Annotation of rpl/lapack/lapack/zgesc2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZGESC2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGESC2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesc2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgesc2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesc2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER LDA, N
! 25: * DOUBLE PRECISION SCALE
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * ), JPIV( * )
! 29: * COMPLEX*16 A( LDA, * ), RHS( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZGESC2 solves a system of linear equations
! 39: *>
! 40: *> A * X = scale* RHS
! 41: *>
! 42: *> with a general N-by-N matrix A using the LU factorization with
! 43: *> complete pivoting computed by ZGETC2.
! 44: *>
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] N
! 51: *> \verbatim
! 52: *> N is INTEGER
! 53: *> The number of columns of the matrix A.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] A
! 57: *> \verbatim
! 58: *> A is COMPLEX*16 array, dimension (LDA, N)
! 59: *> On entry, the LU part of the factorization of the n-by-n
! 60: *> matrix A computed by ZGETC2: A = P * L * U * Q
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] LDA
! 64: *> \verbatim
! 65: *> LDA is INTEGER
! 66: *> The leading dimension of the array A. LDA >= max(1, N).
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in,out] RHS
! 70: *> \verbatim
! 71: *> RHS is COMPLEX*16 array, dimension N.
! 72: *> On entry, the right hand side vector b.
! 73: *> On exit, the solution vector X.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] IPIV
! 77: *> \verbatim
! 78: *> IPIV is INTEGER array, dimension (N).
! 79: *> The pivot indices; for 1 <= i <= N, row i of the
! 80: *> matrix has been interchanged with row IPIV(i).
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] JPIV
! 84: *> \verbatim
! 85: *> JPIV is INTEGER array, dimension (N).
! 86: *> The pivot indices; for 1 <= j <= N, column j of the
! 87: *> matrix has been interchanged with column JPIV(j).
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[out] SCALE
! 91: *> \verbatim
! 92: *> SCALE is DOUBLE PRECISION
! 93: *> On exit, SCALE contains the scale factor. SCALE is chosen
! 94: *> 0 <= SCALE <= 1 to prevent owerflow in the solution.
! 95: *> \endverbatim
! 96: *
! 97: * Authors:
! 98: * ========
! 99: *
! 100: *> \author Univ. of Tennessee
! 101: *> \author Univ. of California Berkeley
! 102: *> \author Univ. of Colorado Denver
! 103: *> \author NAG Ltd.
! 104: *
! 105: *> \date November 2011
! 106: *
! 107: *> \ingroup complex16GEauxiliary
! 108: *
! 109: *> \par Contributors:
! 110: * ==================
! 111: *>
! 112: *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
! 113: *> Umea University, S-901 87 Umea, Sweden.
! 114: *
! 115: * =====================================================================
1.1 bertrand 116: SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
117: *
1.8 ! bertrand 118: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 119: * -- LAPACK is a software package provided by Univ. of Tennessee, --
120: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 121: * November 2011
1.1 bertrand 122: *
123: * .. Scalar Arguments ..
124: INTEGER LDA, N
125: DOUBLE PRECISION SCALE
126: * ..
127: * .. Array Arguments ..
128: INTEGER IPIV( * ), JPIV( * )
129: COMPLEX*16 A( LDA, * ), RHS( * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ZERO, ONE, TWO
136: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
137: * ..
138: * .. Local Scalars ..
139: INTEGER I, J
140: DOUBLE PRECISION BIGNUM, EPS, SMLNUM
141: COMPLEX*16 TEMP
142: * ..
143: * .. External Subroutines ..
144: EXTERNAL ZLASWP, ZSCAL
145: * ..
146: * .. External Functions ..
147: INTEGER IZAMAX
148: DOUBLE PRECISION DLAMCH
149: EXTERNAL IZAMAX, DLAMCH
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC ABS, DBLE, DCMPLX
153: * ..
154: * .. Executable Statements ..
155: *
156: * Set constant to control overflow
157: *
158: EPS = DLAMCH( 'P' )
159: SMLNUM = DLAMCH( 'S' ) / EPS
160: BIGNUM = ONE / SMLNUM
161: CALL DLABAD( SMLNUM, BIGNUM )
162: *
163: * Apply permutations IPIV to RHS
164: *
165: CALL ZLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 )
166: *
167: * Solve for L part
168: *
169: DO 20 I = 1, N - 1
170: DO 10 J = I + 1, N
171: RHS( J ) = RHS( J ) - A( J, I )*RHS( I )
172: 10 CONTINUE
173: 20 CONTINUE
174: *
175: * Solve for U part
176: *
177: SCALE = ONE
178: *
179: * Check for scaling
180: *
181: I = IZAMAX( N, RHS, 1 )
182: IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN
183: TEMP = DCMPLX( ONE / TWO, ZERO ) / ABS( RHS( I ) )
184: CALL ZSCAL( N, TEMP, RHS( 1 ), 1 )
185: SCALE = SCALE*DBLE( TEMP )
186: END IF
187: DO 40 I = N, 1, -1
188: TEMP = DCMPLX( ONE, ZERO ) / A( I, I )
189: RHS( I ) = RHS( I )*TEMP
190: DO 30 J = I + 1, N
191: RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP )
192: 30 CONTINUE
193: 40 CONTINUE
194: *
195: * Apply permutations JPIV to the solution (RHS)
196: *
197: CALL ZLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 )
198: RETURN
199: *
200: * End of ZGESC2
201: *
202: END
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