),\n\
  *  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).\n\
  *\n\
  *  =====================================================================\n\
  *\n\
  *     .. Local Scalars ..\n      LOGICAL            LQUERY, UPPER\n      INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN\n\
  *     ..\n\
  *     .. External Functions ..\n      LOGICAL            LSAME\n      INTEGER            ILAENV\n      EXTERNAL           LSAME, ILAENV\n\
  *     ..\n\
  *     .. External Subroutines ..\n      EXTERNAL           XERBLA, ZLASYF, ZSYTF2\n\
  *     ..\n\
  *     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n\
  *     ..\n"