Annotation of rpl/lapack/lapack/zpbtf2.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZPBTF2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZPBTF2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbtf2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpbtf2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpbtf2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, KD, LDAB, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 AB( LDAB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZPBTF2 computes the Cholesky factorization of a complex Hermitian
! 38: *> positive definite band matrix A.
! 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, U**H is the conjugate transpose
! 44: *> of U, and L is lower triangular.
! 45: *>
! 46: *> This is the unblocked version of the algorithm, calling Level 2 BLAS.
! 47: *> \endverbatim
! 48: *
! 49: * Arguments:
! 50: * ==========
! 51: *
! 52: *> \param[in] UPLO
! 53: *> \verbatim
! 54: *> UPLO is CHARACTER*1
! 55: *> Specifies whether the upper or lower triangular part of the
! 56: *> Hermitian matrix A is stored:
! 57: *> = 'U': Upper triangular
! 58: *> = 'L': Lower triangular
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] N
! 62: *> \verbatim
! 63: *> N is INTEGER
! 64: *> The order of the matrix A. N >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] KD
! 68: *> \verbatim
! 69: *> KD is INTEGER
! 70: *> The number of super-diagonals of the matrix A if UPLO = 'U',
! 71: *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in,out] AB
! 75: *> \verbatim
! 76: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 77: *> On entry, the upper or lower triangle of the Hermitian band
! 78: *> matrix A, stored in the first KD+1 rows of the array. The
! 79: *> j-th column of A is stored in the j-th column of the array AB
! 80: *> as follows:
! 81: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 82: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 83: *>
! 84: *> On exit, if INFO = 0, the triangular factor U or L from the
! 85: *> Cholesky factorization A = U**H *U or A = L*L**H of the band
! 86: *> matrix A, in the same storage format as A.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] LDAB
! 90: *> \verbatim
! 91: *> LDAB is INTEGER
! 92: *> The leading dimension of the array AB. LDAB >= KD+1.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[out] INFO
! 96: *> \verbatim
! 97: *> INFO is INTEGER
! 98: *> = 0: successful exit
! 99: *> < 0: if INFO = -k, the k-th argument had an illegal value
! 100: *> > 0: if INFO = k, the leading minor of order k is not
! 101: *> positive definite, and the factorization could not be
! 102: *> completed.
! 103: *> \endverbatim
! 104: *
! 105: * Authors:
! 106: * ========
! 107: *
! 108: *> \author Univ. of Tennessee
! 109: *> \author Univ. of California Berkeley
! 110: *> \author Univ. of Colorado Denver
! 111: *> \author NAG Ltd.
! 112: *
! 113: *> \date November 2011
! 114: *
! 115: *> \ingroup complex16OTHERcomputational
! 116: *
! 117: *> \par Further Details:
! 118: * =====================
! 119: *>
! 120: *> \verbatim
! 121: *>
! 122: *> The band storage scheme is illustrated by the following example, when
! 123: *> N = 6, KD = 2, and UPLO = 'U':
! 124: *>
! 125: *> On entry: On exit:
! 126: *>
! 127: *> * * a13 a24 a35 a46 * * u13 u24 u35 u46
! 128: *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
! 129: *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
! 130: *>
! 131: *> Similarly, if UPLO = 'L' the format of A is as follows:
! 132: *>
! 133: *> On entry: On exit:
! 134: *>
! 135: *> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
! 136: *> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
! 137: *> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
! 138: *>
! 139: *> Array elements marked * are not used by the routine.
! 140: *> \endverbatim
! 141: *>
! 142: * =====================================================================
1.1 bertrand 143: SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
144: *
1.9 ! bertrand 145: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 146: * -- LAPACK is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 148: * November 2011
1.1 bertrand 149: *
150: * .. Scalar Arguments ..
151: CHARACTER UPLO
152: INTEGER INFO, KD, LDAB, N
153: * ..
154: * .. Array Arguments ..
155: COMPLEX*16 AB( LDAB, * )
156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
161: DOUBLE PRECISION ONE, ZERO
162: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
163: * ..
164: * .. Local Scalars ..
165: LOGICAL UPPER
166: INTEGER J, KLD, KN
167: DOUBLE PRECISION AJJ
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL XERBLA, ZDSCAL, ZHER, ZLACGV
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC DBLE, MAX, MIN, SQRT
178: * ..
179: * .. Executable Statements ..
180: *
181: * Test the input parameters.
182: *
183: INFO = 0
184: UPPER = LSAME( UPLO, 'U' )
185: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
186: INFO = -1
187: ELSE IF( N.LT.0 ) THEN
188: INFO = -2
189: ELSE IF( KD.LT.0 ) THEN
190: INFO = -3
191: ELSE IF( LDAB.LT.KD+1 ) THEN
192: INFO = -5
193: END IF
194: IF( INFO.NE.0 ) THEN
195: CALL XERBLA( 'ZPBTF2', -INFO )
196: RETURN
197: END IF
198: *
199: * Quick return if possible
200: *
201: IF( N.EQ.0 )
202: $ RETURN
203: *
204: KLD = MAX( 1, LDAB-1 )
205: *
206: IF( UPPER ) THEN
207: *
1.8 bertrand 208: * Compute the Cholesky factorization A = U**H * U.
1.1 bertrand 209: *
210: DO 10 J = 1, N
211: *
212: * Compute U(J,J) and test for non-positive-definiteness.
213: *
214: AJJ = DBLE( AB( KD+1, J ) )
215: IF( AJJ.LE.ZERO ) THEN
216: AB( KD+1, J ) = AJJ
217: GO TO 30
218: END IF
219: AJJ = SQRT( AJJ )
220: AB( KD+1, J ) = AJJ
221: *
222: * Compute elements J+1:J+KN of row J and update the
223: * trailing submatrix within the band.
224: *
225: KN = MIN( KD, N-J )
226: IF( KN.GT.0 ) THEN
227: CALL ZDSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD )
228: CALL ZLACGV( KN, AB( KD, J+1 ), KLD )
229: CALL ZHER( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD,
230: $ AB( KD+1, J+1 ), KLD )
231: CALL ZLACGV( KN, AB( KD, J+1 ), KLD )
232: END IF
233: 10 CONTINUE
234: ELSE
235: *
1.8 bertrand 236: * Compute the Cholesky factorization A = L*L**H.
1.1 bertrand 237: *
238: DO 20 J = 1, N
239: *
240: * Compute L(J,J) and test for non-positive-definiteness.
241: *
242: AJJ = DBLE( AB( 1, J ) )
243: IF( AJJ.LE.ZERO ) THEN
244: AB( 1, J ) = AJJ
245: GO TO 30
246: END IF
247: AJJ = SQRT( AJJ )
248: AB( 1, J ) = AJJ
249: *
250: * Compute elements J+1:J+KN of column J and update the
251: * trailing submatrix within the band.
252: *
253: KN = MIN( KD, N-J )
254: IF( KN.GT.0 ) THEN
255: CALL ZDSCAL( KN, ONE / AJJ, AB( 2, J ), 1 )
256: CALL ZHER( 'Lower', KN, -ONE, AB( 2, J ), 1,
257: $ AB( 1, J+1 ), KLD )
258: END IF
259: 20 CONTINUE
260: END IF
261: RETURN
262: *
263: 30 CONTINUE
264: INFO = J
265: RETURN
266: *
267: * End of ZPBTF2
268: *
269: END
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