/* Subroutine */ int zlatdf_(integer *ijob, integer *n, doublecomplex *z__,
integer *ldz, doublecomplex *rhs, doublereal *rdsum, doublereal *
rdscal, integer *ipiv, integer *jpiv)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *);
void z_sqrt(doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, k;
doublecomplex bm, bp, xm[2], xp[2];
integer info;
doublecomplex temp, work[8];
doublereal scale;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
doublecomplex pmone;
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal rtemp, sminu, rwork[2];
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
doublereal splus;
extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zgesc2_(
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublereal *), zgecon_(char *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *);
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *), zlaswp_(integer *, doublecomplex *,
integer *, integer *, integer *, integer *, integer *);
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATDF computes the contribution to the reciprocal Dif-estimate */
/* by solving for x in Z * x = b, where b is chosen such that the norm */
/* of x is as large as possible. It is assumed that LU decomposition */
/* of Z has been computed by ZGETC2. On entry RHS = f holds the */
/* contribution from earlier solved sub-systems, and on return RHS = x. */
/* The factorization of Z returned by ZGETC2 has the form */
/* Z = P * L * U * Q, where P and Q are permutation matrices. L is lower */
/* triangular with unit diagonal elements and U is upper triangular. */
/* Arguments */
/* ========= */
/* IJOB (input) INTEGER */
/* IJOB = 2: First compute an approximative null-vector e */
/* of Z using ZGECON, e is normalized and solve for */
/* Zx = +-e - f with the sign giving the greater value of */
/* 2-norm(x). About 5 times as expensive as Default. */
/* IJOB .ne. 2: Local look ahead strategy where */
/* all entries of the r.h.s. b is choosen as either +1 or */
/* -1. Default. */
/* N (input) INTEGER */
/* The number of columns of the matrix Z. */
/* Z (input) DOUBLE PRECISION array, dimension (LDZ, N) */
/* On entry, the LU part of the factorization of the n-by-n */
/* matrix Z computed by ZGETC2: Z = P * L * U * Q */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDA >= max(1, N). */
/* RHS (input/output) DOUBLE PRECISION array, dimension (N). */
/* On entry, RHS contains contributions from other subsystems. */
/* On exit, RHS contains the solution of the subsystem with */
/* entries according to the value of IJOB (see above). */
/* RDSUM (input/output) DOUBLE PRECISION */
/* On entry, the sum of squares of computed contributions to */
/* the Dif-estimate under computation by ZTGSYL, where the */
/* scaling factor RDSCAL (see below) has been factored out. */
/* On exit, the corresponding sum of squares updated with the */
/* contributions from the current sub-system. */
/* If TRANS = 'T' RDSUM is not touched. */
/* NOTE: RDSUM only makes sense when ZTGSY2 is called by CTGSYL. */
/* RDSCAL (input/output) DOUBLE PRECISION */
/* On entry, scaling factor used to prevent overflow in RDSUM. */
/* On exit, RDSCAL is updated w.r.t. the current contributions */
/* in RDSUM. */
/* If TRANS = 'T', RDSCAL is not touched. */
/* NOTE: RDSCAL only makes sense when ZTGSY2 is called by */
/* ZTGSYL. */
/* IPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= i <= N, row i of the */
/* matrix has been interchanged with row IPIV(i). */
/* JPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= j <= N, column j of the */
/* matrix has been interchanged with column JPIV(j). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* This routine is a further developed implementation of algorithm */
/* BSOLVE in [1] using complete pivoting in the LU factorization. */
/* [1] Bo Kagstrom and Lars Westin, */
/* Generalized Schur Methods with Condition Estimators for */
/* Solving the Generalized Sylvester Equation, IEEE Transactions */
/* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
/* [2] Peter Poromaa, */
/* On Efficient and Robust Estimators for the Separation */
/* between two Regular Matrix Pairs with Applications in */
/* Condition Estimation. Report UMINF-95.05, Department of */
/* Computing Science, Umea University, S-901 87 Umea, Sweden, */
/* 1995. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
if (*ijob != 2) {
/* Apply permutations IPIV to RHS */
i__1 = *n - 1;
zlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
/* Solve for L-part choosing RHS either to +1 or -1. */
z__1.r = -1., z__1.i = -0.;
pmone.r = z__1.r, pmone.i = z__1.i;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
z__1.r = rhs[i__2].r + 1., z__1.i = rhs[i__2].i + 0.;
bp.r = z__1.r, bp.i = z__1.i;
i__2 = j;
z__1.r = rhs[i__2].r - 1., z__1.i = rhs[i__2].i - 0.;
bm.r = z__1.r, bm.i = z__1.i;
splus = 1.;
/* Lockahead for L- part RHS(1:N-1) = +-1 */
/* SPLUS and SMIN computed more efficiently than in BSOLVE[1]. */
i__2 = *n - j;
zdotc_(&z__1, &i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
+ j * z_dim1], &c__1);
splus += z__1.r;
i__2 = *n - j;
zdotc_(&z__1, &i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
&c__1);
sminu = z__1.r;
i__2 = j;
splus *= rhs[i__2].r;
if (splus > sminu) {
i__2 = j;
rhs[i__2].r = bp.r, rhs[i__2].i = bp.i;
} else if (sminu > splus) {
i__2 = j;
rhs[i__2].r = bm.r, rhs[i__2].i = bm.i;
} else {
/* In this case the updating sums are equal and we can */
/* choose RHS(J) +1 or -1. The first time this happens we */
/* choose -1, thereafter +1. This is a simple way to get */
/* good estimates of matrices like Byers well-known example */
/* (see [1]). (Not done in BSOLVE.) */
i__2 = j;
i__3 = j;
z__1.r = rhs[i__3].r + pmone.r, z__1.i = rhs[i__3].i +
pmone.i;
rhs[i__2].r = z__1.r, rhs[i__2].i = z__1.i;
pmone.r = 1., pmone.i = 0.;
}
/* Compute the remaining r.h.s. */
i__2 = j;
z__1.r = -rhs[i__2].r, z__1.i = -rhs[i__2].i;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *n - j;
zaxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
&c__1);
/* L10: */
}
/* Solve for U- part, lockahead for RHS(N) = +-1. This is not done */
/* In BSOLVE and will hopefully give us a better estimate because */
/* any ill-conditioning of the original matrix is transfered to U */
/* and not to L. U(N, N) is an approximation to sigma_min(LU). */
i__1 = *n - 1;
zcopy_(&i__1, &rhs[1], &c__1, work, &c__1);
i__1 = *n - 1;
i__2 = *n;
z__1.r = rhs[i__2].r + 1., z__1.i = rhs[i__2].i + 0.;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = *n;
i__2 = *n;
z__1.r = rhs[i__2].r - 1., z__1.i = rhs[i__2].i - 0.;
rhs[i__1].r = z__1.r, rhs[i__1].i = z__1.i;
splus = 0.;
sminu = 0.;
for (i__ = *n; i__ >= 1; --i__) {
z_div(&z__1, &c_b1, &z__[i__ + i__ * z_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
i__1 = i__ - 1;
i__2 = i__ - 1;
z__1.r = work[i__2].r * temp.r - work[i__2].i * temp.i, z__1.i =
work[i__2].r * temp.i + work[i__2].i * temp.r;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = i__;
i__2 = i__;
z__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, z__1.i =
rhs[i__2].r * temp.i + rhs[i__2].i * temp.r;
rhs[i__1].r = z__1.r, rhs[i__1].i = z__1.i;
i__1 = *n;
for (k = i__ + 1; k <= i__1; ++k) {
i__2 = i__ - 1;
i__3 = i__ - 1;
i__4 = k - 1;
i__5 = i__ + k * z_dim1;
z__3.r = z__[i__5].r * temp.r - z__[i__5].i * temp.i, z__3.i =
z__[i__5].r * temp.i + z__[i__5].i * temp.r;
z__2.r = work[i__4].r * z__3.r - work[i__4].i * z__3.i,
z__2.i = work[i__4].r * z__3.i + work[i__4].i *
z__3.r;
z__1.r = work[i__3].r - z__2.r, z__1.i = work[i__3].i -
z__2.i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
i__2 = i__;
i__3 = i__;
i__4 = k;
i__5 = i__ + k * z_dim1;
z__3.r = z__[i__5].r * temp.r - z__[i__5].i * temp.i, z__3.i =
z__[i__5].r * temp.i + z__[i__5].i * temp.r;
z__2.r = rhs[i__4].r * z__3.r - rhs[i__4].i * z__3.i, z__2.i =
rhs[i__4].r * z__3.i + rhs[i__4].i * z__3.r;
z__1.r = rhs[i__3].r - z__2.r, z__1.i = rhs[i__3].i - z__2.i;
rhs[i__2].r = z__1.r, rhs[i__2].i = z__1.i;
/* L20: */
}
splus += z_abs(&work[i__ - 1]);
sminu += z_abs(&rhs[i__]);
/* L30: */
}
if (splus > sminu) {
zcopy_(n, work, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
i__1 = *n - 1;
zlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
zlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
return 0;
}
/* ENTRY IJOB = 2 */
/* Compute approximate nullvector XM of Z */
zgecon_("I", n, &z__[z_offset], ldz, &c_b24, &rtemp, work, rwork, &info);
zcopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
i__1 = *n - 1;
zlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
zdotc_(&z__3, n, xm, &c__1, xm, &c__1);
z_sqrt(&z__2, &z__3);
z_div(&z__1, &c_b1, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
zscal_(n, &temp, xm, &c__1);
zcopy_(n, xm, &c__1, xp, &c__1);
zaxpy_(n, &c_b1, &rhs[1], &c__1, xp, &c__1);
z__1.r = -1., z__1.i = -0.;
zaxpy_(n, &z__1, xm, &c__1, &rhs[1], &c__1);
zgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &scale);
zgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &scale);
if (dzasum_(n, xp, &c__1) > dzasum_(n, &rhs[1], &c__1)) {
zcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Compute the sum of squares */
zlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
return 0;
/* End of ZLATDF */
} /* zlatdf_ */
int ztgsy2_(char *trans, int *ijob, int *m, int *
n, doublecomplex *a, int *lda, doublecomplex *b, int *ldb,
doublecomplex *c__, int *ldc, doublecomplex *d__, int *ldd,
doublecomplex *e, int *lde, doublecomplex *f, int *ldf,
double *scale, double *rdsum, double *rdscal, int *
info)
{
/* System generated locals */
int a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
i__4;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
int i__, j, k;
doublecomplex z__[4] /* was [2][2] */, rhs[2];
int ierr, ipiv[2], jpiv[2];
doublecomplex alpha;
extern int lsame_(char *, char *);
extern int zscal_(int *, doublecomplex *,
doublecomplex *, int *), zaxpy_(int *, doublecomplex *,
doublecomplex *, int *, doublecomplex *, int *), zgesc2_(
int *, doublecomplex *, int *, doublecomplex *, int *,
int *, double *), zgetc2_(int *, doublecomplex *,
int *, int *, int *, int *);
double scaloc;
extern int xerbla_(char *, int *), zlatdf_(
int *, int *, doublecomplex *, int *, doublecomplex *,
double *, double *, int *, int *);
int notran;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTGSY2 solves the generalized Sylvester equation */
/* A * R - L * B = scale * C (1) */
/* D * R - L * E = scale * F */
/* using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, */
/* (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, */
/* N-by-N and M-by-N, respectively. A, B, D and E are upper triangular */
/* (i.e., (A,D) and (B,E) in generalized Schur form). */
/* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */
/* scaling factor chosen to avoid overflow. */
/* In matrix notation solving equation (1) corresponds to solve */
/* Zx = scale * b, where Z is defined as */
/* Z = [ kron(In, A) -kron(B', Im) ] (2) */
/* [ kron(In, D) -kron(E', Im) ], */
/* Ik is the identity matrix of size k and X' is the transpose of X. */
/* kron(X, Y) is the Kronecker product between the matrices X and Y. */
/* If TRANS = 'C', y in the conjugate transposed system Z'y = scale*b */
/* is solved for, which is equivalent to solve for R and L in */
/* A' * R + D' * L = scale * C (3) */
/* R * B' + L * E' = scale * -F */
/* This case is used to compute an estimate of Dif[(A, D), (B, E)] = */
/* = sigma_MIN(Z) using reverse communicaton with ZLACON. */
/* ZTGSY2 also (IJOB >= 1) contributes to the computation in ZTGSYL */
/* of an upper bound on the separation between to matrix pairs. Then */
/* the input (A, D), (B, E) are sub-pencils of two matrix pairs in */
/* ZTGSYL. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* = 'N', solve the generalized Sylvester equation (1). */
/* = 'T': solve the 'transposed' system (3). */
/* IJOB (input) INTEGER */
/* Specifies what kind of functionality to be performed. */
/* =0: solve (1) only. */
/* =1: A contribution from this subsystem to a Frobenius */
/* norm-based estimate of the separation between two matrix */
/* pairs is computed. (look ahead strategy is used). */
/* =2: A contribution from this subsystem to a Frobenius */
/* norm-based estimate of the separation between two matrix */
/* pairs is computed. (DGECON on sub-systems is used.) */
/* Not referenced if TRANS = 'T'. */
/* M (input) INTEGER */
/* On entry, M specifies the order of A and D, and the row */
/* dimension of C, F, R and L. */
/* N (input) INTEGER */
/* On entry, N specifies the order of B and E, and the column */
/* dimension of C, F, R and L. */
/* A (input) COMPLEX*16 array, dimension (LDA, M) */
/* On entry, A contains an upper triangular matrix. */
/* LDA (input) INTEGER */
/* The leading dimension of the matrix A. LDA >= MAX(1, M). */
/* B (input) COMPLEX*16 array, dimension (LDB, N) */
/* On entry, B contains an upper triangular matrix. */
/* LDB (input) INTEGER */
/* The leading dimension of the matrix B. LDB >= MAX(1, N). */
/* C (input/output) COMPLEX*16 array, dimension (LDC, N) */
/* On entry, C contains the right-hand-side of the first matrix */
/* equation in (1). */
/* On exit, if IJOB = 0, C has been overwritten by the solution */
/* R. */
/* LDC (input) INTEGER */
/* The leading dimension of the matrix C. LDC >= MAX(1, M). */
/* D (input) COMPLEX*16 array, dimension (LDD, M) */
/* On entry, D contains an upper triangular matrix. */
/* LDD (input) INTEGER */
/* The leading dimension of the matrix D. LDD >= MAX(1, M). */
/* E (input) COMPLEX*16 array, dimension (LDE, N) */
/* On entry, E contains an upper triangular matrix. */
/* LDE (input) INTEGER */
/* The leading dimension of the matrix E. LDE >= MAX(1, N). */
/* F (input/output) COMPLEX*16 array, dimension (LDF, N) */
/* On entry, F contains the right-hand-side of the second matrix */
/* equation in (1). */
/* On exit, if IJOB = 0, F has been overwritten by the solution */
/* L. */
/* LDF (input) INTEGER */
/* The leading dimension of the matrix F. LDF >= MAX(1, M). */
/* SCALE (output) DOUBLE PRECISION */
/* On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions */
/* R and L (C and F on entry) will hold the solutions to a */
/* slightly perturbed system but the input matrices A, B, D and */
/* E have not been changed. If SCALE = 0, R and L will hold the */
/* solutions to the homogeneous system with C = F = 0. */
/* Normally, SCALE = 1. */
/* RDSUM (input/output) DOUBLE PRECISION */
/* On entry, the sum of squares of computed contributions to */
/* the Dif-estimate under computation by ZTGSYL, where the */
/* scaling factor RDSCAL (see below) has been factored out. */
/* On exit, the corresponding sum of squares updated with the */
/* contributions from the current sub-system. */
/* If TRANS = 'T' RDSUM is not touched. */
/* NOTE: RDSUM only makes sense when ZTGSY2 is called by */
/* ZTGSYL. */
/* RDSCAL (input/output) DOUBLE PRECISION */
/* On entry, scaling factor used to prevent overflow in RDSUM. */
/* On exit, RDSCAL is updated w.r.t. the current contributions */
/* in RDSUM. */
/* If TRANS = 'T', RDSCAL is not touched. */
/* NOTE: RDSCAL only makes sense when ZTGSY2 is called by */
/* ZTGSYL. */
/* INFO (output) INTEGER */
/* On exit, if INFO is set to */
/* =0: Successful exit */
/* <0: If INFO = -i, input argument number i is illegal. */
/* >0: The matrix pairs (A, D) and (B, E) have common or very */
/* close eigenvalues. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
d_dim1 = *ldd;
d_offset = 1 + d_dim1;
d__ -= d_offset;
e_dim1 = *lde;
e_offset = 1 + e_dim1;
e -= e_offset;
f_dim1 = *ldf;
f_offset = 1 + f_dim1;
f -= f_offset;
/* Function Body */
*info = 0;
ierr = 0;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "C")) {
*info = -1;
} else if (notran) {
if (*ijob < 0 || *ijob > 2) {
*info = -2;
}
}
if (*info == 0) {
if (*m <= 0) {
*info = -3;
} else if (*n <= 0) {
*info = -4;
} else if (*lda < MAX(1,*m)) {
*info = -5;
} else if (*ldb < MAX(1,*n)) {
*info = -8;
} else if (*ldc < MAX(1,*m)) {
*info = -10;
} else if (*ldd < MAX(1,*m)) {
*info = -12;
} else if (*lde < MAX(1,*n)) {
*info = -14;
} else if (*ldf < MAX(1,*m)) {
*info = -16;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTGSY2", &i__1);
return 0;
}
if (notran) {
/* Solve (I, J) - system */
/* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
/* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
/* for I = M, M - 1, ..., 1; J = 1, 2, ..., N */
*scale = 1.;
scaloc = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
/* Build 2 by 2 system */
i__2 = i__ + i__ * a_dim1;
z__[0].r = a[i__2].r, z__[0].i = a[i__2].i;
i__2 = i__ + i__ * d_dim1;
z__[1].r = d__[i__2].r, z__[1].i = d__[i__2].i;
i__2 = j + j * b_dim1;
z__1.r = -b[i__2].r, z__1.i = -b[i__2].i;
z__[2].r = z__1.r, z__[2].i = z__1.i;
i__2 = j + j * e_dim1;
z__1.r = -e[i__2].r, z__1.i = -e[i__2].i;
z__[3].r = z__1.r, z__[3].i = z__1.i;
/* Set up right hand side(s) */
i__2 = i__ + j * c_dim1;
rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i;
i__2 = i__ + j * f_dim1;
rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i;
/* Solve Z * x = RHS */
zgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
if (*ijob == 0) {
zgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
z__1.r = scaloc, z__1.i = 0.;
zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1);
z__1.r = scaloc, z__1.i = 0.;
zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1);
/* L10: */
}
*scale *= scaloc;
}
} else {
zlatdf_(ijob, &c__2, z__, &c__2, rhs, rdsum, rdscal, ipiv,
jpiv);
}
/* Unpack solution vector(s) */
i__2 = i__ + j * c_dim1;
c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i;
i__2 = i__ + j * f_dim1;
f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i;
/* Substitute R(I, J) and L(I, J) into remaining equation. */
if (i__ > 1) {
z__1.r = -rhs[0].r, z__1.i = -rhs[0].i;
alpha.r = z__1.r, alpha.i = z__1.i;
i__2 = i__ - 1;
zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &c__[j
* c_dim1 + 1], &c__1);
i__2 = i__ - 1;
zaxpy_(&i__2, &alpha, &d__[i__ * d_dim1 + 1], &c__1, &f[j
* f_dim1 + 1], &c__1);
}
if (j < *n) {
i__2 = *n - j;
zaxpy_(&i__2, &rhs[1], &b[j + (j + 1) * b_dim1], ldb, &
c__[i__ + (j + 1) * c_dim1], ldc);
i__2 = *n - j;
zaxpy_(&i__2, &rhs[1], &e[j + (j + 1) * e_dim1], lde, &f[
i__ + (j + 1) * f_dim1], ldf);
}
/* L20: */
}
/* L30: */
}
} else {
/* Solve transposed (I, J) - system: */
/* A(I, I)' * R(I, J) + D(I, I)' * L(J, J) = C(I, J) */
/* R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */
/* for I = 1, 2, ..., M, J = N, N - 1, ..., 1 */
*scale = 1.;
scaloc = 1.;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
for (j = *n; j >= 1; --j) {
/* Build 2 by 2 system Z' */
d_cnjg(&z__1, &a[i__ + i__ * a_dim1]);
z__[0].r = z__1.r, z__[0].i = z__1.i;
d_cnjg(&z__2, &b[j + j * b_dim1]);
z__1.r = -z__2.r, z__1.i = -z__2.i;
z__[1].r = z__1.r, z__[1].i = z__1.i;
d_cnjg(&z__1, &d__[i__ + i__ * d_dim1]);
z__[2].r = z__1.r, z__[2].i = z__1.i;
d_cnjg(&z__2, &e[j + j * e_dim1]);
z__1.r = -z__2.r, z__1.i = -z__2.i;
z__[3].r = z__1.r, z__[3].i = z__1.i;
/* Set up right hand side(s) */
i__2 = i__ + j * c_dim1;
rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i;
i__2 = i__ + j * f_dim1;
rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i;
/* Solve Z' * x = RHS */
zgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr);
if (ierr > 0) {
*info = ierr;
}
zgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc);
if (scaloc != 1.) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
z__1.r = scaloc, z__1.i = 0.;
zscal_(m, &z__1, &c__[k * c_dim1 + 1], &c__1);
z__1.r = scaloc, z__1.i = 0.;
zscal_(m, &z__1, &f[k * f_dim1 + 1], &c__1);
/* L40: */
}
*scale *= scaloc;
}
/* Unpack solution vector(s) */
i__2 = i__ + j * c_dim1;
c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i;
i__2 = i__ + j * f_dim1;
f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i;
/* Substitute R(I, J) and L(I, J) into remaining equation. */
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = i__ + k * f_dim1;
i__4 = i__ + k * f_dim1;
d_cnjg(&z__4, &b[k + j * b_dim1]);
z__3.r = rhs[0].r * z__4.r - rhs[0].i * z__4.i, z__3.i =
rhs[0].r * z__4.i + rhs[0].i * z__4.r;
z__2.r = f[i__4].r + z__3.r, z__2.i = f[i__4].i + z__3.i;
d_cnjg(&z__6, &e[k + j * e_dim1]);
z__5.r = rhs[1].r * z__6.r - rhs[1].i * z__6.i, z__5.i =
rhs[1].r * z__6.i + rhs[1].i * z__6.r;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
f[i__3].r = z__1.r, f[i__3].i = z__1.i;
/* L50: */
}
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
i__3 = k + j * c_dim1;
i__4 = k + j * c_dim1;
d_cnjg(&z__4, &a[i__ + k * a_dim1]);
z__3.r = z__4.r * rhs[0].r - z__4.i * rhs[0].i, z__3.i =
z__4.r * rhs[0].i + z__4.i * rhs[0].r;
z__2.r = c__[i__4].r - z__3.r, z__2.i = c__[i__4].i -
z__3.i;
d_cnjg(&z__6, &d__[i__ + k * d_dim1]);
z__5.r = z__6.r * rhs[1].r - z__6.i * rhs[1].i, z__5.i =
z__6.r * rhs[1].i + z__6.i * rhs[1].r;
z__1.r = z__2.r - z__5.r, z__1.i = z__2.i - z__5.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L60: */
}
/* L70: */
}
/* L80: */
}
}
return 0;
/* End of ZTGSY2 */
} /* ztgsy2_ */