📄 zlatrs.f
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*
* Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
$ GO TO 90
*
* G(j) = ( 1 + CNORM(j) )*G(j-1)
*
XJ = ONE + CNORM( J )
GROW = GROW / XJ
80 CONTINUE
END IF
90 CONTINUE
END IF
*
IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN
*
* Use the Level 2 BLAS solve if the reciprocal of the bound on
* elements of X is not too small.
*
CALL ZTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, 1 )
ELSE
*
* Use a Level 1 BLAS solve, scaling intermediate results.
*
IF( XMAX.GT.BIGNUM*HALF ) THEN
*
* Scale X so that its components are less than or equal to
* BIGNUM in absolute value.
*
SCALE = ( BIGNUM*HALF ) / XMAX
CALL ZDSCAL( N, SCALE, X, 1 )
XMAX = BIGNUM
ELSE
XMAX = XMAX*TWO
END IF
*
IF( NOTRAN ) THEN
*
* Solve A * x = b
*
DO 120 J = JFIRST, JLAST, JINC
*
* Compute x(j) = b(j) / A(j,j), scaling x if necessary.
*
XJ = CABS1( X( J ) )
IF( NOUNIT ) THEN
TJJS = A( J, J )*TSCAL
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
$ GO TO 110
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
* abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by 1/b(j).
*
REC = ONE / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J ) = ZLADIV( X( J ), TJJS )
XJ = CABS1( X( J ) )
ELSE IF( TJJ.GT.ZERO ) THEN
*
* 0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM
* to avoid overflow when dividing by A(j,j).
*
REC = ( TJJ*BIGNUM ) / XJ
IF( CNORM( J ).GT.ONE ) THEN
*
* Scale by 1/CNORM(j) to avoid overflow when
* multiplying x(j) times column j.
*
REC = REC / CNORM( J )
END IF
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
X( J ) = ZLADIV( X( J ), TJJS )
XJ = CABS1( X( J ) )
ELSE
*
* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
* scale = 0, and compute a solution to A*x = 0.
*
DO 100 I = 1, N
X( I ) = ZERO
100 CONTINUE
X( J ) = ONE
XJ = ONE
SCALE = ZERO
XMAX = ZERO
END IF
110 CONTINUE
*
* Scale x if necessary to avoid overflow when adding a
* multiple of column j of A.
*
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( CNORM( J ).GT.( BIGNUM-XMAX )*REC ) THEN
*
* Scale x by 1/(2*abs(x(j))).
*
REC = REC*HALF
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
END IF
ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX ) ) THEN
*
* Scale x by 1/2.
*
CALL ZDSCAL( N, HALF, X, 1 )
SCALE = SCALE*HALF
END IF
*
IF( UPPER ) THEN
IF( J.GT.1 ) THEN
*
* Compute the update
* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j)
*
CALL ZAXPY( J-1, -X( J )*TSCAL, A( 1, J ), 1, X,
$ 1 )
I = IZAMAX( J-1, X, 1 )
XMAX = CABS1( X( I ) )
END IF
ELSE
IF( J.LT.N ) THEN
*
* Compute the update
* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j)
*
CALL ZAXPY( N-J, -X( J )*TSCAL, A( J+1, J ), 1,
$ X( J+1 ), 1 )
I = J + IZAMAX( N-J, X( J+1 ), 1 )
XMAX = CABS1( X( I ) )
END IF
END IF
120 CONTINUE
*
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
*
* Solve A**T * x = b
*
DO 170 J = JFIRST, JLAST, JINC
*
* Compute x(j) = b(j) - sum A(k,j)*x(k).
* k<>j
*
XJ = CABS1( X( J ) )
USCAL = TSCAL
REC = ONE / MAX( XMAX, ONE )
IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
* If x(j) could overflow, scale x by 1/(2*XMAX).
*
REC = REC*HALF
IF( NOUNIT ) THEN
TJJS = A( J, J )*TSCAL
ELSE
TJJS = TSCAL
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.ONE ) THEN
*
* Divide by A(j,j) when scaling x if A(j,j) > 1.
*
REC = MIN( ONE, REC*TJJ )
USCAL = ZLADIV( USCAL, TJJS )
END IF
IF( REC.LT.ONE ) THEN
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
*
CSUMJ = ZERO
IF( USCAL.EQ.DCMPLX( ONE ) ) THEN
*
* If the scaling needed for A in the dot product is 1,
* call ZDOTU to perform the dot product.
*
IF( UPPER ) THEN
CSUMJ = ZDOTU( J-1, A( 1, J ), 1, X, 1 )
ELSE IF( J.LT.N ) THEN
CSUMJ = ZDOTU( N-J, A( J+1, J ), 1, X( J+1 ), 1 )
END IF
ELSE
*
* Otherwise, use in-line code for the dot product.
*
IF( UPPER ) THEN
DO 130 I = 1, J - 1
CSUMJ = CSUMJ + ( A( I, J )*USCAL )*X( I )
130 CONTINUE
ELSE IF( J.LT.N ) THEN
DO 140 I = J + 1, N
CSUMJ = CSUMJ + ( A( I, J )*USCAL )*X( I )
140 CONTINUE
END IF
END IF
*
IF( USCAL.EQ.DCMPLX( TSCAL ) ) THEN
*
* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
* was not used to scale the dotproduct.
*
X( J ) = X( J ) - CSUMJ
XJ = CABS1( X( J ) )
IF( NOUNIT ) THEN
TJJS = A( J, J )*TSCAL
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
$ GO TO 160
END IF
*
* Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
* abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale X by 1/abs(x(j)).
*
REC = ONE / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE IF( TJJ.GT.ZERO ) THEN
*
* 0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
REC = ( TJJ*BIGNUM ) / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE
*
* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
* scale = 0 and compute a solution to A**T *x = 0.
*
DO 150 I = 1, N
X( I ) = ZERO
150 CONTINUE
X( J ) = ONE
SCALE = ZERO
XMAX = ZERO
END IF
160 CONTINUE
ELSE
*
* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
* product has already been divided by 1/A(j,j).
*
X( J ) = ZLADIV( X( J ), TJJS ) - CSUMJ
END IF
XMAX = MAX( XMAX, CABS1( X( J ) ) )
170 CONTINUE
*
ELSE
*
* Solve A**H * x = b
*
DO 220 J = JFIRST, JLAST, JINC
*
* Compute x(j) = b(j) - sum A(k,j)*x(k).
* k<>j
*
XJ = CABS1( X( J ) )
USCAL = TSCAL
REC = ONE / MAX( XMAX, ONE )
IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
* If x(j) could overflow, scale x by 1/(2*XMAX).
*
REC = REC*HALF
IF( NOUNIT ) THEN
TJJS = DCONJG( A( J, J ) )*TSCAL
ELSE
TJJS = TSCAL
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.ONE ) THEN
*
* Divide by A(j,j) when scaling x if A(j,j) > 1.
*
REC = MIN( ONE, REC*TJJ )
USCAL = ZLADIV( USCAL, TJJS )
END IF
IF( REC.LT.ONE ) THEN
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
*
CSUMJ = ZERO
IF( USCAL.EQ.DCMPLX( ONE ) ) THEN
*
* If the scaling needed for A in the dot product is 1,
* call ZDOTC to perform the dot product.
*
IF( UPPER ) THEN
CSUMJ = ZDOTC( J-1, A( 1, J ), 1, X, 1 )
ELSE IF( J.LT.N ) THEN
CSUMJ = ZDOTC( N-J, A( J+1, J ), 1, X( J+1 ), 1 )
END IF
ELSE
*
* Otherwise, use in-line code for the dot product.
*
IF( UPPER ) THEN
DO 180 I = 1, J - 1
CSUMJ = CSUMJ + ( DCONJG( A( I, J ) )*USCAL )*
$ X( I )
180 CONTINUE
ELSE IF( J.LT.N ) THEN
DO 190 I = J + 1, N
CSUMJ = CSUMJ + ( DCONJG( A( I, J ) )*USCAL )*
$ X( I )
190 CONTINUE
END IF
END IF
*
IF( USCAL.EQ.DCMPLX( TSCAL ) ) THEN
*
* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
* was not used to scale the dotproduct.
*
X( J ) = X( J ) - CSUMJ
XJ = CABS1( X( J ) )
IF( NOUNIT ) THEN
TJJS = DCONJG( A( J, J ) )*TSCAL
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
$ GO TO 210
END IF
*
* Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
* abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale X by 1/abs(x(j)).
*
REC = ONE / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE IF( TJJ.GT.ZERO ) THEN
*
* 0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
REC = ( TJJ*BIGNUM ) / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE
*
* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and
* scale = 0 and compute a solution to A**H *x = 0.
*
DO 200 I = 1, N
X( I ) = ZERO
200 CONTINUE
X( J ) = ONE
SCALE = ZERO
XMAX = ZERO
END IF
210 CONTINUE
ELSE
*
* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
* product has already been divided by 1/A(j,j).
*
X( J ) = ZLADIV( X( J ), TJJS ) - CSUMJ
END IF
XMAX = MAX( XMAX, CABS1( X( J ) ) )
220 CONTINUE
END IF
SCALE = SCALE / TSCAL
END IF
*
* Scale the column norms by 1/TSCAL for return.
*
IF( TSCAL.NE.ONE ) THEN
CALL DSCAL( N, ONE / TSCAL, CNORM, 1 )
END IF
*
RETURN
*
* End of ZLATRS
*
END
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