Annotation of rpl/lapack/lapack/zgbsv.f, revision 1.8
1.8 ! bertrand 1: *> \brief <b> ZGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simple driver)
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGBSV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbsv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbsv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbsv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER IPIV( * )
! 28: * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZGBSV computes the solution to a complex system of linear equations
! 38: *> A * X = B, where A is a band matrix of order N with KL subdiagonals
! 39: *> and KU superdiagonals, and X and B are N-by-NRHS matrices.
! 40: *>
! 41: *> The LU decomposition with partial pivoting and row interchanges is
! 42: *> used to factor A as A = L * U, where L is a product of permutation
! 43: *> and unit lower triangular matrices with KL subdiagonals, and U is
! 44: *> upper triangular with KL+KU superdiagonals. The factored form of A
! 45: *> is then used to solve the system of equations A * X = B.
! 46: *> \endverbatim
! 47: *
! 48: * Arguments:
! 49: * ==========
! 50: *
! 51: *> \param[in] N
! 52: *> \verbatim
! 53: *> N is INTEGER
! 54: *> The number of linear equations, i.e., the order of the
! 55: *> matrix A. N >= 0.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] KL
! 59: *> \verbatim
! 60: *> KL is INTEGER
! 61: *> The number of subdiagonals within the band of A. KL >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] KU
! 65: *> \verbatim
! 66: *> KU is INTEGER
! 67: *> The number of superdiagonals within the band of A. KU >= 0.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] NRHS
! 71: *> \verbatim
! 72: *> NRHS is INTEGER
! 73: *> The number of right hand sides, i.e., the number of columns
! 74: *> of the matrix B. NRHS >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in,out] AB
! 78: *> \verbatim
! 79: *> AB is COMPLEX*16 array, dimension (LDAB,N)
! 80: *> On entry, the matrix A in band storage, in rows KL+1 to
! 81: *> 2*KL+KU+1; rows 1 to KL of the array need not be set.
! 82: *> The j-th column of A is stored in the j-th column of the
! 83: *> array AB as follows:
! 84: *> AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
! 85: *> On exit, details of the factorization: U is stored as an
! 86: *> upper triangular band matrix with KL+KU superdiagonals in
! 87: *> rows 1 to KL+KU+1, and the multipliers used during the
! 88: *> factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
! 89: *> See below for further details.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] LDAB
! 93: *> \verbatim
! 94: *> LDAB is INTEGER
! 95: *> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[out] IPIV
! 99: *> \verbatim
! 100: *> IPIV is INTEGER array, dimension (N)
! 101: *> The pivot indices that define the permutation matrix P;
! 102: *> row i of the matrix was interchanged with row IPIV(i).
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in,out] B
! 106: *> \verbatim
! 107: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 108: *> On entry, the N-by-NRHS right hand side matrix B.
! 109: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 110: *> \endverbatim
! 111: *>
! 112: *> \param[in] LDB
! 113: *> \verbatim
! 114: *> LDB is INTEGER
! 115: *> The leading dimension of the array B. LDB >= max(1,N).
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[out] INFO
! 119: *> \verbatim
! 120: *> INFO is INTEGER
! 121: *> = 0: successful exit
! 122: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 123: *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
! 124: *> has been completed, but the factor U is exactly
! 125: *> singular, and the solution has not been computed.
! 126: *> \endverbatim
! 127: *
! 128: * Authors:
! 129: * ========
! 130: *
! 131: *> \author Univ. of Tennessee
! 132: *> \author Univ. of California Berkeley
! 133: *> \author Univ. of Colorado Denver
! 134: *> \author NAG Ltd.
! 135: *
! 136: *> \date November 2011
! 137: *
! 138: *> \ingroup complex16GBsolve
! 139: *
! 140: *> \par Further Details:
! 141: * =====================
! 142: *>
! 143: *> \verbatim
! 144: *>
! 145: *> The band storage scheme is illustrated by the following example, when
! 146: *> M = N = 6, KL = 2, KU = 1:
! 147: *>
! 148: *> On entry: On exit:
! 149: *>
! 150: *> * * * + + + * * * u14 u25 u36
! 151: *> * * + + + + * * u13 u24 u35 u46
! 152: *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
! 153: *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
! 154: *> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
! 155: *> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
! 156: *>
! 157: *> Array elements marked * are not used by the routine; elements marked
! 158: *> + need not be set on entry, but are required by the routine to store
! 159: *> elements of U because of fill-in resulting from the row interchanges.
! 160: *> \endverbatim
! 161: *>
! 162: * =====================================================================
1.1 bertrand 163: SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
164: *
1.8 ! bertrand 165: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 166: * -- LAPACK is a software package provided by Univ. of Tennessee, --
167: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 168: * November 2011
1.1 bertrand 169: *
170: * .. Scalar Arguments ..
171: INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
172: * ..
173: * .. Array Arguments ..
174: INTEGER IPIV( * )
175: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
176: * ..
177: *
178: * =====================================================================
179: *
180: * .. External Subroutines ..
181: EXTERNAL XERBLA, ZGBTRF, ZGBTRS
182: * ..
183: * .. Intrinsic Functions ..
184: INTRINSIC MAX
185: * ..
186: * .. Executable Statements ..
187: *
188: * Test the input parameters.
189: *
190: INFO = 0
191: IF( N.LT.0 ) THEN
192: INFO = -1
193: ELSE IF( KL.LT.0 ) THEN
194: INFO = -2
195: ELSE IF( KU.LT.0 ) THEN
196: INFO = -3
197: ELSE IF( NRHS.LT.0 ) THEN
198: INFO = -4
199: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
200: INFO = -6
201: ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
202: INFO = -9
203: END IF
204: IF( INFO.NE.0 ) THEN
205: CALL XERBLA( 'ZGBSV ', -INFO )
206: RETURN
207: END IF
208: *
209: * Compute the LU factorization of the band matrix A.
210: *
211: CALL ZGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
212: IF( INFO.EQ.0 ) THEN
213: *
214: * Solve the system A*X = B, overwriting B with X.
215: *
216: CALL ZGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
217: $ B, LDB, INFO )
218: END IF
219: RETURN
220: *
221: * End of ZGBSV
222: *
223: END
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