numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/zgesc2.f | 5420B | -rw-r--r-- |
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*> \brief \b ZGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGESC2 + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesc2.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgesc2.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesc2.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) * * .. Scalar Arguments .. * INTEGER LDA, N * DOUBLE PRECISION SCALE * .. * .. Array Arguments .. * INTEGER IPIV( * ), JPIV( * ) * COMPLEX*16 A( LDA, * ), RHS( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGESC2 solves a system of linear equations *> *> A * X = scale* RHS *> *> with a general N-by-N matrix A using the LU factorization with *> complete pivoting computed by ZGETC2. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the LU part of the factorization of the n-by-n *> matrix A computed by ZGETC2: A = P * L * U * Q *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1, N). *> \endverbatim *> *> \param[in,out] RHS *> \verbatim *> RHS is COMPLEX*16 array, dimension N. *> On entry, the right hand side vector b. *> On exit, the solution vector X. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N). *> The pivot indices; for 1 <= i <= N, row i of the *> matrix has been interchanged with row IPIV(i). *> \endverbatim *> *> \param[in] JPIV *> \verbatim *> JPIV is INTEGER array, dimension (N). *> The pivot indices; for 1 <= j <= N, column j of the *> matrix has been interchanged with column JPIV(j). *> \endverbatim *> *> \param[out] SCALE *> \verbatim *> SCALE is DOUBLE PRECISION *> On exit, SCALE contains the scale factor. SCALE is chosen *> 0 <= SCALE <= 1 to prevent overflow in the solution. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup gesc2 * *> \par Contributors: * ================== *> *> Bo Kagstrom and Peter Poromaa, Department of Computing Science, *> Umea University, S-901 87 Umea, Sweden. * * ===================================================================== SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER LDA, N DOUBLE PRECISION SCALE * .. * .. Array Arguments .. INTEGER IPIV( * ), JPIV( * ) COMPLEX*16 A( LDA, * ), RHS( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION BIGNUM, EPS, SMLNUM COMPLEX*16 TEMP * .. * .. External Subroutines .. EXTERNAL ZLASWP, ZSCAL * .. * .. External Functions .. INTEGER IZAMAX DOUBLE PRECISION DLAMCH EXTERNAL IZAMAX, DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX * .. * .. Executable Statements .. * * Set constant to control overflow * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM * * Apply permutations IPIV to RHS * CALL ZLASWP( 1, RHS, LDA, 1, N-1, IPIV, 1 ) * * Solve for L part * DO 20 I = 1, N - 1 DO 10 J = I + 1, N RHS( J ) = RHS( J ) - A( J, I )*RHS( I ) 10 CONTINUE 20 CONTINUE * * Solve for U part * SCALE = ONE * * Check for scaling * I = IZAMAX( N, RHS, 1 ) IF( TWO*SMLNUM*ABS( RHS( I ) ).GT.ABS( A( N, N ) ) ) THEN TEMP = DCMPLX( ONE / TWO, ZERO ) / ABS( RHS( I ) ) CALL ZSCAL( N, TEMP, RHS( 1 ), 1 ) SCALE = SCALE*DBLE( TEMP ) END IF DO 40 I = N, 1, -1 TEMP = DCMPLX( ONE, ZERO ) / A( I, I ) RHS( I ) = RHS( I )*TEMP DO 30 J = I + 1, N RHS( I ) = RHS( I ) - RHS( J )*( A( I, J )*TEMP ) 30 CONTINUE 40 CONTINUE * * Apply permutations JPIV to the solution (RHS) * CALL ZLASWP( 1, RHS, LDA, 1, N-1, JPIV, -1 ) RETURN * * End of ZGESC2 * END