LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zppsv.f
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1*> \brief <b> ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zppsv.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zppsv.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zppsv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INFO, LDB, N, NRHS
26* ..
27* .. Array Arguments ..
28* COMPLEX*16 AP( * ), B( LDB, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> ZPPSV computes the solution to a complex system of linear equations
38*> A * X = B,
39*> where A is an N-by-N Hermitian positive definite matrix stored in
40*> packed format and X and B are N-by-NRHS matrices.
41*>
42*> The Cholesky decomposition is used to factor A as
43*> A = U**H * U, if UPLO = 'U', or
44*> A = L * L**H, if UPLO = 'L',
45*> where U is an upper triangular matrix and L is a lower triangular
46*> matrix. The factored form of A is then used to solve the system of
47*> equations A * X = B.
48*> \endverbatim
49*
50* Arguments:
51* ==========
52*
53*> \param[in] UPLO
54*> \verbatim
55*> UPLO is CHARACTER*1
56*> = 'U': Upper triangle of A is stored;
57*> = 'L': Lower triangle of A is stored.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*> N is INTEGER
63*> The number of linear equations, i.e., the order of the
64*> matrix A. N >= 0.
65*> \endverbatim
66*>
67*> \param[in] NRHS
68*> \verbatim
69*> NRHS is INTEGER
70*> The number of right hand sides, i.e., the number of columns
71*> of the matrix B. NRHS >= 0.
72*> \endverbatim
73*>
74*> \param[in,out] AP
75*> \verbatim
76*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
77*> On entry, the upper or lower triangle of the Hermitian matrix
78*> A, packed columnwise in a linear array. The j-th column of A
79*> is stored in the array AP as follows:
80*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
81*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
82*> See below for further details.
83*>
84*> On exit, if INFO = 0, the factor U or L from the Cholesky
85*> factorization A = U**H*U or A = L*L**H, in the same storage
86*> format as A.
87*> \endverbatim
88*>
89*> \param[in,out] B
90*> \verbatim
91*> B is COMPLEX*16 array, dimension (LDB,NRHS)
92*> On entry, the N-by-NRHS right hand side matrix B.
93*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
94*> \endverbatim
95*>
96*> \param[in] LDB
97*> \verbatim
98*> LDB is INTEGER
99*> The leading dimension of the array B. LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] INFO
103*> \verbatim
104*> INFO is INTEGER
105*> = 0: successful exit
106*> < 0: if INFO = -i, the i-th argument had an illegal value
107*> > 0: if INFO = i, the leading principal minor of order i
108*> of A is not positive, so the factorization could not
109*> be completed, and the solution has not been computed.
110*> \endverbatim
111*
112* Authors:
113* ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup ppsv
121*
122*> \par Further Details:
123* =====================
124*>
125*> \verbatim
126*>
127*> The packed storage scheme is illustrated by the following example
128*> when N = 4, UPLO = 'U':
129*>
130*> Two-dimensional storage of the Hermitian matrix A:
131*>
132*> a11 a12 a13 a14
133*> a22 a23 a24
134*> a33 a34 (aij = conjg(aji))
135*> a44
136*>
137*> Packed storage of the upper triangle of A:
138*>
139*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
140*> \endverbatim
141*>
142* =====================================================================
143 SUBROUTINE zppsv( UPLO, N, NRHS, AP, B, LDB, INFO )
144*
145* -- LAPACK driver routine --
146* -- LAPACK is a software package provided by Univ. of Tennessee, --
147* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148*
149* .. Scalar Arguments ..
150 CHARACTER UPLO
151 INTEGER INFO, LDB, N, NRHS
152* ..
153* .. Array Arguments ..
154 COMPLEX*16 AP( * ), B( LDB, * )
155* ..
156*
157* =====================================================================
158*
159* .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL lsame
162* ..
163* .. External Subroutines ..
164 EXTERNAL xerbla, zpptrf, zpptrs
165* ..
166* .. Intrinsic Functions ..
167 INTRINSIC max
168* ..
169* .. Executable Statements ..
170*
171* Test the input parameters.
172*
173 info = 0
174 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
175 info = -1
176 ELSE IF( n.LT.0 ) THEN
177 info = -2
178 ELSE IF( nrhs.LT.0 ) THEN
179 info = -3
180 ELSE IF( ldb.LT.max( 1, n ) ) THEN
181 info = -6
182 END IF
183 IF( info.NE.0 ) THEN
184 CALL xerbla( 'ZPPSV ', -info )
185 RETURN
186 END IF
187*
188* Compute the Cholesky factorization A = U**H *U or A = L*L**H.
189*
190 CALL zpptrf( uplo, n, ap, info )
191 IF( info.EQ.0 ) THEN
192*
193* Solve the system A*X = B, overwriting B with X.
194*
195 CALL zpptrs( uplo, n, nrhs, ap, b, ldb, info )
196*
197 END IF
198 RETURN
199*
200* End of ZPPSV
201*
202 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zppsv(uplo, n, nrhs, ap, b, ldb, info)
ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition zppsv.f:144
subroutine zpptrf(uplo, n, ap, info)
ZPPTRF
Definition zpptrf.f:119
subroutine zpptrs(uplo, n, nrhs, ap, b, ldb, info)
ZPPTRS
Definition zpptrs.f:108