📄 dsptrf.c
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/* Perform a rank-1 update of A(1:k-1,1:k-1) as */
/* A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)' */
/*< R1 = ONE / AP( KC+K-1 ) >*/
r1 = 1. / ap[kc + k - 1];
/*< CALL DSPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) >*/
i__1 = k - 1;
d__1 = -r1;
dspr_(uplo, &i__1, &d__1, &ap[kc], &c__1, &ap[1], (ftnlen)1);
/* Store U(k) in column k */
/*< CALL DSCAL( K-1, R1, AP( KC ), 1 ) >*/
i__1 = k - 1;
dscal_(&i__1, &r1, &ap[kc], &c__1);
/*< ELSE >*/
} else {
/* 2-by-2 pivot block D(k): columns k and k-1 now hold */
/* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */
/* where U(k) and U(k-1) are the k-th and (k-1)-th columns */
/* of U */
/* Perform a rank-2 update of A(1:k-2,1:k-2) as */
/* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )' */
/* = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' */
/* Convert this to two rank-1 updates by using the eigen- */
/* decomposition of D(k) */
/*< >*/
dlaev2_(&ap[kc - 1], &ap[kc + k - 2], &ap[kc + k - 1], &r1, &
r2, &c__, &s);
/*< R1 = ONE / R1 >*/
r1 = 1. / r1;
/*< R2 = ONE / R2 >*/
r2 = 1. / r2;
/*< CALL DROT( K-2, AP( KNC ), 1, AP( KC ), 1, C, S ) >*/
i__1 = k - 2;
drot_(&i__1, &ap[knc], &c__1, &ap[kc], &c__1, &c__, &s);
/*< CALL DSPR( UPLO, K-2, -R1, AP( KNC ), 1, AP ) >*/
i__1 = k - 2;
d__1 = -r1;
dspr_(uplo, &i__1, &d__1, &ap[knc], &c__1, &ap[1], (ftnlen)1);
/*< CALL DSPR( UPLO, K-2, -R2, AP( KC ), 1, AP ) >*/
i__1 = k - 2;
d__1 = -r2;
dspr_(uplo, &i__1, &d__1, &ap[kc], &c__1, &ap[1], (ftnlen)1);
/* Store U(k) and U(k-1) in columns k and k-1 */
/*< CALL DSCAL( K-2, R1, AP( KNC ), 1 ) >*/
i__1 = k - 2;
dscal_(&i__1, &r1, &ap[knc], &c__1);
/*< CALL DSCAL( K-2, R2, AP( KC ), 1 ) >*/
i__1 = k - 2;
dscal_(&i__1, &r2, &ap[kc], &c__1);
/*< CALL DROT( K-2, AP( KNC ), 1, AP( KC ), 1, C, -S ) >*/
i__1 = k - 2;
d__1 = -s;
drot_(&i__1, &ap[knc], &c__1, &ap[kc], &c__1, &c__, &d__1);
/*< END IF >*/
}
/*< END IF >*/
}
/* Store details of the interchanges in IPIV */
/*< IF( KSTEP.EQ.1 ) THEN >*/
if (kstep == 1) {
/*< IPIV( K ) = KP >*/
ipiv[k] = kp;
/*< ELSE >*/
} else {
/*< IPIV( K ) = -KP >*/
ipiv[k] = -kp;
/*< IPIV( K-1 ) = -KP >*/
ipiv[k - 1] = -kp;
/*< END IF >*/
}
/* Decrease K and return to the start of the main loop */
/*< K = K - KSTEP >*/
k -= kstep;
/*< KC = KNC - K >*/
kc = knc - k;
/*< GO TO 10 >*/
goto L10;
/*< ELSE >*/
} else {
/* Factorize A as L*D*L' using the lower triangle of A */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2 */
/*< K = 1 >*/
k = 1;
/*< KC = 1 >*/
kc = 1;
/*< NPP = N*( N+1 ) / 2 >*/
npp = *n * (*n + 1) / 2;
/*< 40 CONTINUE >*/
L40:
/*< KNC = KC >*/
knc = kc;
/* If K > N, exit from loop */
/*< >*/
if (k > *n) {
goto L70;
}
/*< KSTEP = 1 >*/
kstep = 1;
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
/*< ABSAKK = ABS( AP( KC ) ) >*/
absakk = (d__1 = ap[kc], abs(d__1));
/* IMAX is the row-index of the largest off-diagonal element in */
/* column K, and COLMAX is its absolute value */
/*< IF( K.LT.N ) THEN >*/
if (k < *n) {
/*< IMAX = K + IDAMAX( N-K, AP( KC+1 ), 1 ) >*/
i__1 = *n - k;
imax = k + idamax_(&i__1, &ap[kc + 1], &c__1);
/*< COLMAX = ABS( AP( KC+IMAX-K ) ) >*/
colmax = (d__1 = ap[kc + imax - k], abs(d__1));
/*< ELSE >*/
} else {
/*< COLMAX = ZERO >*/
colmax = 0.;
/*< END IF >*/
}
/*< IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN >*/
if (max(absakk,colmax) == 0.) {
/* Column K is zero: set INFO and continue */
/*< >*/
if (*info == 0) {
*info = k;
}
/*< KP = K >*/
kp = k;
/*< ELSE >*/
} else {
/*< IF( ABSAKK.GE.ALPHA*COLMAX ) THEN >*/
if (absakk >= alpha * colmax) {
/* no interchange, use 1-by-1 pivot block */
/*< KP = K >*/
kp = k;
/*< ELSE >*/
} else {
/* JMAX is the column-index of the largest off-diagonal */
/* element in row IMAX, and ROWMAX is its absolute value */
/*< ROWMAX = ZERO >*/
rowmax = 0.;
/*< KX = KC + IMAX - K >*/
kx = kc + imax - k;
/*< DO 50 J = K, IMAX - 1 >*/
i__1 = imax - 1;
for (j = k; j <= i__1; ++j) {
/*< IF( ABS( AP( KX ) ).GT.ROWMAX ) THEN >*/
if ((d__1 = ap[kx], abs(d__1)) > rowmax) {
/*< ROWMAX = ABS( AP( KX ) ) >*/
rowmax = (d__1 = ap[kx], abs(d__1));
/*< JMAX = J >*/
jmax = j;
/*< END IF >*/
}
/*< KX = KX + N - J >*/
kx = kx + *n - j;
/*< 50 CONTINUE >*/
/* L50: */
}
/*< KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1 >*/
kpc = npp - (*n - imax + 1) * (*n - imax + 2) / 2 + 1;
/*< IF( IMAX.LT.N ) THEN >*/
if (imax < *n) {
/*< JMAX = IMAX + IDAMAX( N-IMAX, AP( KPC+1 ), 1 ) >*/
i__1 = *n - imax;
jmax = imax + idamax_(&i__1, &ap[kpc + 1], &c__1);
/*< ROWMAX = MAX( ROWMAX, ABS( AP( KPC+JMAX-IMAX ) ) ) >*/
/* Computing MAX */
d__2 = rowmax, d__3 = (d__1 = ap[kpc + jmax - imax], abs(
d__1));
rowmax = max(d__2,d__3);
/*< END IF >*/
}
/*< IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN >*/
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
/*< KP = K >*/
kp = k;
/*< ELSE IF( ABS( AP( KPC ) ).GE.ALPHA*ROWMAX ) THEN >*/
} else if ((d__1 = ap[kpc], abs(d__1)) >= alpha * rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1 */
/* pivot block */
/*< KP = IMAX >*/
kp = imax;
/*< ELSE >*/
} else {
/* interchange rows and columns K+1 and IMAX, use 2-by-2 */
/* pivot block */
/*< KP = IMAX >*/
kp = imax;
/*< KSTEP = 2 >*/
kstep = 2;
/*< END IF >*/
}
/*< END IF >*/
}
/*< KK = K + KSTEP - 1 >*/
kk = k + kstep - 1;
/*< >*/
if (kstep == 2) {
knc = knc + *n - k + 1;
}
/*< IF( KP.NE.KK ) THEN >*/
if (kp != kk) {
/* Interchange rows and columns KK and KP in the trailing */
/* submatrix A(k:n,k:n) */
/*< >*/
if (kp < *n) {
i__1 = *n - kp;
dswap_(&i__1, &ap[knc + kp - kk + 1], &c__1, &ap[kpc + 1],
&c__1);
}
/*< KX = KNC + KP - KK >*/
kx = knc + kp - kk;
/*< DO 60 J = KK + 1, KP - 1 >*/
i__1 = kp - 1;
for (j = kk + 1; j <= i__1; ++j) {
/*< KX = KX + N - J + 1 >*/
kx = kx + *n - j + 1;
/*< T = AP( KNC+J-KK ) >*/
t = ap[knc + j - kk];
/*< AP( KNC+J-KK ) = AP( KX ) >*/
ap[knc + j - kk] = ap[kx];
/*< AP( KX ) = T >*/
ap[kx] = t;
/*< 60 CONTINUE >*/
/* L60: */
}
/*< T = AP( KNC ) >*/
t = ap[knc];
/*< AP( KNC ) = AP( KPC ) >*/
ap[knc] = ap[kpc];
/*< AP( KPC ) = T >*/
ap[kpc] = t;
/*< IF( KSTEP.EQ.2 ) THEN >*/
if (kstep == 2) {
/*< T = AP( KC+1 ) >*/
t = ap[kc + 1];
/*< AP( KC+1 ) = AP( KC+KP-K ) >*/
ap[kc + 1] = ap[kc + kp - k];
/*< AP( KC+KP-K ) = T >*/
ap[kc + kp - k] = t;
/*< END IF >*/
}
/*< END IF >*/
}
/* Update the trailing submatrix */
/*< IF( KSTEP.EQ.1 ) THEN >*/
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column k now holds */
/* W(k) = L(k)*D(k) */
/* where L(k) is the k-th column of L */
/*< IF( K.LT.N ) THEN >*/
if (k < *n) {
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
/* A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' */
/*< R1 = ONE / AP( KC ) >*/
r1 = 1. / ap[kc];
/*< >*/
i__1 = *n - k;
d__1 = -r1;
dspr_(uplo, &i__1, &d__1, &ap[kc + 1], &c__1, &ap[kc + *n
- k + 1], (ftnlen)1);
/* Store L(k) in column K */
/*< CALL DSCAL( N-K, R1, AP( KC+1 ), 1 ) >*/
i__1 = *n - k;
dscal_(&i__1, &r1, &ap[kc + 1], &c__1);
/*< END IF >*/
}
/*< ELSE >*/
} else {
/* 2-by-2 pivot block D(k): columns K and K+1 now hold */
/* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */
/* where L(k) and L(k+1) are the k-th and (k+1)-th columns */
/* of L */
/*< IF( K.LT.N-1 ) THEN >*/
if (k < *n - 1) {
/* Perform a rank-2 update of A(k+2:n,k+2:n) as */
/* A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )' */
/* = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )' */
/* Convert this to two rank-1 updates by using the eigen- */
/* decomposition of D(k) */
/*< >*/
dlaev2_(&ap[kc], &ap[kc + 1], &ap[knc], &r1, &r2, &c__, &
s);
/*< R1 = ONE / R1 >*/
r1 = 1. / r1;
/*< R2 = ONE / R2 >*/
r2 = 1. / r2;
/*< >*/
i__1 = *n - k - 1;
drot_(&i__1, &ap[kc + 2], &c__1, &ap[knc + 1], &c__1, &
c__, &s);
/*< >*/
i__1 = *n - k - 1;
d__1 = -r1;
dspr_(uplo, &i__1, &d__1, &ap[kc + 2], &c__1, &ap[knc + *
n - k], (ftnlen)1);
/*< >*/
i__1 = *n - k - 1;
d__1 = -r2;
dspr_(uplo, &i__1, &d__1, &ap[knc + 1], &c__1, &ap[knc + *
n - k], (ftnlen)1);
/* Store L(k) and L(k+1) in columns k and k+1 */
/*< CALL DSCAL( N-K-1, R1, AP( KC+2 ), 1 ) >*/
i__1 = *n - k - 1;
dscal_(&i__1, &r1, &ap[kc + 2], &c__1);
/*< CALL DSCAL( N-K-1, R2, AP( KNC+1 ), 1 ) >*/
i__1 = *n - k - 1;
dscal_(&i__1, &r2, &ap[knc + 1], &c__1);
/*< >*/
i__1 = *n - k - 1;
d__1 = -s;
drot_(&i__1, &ap[kc + 2], &c__1, &ap[knc + 1], &c__1, &
c__, &d__1);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/* Store details of the interchanges in IPIV */
/*< IF( KSTEP.EQ.1 ) THEN >*/
if (kstep == 1) {
/*< IPIV( K ) = KP >*/
ipiv[k] = kp;
/*< ELSE >*/
} else {
/*< IPIV( K ) = -KP >*/
ipiv[k] = -kp;
/*< IPIV( K+1 ) = -KP >*/
ipiv[k + 1] = -kp;
/*< END IF >*/
}
/* Increase K and return to the start of the main loop */
/*< K = K + KSTEP >*/
k += kstep;
/*< KC = KNC + N - K + 2 >*/
kc = knc + *n - k + 2;
/*< GO TO 40 >*/
goto L40;
/*< END IF >*/
}
/*< 70 CONTINUE >*/
L70:
/*< RETURN >*/
return 0;
/* End of DSPTRF */
/*< END >*/
} /* dsptrf_ */
#ifdef __cplusplus
}
#endif
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