Annotation of rpl/lapack/lapack/zpotrs.f, revision 1.15
1.9 bertrand 1: *> \brief \b ZPOTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 ! bertrand 9: *> Download ZPOTRS + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpotrs.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpotrs.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpotrs.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 ! bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
1.15 ! bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 A( LDA, * ), B( LDB, * )
29: * ..
1.15 ! bertrand 30: *
1.9 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZPOTRS solves a system of linear equations A*X = B with a Hermitian
38: *> positive definite matrix A using the Cholesky factorization
39: *> A = U**H * U or A = L * L**H computed by ZPOTRF.
40: *> \endverbatim
41: *
42: * Arguments:
43: * ==========
44: *
45: *> \param[in] UPLO
46: *> \verbatim
47: *> UPLO is CHARACTER*1
48: *> = 'U': Upper triangle of A is stored;
49: *> = 'L': Lower triangle of A is stored.
50: *> \endverbatim
51: *>
52: *> \param[in] N
53: *> \verbatim
54: *> N is INTEGER
55: *> The order of the matrix A. N >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in] NRHS
59: *> \verbatim
60: *> NRHS is INTEGER
61: *> The number of right hand sides, i.e., the number of columns
62: *> of the matrix B. NRHS >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] A
66: *> \verbatim
67: *> A is COMPLEX*16 array, dimension (LDA,N)
68: *> The triangular factor U or L from the Cholesky factorization
69: *> A = U**H * U or A = L * L**H, as computed by ZPOTRF.
70: *> \endverbatim
71: *>
72: *> \param[in] LDA
73: *> \verbatim
74: *> LDA is INTEGER
75: *> The leading dimension of the array A. LDA >= max(1,N).
76: *> \endverbatim
77: *>
78: *> \param[in,out] B
79: *> \verbatim
80: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
81: *> On entry, the right hand side matrix B.
82: *> On exit, the solution matrix X.
83: *> \endverbatim
84: *>
85: *> \param[in] LDB
86: *> \verbatim
87: *> LDB is INTEGER
88: *> The leading dimension of the array B. LDB >= max(1,N).
89: *> \endverbatim
90: *>
91: *> \param[out] INFO
92: *> \verbatim
93: *> INFO is INTEGER
94: *> = 0: successful exit
95: *> < 0: if INFO = -i, the i-th argument had an illegal value
96: *> \endverbatim
97: *
98: * Authors:
99: * ========
100: *
1.15 ! bertrand 101: *> \author Univ. of Tennessee
! 102: *> \author Univ. of California Berkeley
! 103: *> \author Univ. of Colorado Denver
! 104: *> \author NAG Ltd.
1.9 bertrand 105: *
1.15 ! bertrand 106: *> \date December 2016
1.9 bertrand 107: *
108: *> \ingroup complex16POcomputational
109: *
110: * =====================================================================
1.1 bertrand 111: SUBROUTINE ZPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
112: *
1.15 ! bertrand 113: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 114: * -- LAPACK is a software package provided by Univ. of Tennessee, --
115: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 ! bertrand 116: * December 2016
1.1 bertrand 117: *
118: * .. Scalar Arguments ..
119: CHARACTER UPLO
120: INTEGER INFO, LDA, LDB, N, NRHS
121: * ..
122: * .. Array Arguments ..
123: COMPLEX*16 A( LDA, * ), B( LDB, * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: COMPLEX*16 ONE
130: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
131: * ..
132: * .. Local Scalars ..
133: LOGICAL UPPER
134: * ..
135: * .. External Functions ..
136: LOGICAL LSAME
137: EXTERNAL LSAME
138: * ..
139: * .. External Subroutines ..
140: EXTERNAL XERBLA, ZTRSM
141: * ..
142: * .. Intrinsic Functions ..
143: INTRINSIC MAX
144: * ..
145: * .. Executable Statements ..
146: *
147: * Test the input parameters.
148: *
149: INFO = 0
150: UPPER = LSAME( UPLO, 'U' )
151: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
152: INFO = -1
153: ELSE IF( N.LT.0 ) THEN
154: INFO = -2
155: ELSE IF( NRHS.LT.0 ) THEN
156: INFO = -3
157: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
158: INFO = -5
159: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
160: INFO = -7
161: END IF
162: IF( INFO.NE.0 ) THEN
163: CALL XERBLA( 'ZPOTRS', -INFO )
164: RETURN
165: END IF
166: *
167: * Quick return if possible
168: *
169: IF( N.EQ.0 .OR. NRHS.EQ.0 )
170: $ RETURN
171: *
172: IF( UPPER ) THEN
173: *
1.8 bertrand 174: * Solve A*X = B where A = U**H *U.
1.1 bertrand 175: *
1.8 bertrand 176: * Solve U**H *X = B, overwriting B with X.
1.1 bertrand 177: *
178: CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose', 'Non-unit',
179: $ N, NRHS, ONE, A, LDA, B, LDB )
180: *
181: * Solve U*X = B, overwriting B with X.
182: *
183: CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
184: $ NRHS, ONE, A, LDA, B, LDB )
185: ELSE
186: *
1.8 bertrand 187: * Solve A*X = B where A = L*L**H.
1.1 bertrand 188: *
189: * Solve L*X = B, overwriting B with X.
190: *
191: CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
192: $ NRHS, ONE, A, LDA, B, LDB )
193: *
1.8 bertrand 194: * Solve L**H *X = B, overwriting B with X.
1.1 bertrand 195: *
196: CALL ZTRSM( 'Left', 'Lower', 'Conjugate transpose', 'Non-unit',
197: $ N, NRHS, ONE, A, LDA, B, LDB )
198: END IF
199: *
200: RETURN
201: *
202: * End of ZPOTRS
203: *
204: END
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