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SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
* * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. INTEGER LDA, N DOUBLE PRECISION SCALE * .. * .. Array Arguments .. INTEGER IPIV( * ), JPIV( * ) COMPLEX*16 A( LDA, * ), RHS( * ) * .. * * Purpose * ======= * * 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. * * * Arguments * ========= * * N (input) INTEGER * The number of columns of the matrix A. * * A (input) 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 * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1, N). * * RHS (input/output) COMPLEX*16 array, dimension N. * On entry, the right hand side vector b. * On exit, the solution vector X. * * IPIV (input) INTEGER array, dimension (N). * The pivot indices; for 1 <= i <= N, row i of the * matrix has been interchanged with row IPIV(i). * * JPIV (input) INTEGER array, dimension (N). * The pivot indices; for 1 <= j <= N, column j of the * matrix has been interchanged with column JPIV(j). * * SCALE (output) DOUBLE PRECISION * On exit, SCALE contains the scale factor. SCALE is chosen * 0 <= SCALE <= 1 to prevent owerflow in the solution. * * Further Details * =============== * * Based on contributions by * Bo Kagstrom and Peter Poromaa, Department of Computing Science, * Umea University, S-901 87 Umea, Sweden. * * ===================================================================== * * .. 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 CALL DLABAD( SMLNUM, BIGNUM ) * * 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 |