*DECK CGEFA SUBROUTINE CGEFA (A, LDA, N, IPVT, INFO) C***BEGIN PROLOGUE CGEFA C***PURPOSE Factor a matrix using Gaussian elimination. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2C1 C***TYPE COMPLEX (SGEFA-S, DGEFA-D, CGEFA-C) C***KEYWORDS GENERAL MATRIX, LINEAR ALGEBRA, LINPACK, C MATRIX FACTORIZATION C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C CGEFA factors a complex matrix by Gaussian elimination. C C CGEFA is usually called by CGECO, but it can be called C directly with a saving in time if RCOND is not needed. C (Time for CGECO) = (1 + 9/N)*(Time for CGEFA) . C C On Entry C C A COMPLEX(LDA, N) C the matrix to be factored. C C LDA INTEGER C the leading dimension of the array A . C C N INTEGER C the order of the matrix A . C C On Return C C A an upper triangular matrix and the multipliers C which were used to obtain it. C The factorization can be written A = L*U where C L is a product of permutation and unit lower C triangular matrices and U is upper triangular. C C IPVT INTEGER(N) C an integer vector of pivot indices. C C INFO INTEGER C = 0 normal value. C = K if U(K,K) .EQ. 0.0 . This is not an error C condition for this subroutine, but it does C indicate that CGESL or CGEDI will divide by zero C if called. Use RCOND in CGECO for a reliable C indication of singularity. C C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. C Stewart, LINPACK Users' Guide, SIAM, 1979. C***ROUTINES CALLED CAXPY, CSCAL, ICAMAX C***REVISION HISTORY (YYMMDD) C 780814 DATE WRITTEN C 890831 Modified array declarations. (WRB) C 890831 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 900326 Removed duplicate information from DESCRIPTION section. C (WRB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE CGEFA INTEGER LDA,N,IPVT(*),INFO COMPLEX A(LDA,*) C COMPLEX T INTEGER ICAMAX,J,K,KP1,L,NM1 COMPLEX ZDUM REAL CABS1 CABS1(ZDUM) = ABS(REAL(ZDUM)) + ABS(AIMAG(ZDUM)) C C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING C C***FIRST EXECUTABLE STATEMENT CGEFA INFO = 0 NM1 = N - 1 IF (NM1 .LT. 1) GO TO 70 DO 60 K = 1, NM1 KP1 = K + 1 C C FIND L = PIVOT INDEX C L = ICAMAX(N-K+1,A(K,K),1) + K - 1 IPVT(K) = L C C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED C IF (CABS1(A(L,K)) .EQ. 0.0E0) GO TO 40 C C INTERCHANGE IF NECESSARY C IF (L .EQ. K) GO TO 10 T = A(L,K) A(L,K) = A(K,K) A(K,K) = T 10 CONTINUE C C COMPUTE MULTIPLIERS C T = -(1.0E0,0.0E0)/A(K,K) CALL CSCAL(N-K,T,A(K+1,K),1) C C ROW ELIMINATION WITH COLUMN INDEXING C DO 30 J = KP1, N T = A(L,J) IF (L .EQ. K) GO TO 20 A(L,J) = A(K,J) A(K,J) = T 20 CONTINUE CALL CAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1) 30 CONTINUE GO TO 50 40 CONTINUE INFO = K 50 CONTINUE 60 CONTINUE 70 CONTINUE IPVT(N) = N IF (CABS1(A(N,N)) .EQ. 0.0E0) INFO = N RETURN END