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spofa.f
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1996-07-19
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SUBROUTINE SPOFA(A,LDA,N,INFO)
INTEGER LDA,N,INFO
REAL A(LDA,1)
C
C SPOFA FACTORS A REAL SYMMETRIC POSITIVE DEFINITE MATRIX.
C
C SPOFA IS USUALLY CALLED BY SPOCO, BUT IT CAN BE CALLED
C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED.
C (TIME FOR SPOCO) = (1 + 18/N)*(TIME FOR SPOFA) .
C
C ON ENTRY
C
C A REAL(LDA, N)
C THE SYMMETRIC MATRIX TO BE FACTORED. ONLY THE
C DIAGONAL AND UPPER TRIANGLE ARE USED.
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 R SO THAT A = TRANS(R)*R
C WHERE TRANS(R) IS THE TRANSPOSE.
C THE STRICT LOWER TRIANGLE IS UNALTERED.
C IF INFO .NE. 0 , THE FACTORIZATION IS NOT COMPLETE.
C
C INFO INTEGER
C = 0 FOR NORMAL RETURN.
C = K SIGNALS AN ERROR CONDITION. THE LEADING MINOR
C OF ORDER K IS NOT POSITIVE DEFINITE.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C SUBROUTINES AND FUNCTIONS
C
C BLAS SDOT
C FORTRAN SQRT
C
C INTERNAL VARIABLES
C
REAL SDOT,T
REAL S
INTEGER J,JM1,K
C BEGIN BLOCK WITH ...EXITS TO 40
C
C
DO 30 J = 1, N
INFO = J
S = 0.0E0
JM1 = J - 1
IF (JM1 .LT. 1) GO TO 20
DO 10 K = 1, JM1
T = A(K,J) - SDOT(K-1,A(1,K),1,A(1,J),1)
T = T/A(K,K)
A(K,J) = T
S = S + T*T
10 CONTINUE
20 CONTINUE
S = A(J,J) - S
C ......EXIT
IF (S .LE. 0.0E0) GO TO 40
A(J,J) = SQRT(S)
30 CONTINUE
INFO = 0
40 CONTINUE
RETURN
END