Annotation of rpl/lapack/lapack/zpptrf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZPPTRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZPPTRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 AP( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZPPTRF computes the Cholesky factorization of a complex Hermitian
! 38: *> positive definite matrix A stored in packed format.
! 39: *>
! 40: *> The factorization has the form
! 41: *> A = U**H * U, if UPLO = 'U', or
! 42: *> A = L * L**H, if UPLO = 'L',
! 43: *> where U is an upper triangular matrix and L is lower triangular.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] UPLO
! 50: *> \verbatim
! 51: *> UPLO is CHARACTER*1
! 52: *> = 'U': Upper triangle of A is stored;
! 53: *> = 'L': Lower triangle of A is stored.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] N
! 57: *> \verbatim
! 58: *> N is INTEGER
! 59: *> The order of the matrix A. N >= 0.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in,out] AP
! 63: *> \verbatim
! 64: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 65: *> On entry, the upper or lower triangle of the Hermitian matrix
! 66: *> A, packed columnwise in a linear array. The j-th column of A
! 67: *> is stored in the array AP as follows:
! 68: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 69: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 70: *> See below for further details.
! 71: *>
! 72: *> On exit, if INFO = 0, the triangular factor U or L from the
! 73: *> Cholesky factorization A = U**H*U or A = L*L**H, in the same
! 74: *> storage format as A.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[out] INFO
! 78: *> \verbatim
! 79: *> INFO is INTEGER
! 80: *> = 0: successful exit
! 81: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 82: *> > 0: if INFO = i, the leading minor of order i is not
! 83: *> positive definite, and the factorization could not be
! 84: *> completed.
! 85: *> \endverbatim
! 86: *
! 87: * Authors:
! 88: * ========
! 89: *
! 90: *> \author Univ. of Tennessee
! 91: *> \author Univ. of California Berkeley
! 92: *> \author Univ. of Colorado Denver
! 93: *> \author NAG Ltd.
! 94: *
! 95: *> \date November 2011
! 96: *
! 97: *> \ingroup complex16OTHERcomputational
! 98: *
! 99: *> \par Further Details:
! 100: * =====================
! 101: *>
! 102: *> \verbatim
! 103: *>
! 104: *> The packed storage scheme is illustrated by the following example
! 105: *> when N = 4, UPLO = 'U':
! 106: *>
! 107: *> Two-dimensional storage of the Hermitian matrix A:
! 108: *>
! 109: *> a11 a12 a13 a14
! 110: *> a22 a23 a24
! 111: *> a33 a34 (aij = conjg(aji))
! 112: *> a44
! 113: *>
! 114: *> Packed storage of the upper triangle of A:
! 115: *>
! 116: *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
! 117: *> \endverbatim
! 118: *>
! 119: * =====================================================================
1.1 bertrand 120: SUBROUTINE ZPPTRF( UPLO, N, AP, INFO )
121: *
1.9 ! bertrand 122: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 123: * -- LAPACK is a software package provided by Univ. of Tennessee, --
124: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 125: * November 2011
1.1 bertrand 126: *
127: * .. Scalar Arguments ..
128: CHARACTER UPLO
129: INTEGER INFO, N
130: * ..
131: * .. Array Arguments ..
132: COMPLEX*16 AP( * )
133: * ..
134: *
135: * =====================================================================
136: *
137: * .. Parameters ..
138: DOUBLE PRECISION ZERO, ONE
139: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
140: * ..
141: * .. Local Scalars ..
142: LOGICAL UPPER
143: INTEGER J, JC, JJ
144: DOUBLE PRECISION AJJ
145: * ..
146: * .. External Functions ..
147: LOGICAL LSAME
148: COMPLEX*16 ZDOTC
149: EXTERNAL LSAME, ZDOTC
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPSV
153: * ..
154: * .. Intrinsic Functions ..
155: INTRINSIC DBLE, SQRT
156: * ..
157: * .. Executable Statements ..
158: *
159: * Test the input parameters.
160: *
161: INFO = 0
162: UPPER = LSAME( UPLO, 'U' )
163: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
164: INFO = -1
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -2
167: END IF
168: IF( INFO.NE.0 ) THEN
169: CALL XERBLA( 'ZPPTRF', -INFO )
170: RETURN
171: END IF
172: *
173: * Quick return if possible
174: *
175: IF( N.EQ.0 )
176: $ RETURN
177: *
178: IF( UPPER ) THEN
179: *
1.8 bertrand 180: * Compute the Cholesky factorization A = U**H * U.
1.1 bertrand 181: *
182: JJ = 0
183: DO 10 J = 1, N
184: JC = JJ + 1
185: JJ = JJ + J
186: *
187: * Compute elements 1:J-1 of column J.
188: *
189: IF( J.GT.1 )
190: $ CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit',
191: $ J-1, AP, AP( JC ), 1 )
192: *
193: * Compute U(J,J) and test for non-positive-definiteness.
194: *
195: AJJ = DBLE( AP( JJ ) ) - ZDOTC( J-1, AP( JC ), 1, AP( JC ),
196: $ 1 )
197: IF( AJJ.LE.ZERO ) THEN
198: AP( JJ ) = AJJ
199: GO TO 30
200: END IF
201: AP( JJ ) = SQRT( AJJ )
202: 10 CONTINUE
203: ELSE
204: *
1.8 bertrand 205: * Compute the Cholesky factorization A = L * L**H.
1.1 bertrand 206: *
207: JJ = 1
208: DO 20 J = 1, N
209: *
210: * Compute L(J,J) and test for non-positive-definiteness.
211: *
212: AJJ = DBLE( AP( JJ ) )
213: IF( AJJ.LE.ZERO ) THEN
214: AP( JJ ) = AJJ
215: GO TO 30
216: END IF
217: AJJ = SQRT( AJJ )
218: AP( JJ ) = AJJ
219: *
220: * Compute elements J+1:N of column J and update the trailing
221: * submatrix.
222: *
223: IF( J.LT.N ) THEN
224: CALL ZDSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
225: CALL ZHPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
226: $ AP( JJ+N-J+1 ) )
227: JJ = JJ + N - J + 1
228: END IF
229: 20 CONTINUE
230: END IF
231: GO TO 40
232: *
233: 30 CONTINUE
234: INFO = J
235: *
236: 40 CONTINUE
237: RETURN
238: *
239: * End of ZPPTRF
240: *
241: END
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