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117 lines
3.4 KiB
Fortran
117 lines
3.4 KiB
Fortran
*DECK SGEFA
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SUBROUTINE SGEFA (A, LDA, N, IPVT, INFO)
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C***BEGIN PROLOGUE SGEFA
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C***PURPOSE Factor a matrix using Gaussian elimination.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D2A1
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C***TYPE SINGLE PRECISION (SGEFA-S, DGEFA-D, CGEFA-C)
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C***KEYWORDS GENERAL MATRIX, LINEAR ALGEBRA, LINPACK,
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C MATRIX FACTORIZATION
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C***AUTHOR Moler, C. B., (U. of New Mexico)
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C***DESCRIPTION
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C
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C SGEFA factors a real matrix by Gaussian elimination.
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C
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C SGEFA is usually called by SGECO, but it can be called
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C directly with a saving in time if RCOND is not needed.
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C (Time for SGECO) = (1 + 9/N)*(Time for SGEFA) .
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C
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C On Entry
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C
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C A REAL(LDA, N)
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C the matrix to be factored.
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C
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C LDA INTEGER
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C the leading dimension of the array A .
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C
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C N INTEGER
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C the order of the matrix A .
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C
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C On Return
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C
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C A an upper triangular matrix and the multipliers
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C which were used to obtain it.
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C The factorization can be written A = L*U , where
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C L is a product of permutation and unit lower
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C triangular matrices and U is upper triangular.
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C
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C IPVT INTEGER(N)
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C an integer vector of pivot indices.
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C
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C INFO INTEGER
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C = 0 normal value.
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C = K if U(K,K) .EQ. 0.0 . This is not an error
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C condition for this subroutine, but it does
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C indicate that SGESL or SGEDI will divide by zero
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C if called. Use RCOND in SGECO for a reliable
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C indication of singularity.
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C
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C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
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C Stewart, LINPACK Users' Guide, SIAM, 1979.
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C***ROUTINES CALLED ISAMAX, SAXPY, SSCAL
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C***REVISION HISTORY (YYMMDD)
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C 780814 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE SGEFA
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INTEGER LDA,N,IPVT(*),INFO
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REAL A(LDA,*)
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C
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REAL T
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INTEGER ISAMAX,J,K,KP1,L,NM1
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C
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C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
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C
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C***FIRST EXECUTABLE STATEMENT SGEFA
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INFO = 0
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NM1 = N - 1
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IF (NM1 .LT. 1) GO TO 70
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DO 60 K = 1, NM1
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KP1 = K + 1
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C
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C FIND L = PIVOT INDEX
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C
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L = ISAMAX(N-K+1,A(K,K),1) + K - 1
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IPVT(K) = L
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C
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C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
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C
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IF (A(L,K) .EQ. 0.0E0) GO TO 40
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C
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C INTERCHANGE IF NECESSARY
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C
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IF (L .EQ. K) GO TO 10
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T = A(L,K)
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A(L,K) = A(K,K)
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A(K,K) = T
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10 CONTINUE
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C
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C COMPUTE MULTIPLIERS
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C
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T = -1.0E0/A(K,K)
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CALL SSCAL(N-K,T,A(K+1,K),1)
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C
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C ROW ELIMINATION WITH COLUMN INDEXING
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C
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DO 30 J = KP1, N
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T = A(L,J)
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IF (L .EQ. K) GO TO 20
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A(L,J) = A(K,J)
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A(K,J) = T
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20 CONTINUE
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CALL SAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1)
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30 CONTINUE
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GO TO 50
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40 CONTINUE
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INFO = K
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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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IPVT(N) = N
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IF (A(N,N) .EQ. 0.0E0) INFO = N
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RETURN
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END
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