Annotation of rpl/lapack/lapack/zpbsv.f, revision 1.9
1.9 ! bertrand 1: *> \brief <b> ZPBSV 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
! 9: *> Download ZPBSV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbsv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpbsv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpbsv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, KD, LDAB, LDB, N, NRHS
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZPBSV 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 band matrix and X
! 40: *> 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 band matrix, and L is a lower
! 46: *> triangular band matrix, with the same number of superdiagonals or
! 47: *> subdiagonals as A. The factored form of A is then used to solve the
! 48: *> system of equations A * X = B.
! 49: *> \endverbatim
! 50: *
! 51: * Arguments:
! 52: * ==========
! 53: *
! 54: *> \param[in] UPLO
! 55: *> \verbatim
! 56: *> UPLO is CHARACTER*1
! 57: *> = 'U': Upper triangle of A is stored;
! 58: *> = 'L': Lower triangle of A is stored.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] N
! 62: *> \verbatim
! 63: *> N is INTEGER
! 64: *> The number of linear equations, i.e., the order of the
! 65: *> matrix A. N >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] KD
! 69: *> \verbatim
! 70: *> KD is INTEGER
! 71: *> The number of superdiagonals of the matrix A if UPLO = 'U',
! 72: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] NRHS
! 76: *> \verbatim
! 77: *> NRHS is INTEGER
! 78: *> The number of right hand sides, i.e., the number of columns
! 79: *> of the matrix B. NRHS >= 0.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in,out] AB
! 83: *> \verbatim
! 84: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 85: *> On entry, the upper or lower triangle of the Hermitian band
! 86: *> matrix A, stored in the first KD+1 rows of the array. The
! 87: *> j-th column of A is stored in the j-th column of the array AB
! 88: *> as follows:
! 89: *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
! 90: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
! 91: *> See below for further details.
! 92: *>
! 93: *> On exit, if INFO = 0, the triangular factor U or L from the
! 94: *> Cholesky factorization A = U**H *U or A = L*L**H of the band
! 95: *> matrix A, in the same storage format as A.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] LDAB
! 99: *> \verbatim
! 100: *> LDAB is INTEGER
! 101: *> The leading dimension of the array AB. LDAB >= KD+1.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[in,out] B
! 105: *> \verbatim
! 106: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 107: *> On entry, the N-by-NRHS right hand side matrix B.
! 108: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[in] LDB
! 112: *> \verbatim
! 113: *> LDB is INTEGER
! 114: *> The leading dimension of the array B. LDB >= max(1,N).
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[out] INFO
! 118: *> \verbatim
! 119: *> INFO is INTEGER
! 120: *> = 0: successful exit
! 121: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 122: *> > 0: if INFO = i, the leading minor of order i of A is not
! 123: *> positive definite, so the factorization could not be
! 124: *> completed, and the solution has not been computed.
! 125: *> \endverbatim
! 126: *
! 127: * Authors:
! 128: * ========
! 129: *
! 130: *> \author Univ. of Tennessee
! 131: *> \author Univ. of California Berkeley
! 132: *> \author Univ. of Colorado Denver
! 133: *> \author NAG Ltd.
! 134: *
! 135: *> \date November 2011
! 136: *
! 137: *> \ingroup complex16OTHERsolve
! 138: *
! 139: *> \par Further Details:
! 140: * =====================
! 141: *>
! 142: *> \verbatim
! 143: *>
! 144: *> The band storage scheme is illustrated by the following example, when
! 145: *> N = 6, KD = 2, and UPLO = 'U':
! 146: *>
! 147: *> On entry: On exit:
! 148: *>
! 149: *> * * a13 a24 a35 a46 * * u13 u24 u35 u46
! 150: *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
! 151: *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
! 152: *>
! 153: *> Similarly, if UPLO = 'L' the format of A is as follows:
! 154: *>
! 155: *> On entry: On exit:
! 156: *>
! 157: *> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
! 158: *> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
! 159: *> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
! 160: *>
! 161: *> Array elements marked * are not used by the routine.
! 162: *> \endverbatim
! 163: *>
! 164: * =====================================================================
1.1 bertrand 165: SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
166: *
1.9 ! bertrand 167: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 168: * -- LAPACK is a software package provided by Univ. of Tennessee, --
169: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 170: * November 2011
1.1 bertrand 171: *
172: * .. Scalar Arguments ..
173: CHARACTER UPLO
174: INTEGER INFO, KD, LDAB, LDB, N, NRHS
175: * ..
176: * .. Array Arguments ..
177: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
178: * ..
179: *
180: * =====================================================================
181: *
182: * .. External Functions ..
183: LOGICAL LSAME
184: EXTERNAL LSAME
185: * ..
186: * .. External Subroutines ..
187: EXTERNAL XERBLA, ZPBTRF, ZPBTRS
188: * ..
189: * .. Intrinsic Functions ..
190: INTRINSIC MAX
191: * ..
192: * .. Executable Statements ..
193: *
194: * Test the input parameters.
195: *
196: INFO = 0
197: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
198: INFO = -1
199: ELSE IF( N.LT.0 ) THEN
200: INFO = -2
201: ELSE IF( KD.LT.0 ) THEN
202: INFO = -3
203: ELSE IF( NRHS.LT.0 ) THEN
204: INFO = -4
205: ELSE IF( LDAB.LT.KD+1 ) THEN
206: INFO = -6
207: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
208: INFO = -8
209: END IF
210: IF( INFO.NE.0 ) THEN
211: CALL XERBLA( 'ZPBSV ', -INFO )
212: RETURN
213: END IF
214: *
1.8 bertrand 215: * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
1.1 bertrand 216: *
217: CALL ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )
218: IF( INFO.EQ.0 ) THEN
219: *
220: * Solve the system A*X = B, overwriting B with X.
221: *
222: CALL ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
223: *
224: END IF
225: RETURN
226: *
227: * End of ZPBSV
228: *
229: END
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