#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int stgex2_(logical *wantq, logical *wantz, integer *n, real *a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real * z__, integer *ldz, integer *j1, integer *n1, integer *n2, real *work, integer *lwork, integer *info) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation. (A, B) must be in generalized real Schur canonical form (as returned by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper triangular. Optionally, the matrices Q and Z of generalized Schur vectors are updated. Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' Arguments ========= WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix Q; .FALSE.: do not update Q. WANTZ (input) LOGICAL .TRUE. : update the right transformation matrix Z; .FALSE.: do not update Z. N (input) INTEGER The order of the matrices A and B. N >= 0. A (input/output) REAL arrays, dimensions (LDA,N) On entry, the matrix A in the pair (A, B). On exit, the updated matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) REAL arrays, dimensions (LDB,N) On entry, the matrix B in the pair (A, B). On exit, the updated matrix B. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). Q (input/output) REAL array, dimension (LDZ,N) On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE.. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N. Z (input/output) REAL array, dimension (LDZ,N) On entry, if WANTZ =.TRUE., the orthogonal matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE.. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N. J1 (input) INTEGER The index to the first block (A11, B11). 1 <= J1 <= N. N1 (input) INTEGER The order of the first block (A11, B11). N1 = 0, 1 or 2. N2 (input) INTEGER The order of the second block (A22, B22). N2 = 0, 1 or 2. WORK (workspace) REAL array, dimension (MAX(1,LWORK)). LWORK (input) INTEGER The dimension of the array WORK. LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ) INFO (output) INTEGER =0: Successful exit >0: If INFO = 1, the transformed matrix (A, B) would be too far from generalized Schur form; the blocks are not swapped and (A, B) and (Q, Z) are unchanged. The problem of swapping is too ill-conditioned. <0: If INFO = -16: LWORK is too small. Appropriate value for LWORK is returned in WORK(1). Further Details =============== Based on contributions by Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden. In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details. [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the Generalized Real Schur Form of a Regular Matrix Pair (A, B), in M.S. Moonen et al (eds), Linear Algebra for Large Scale and Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF - 94.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. To appear in Numerical Algorithms, 1996. ===================================================================== Replaced various illegal calls to SCOPY by calls to SLASET, or by DO loops. Sven Hammarling, 1/5/02. Parameter adjustments */ /* Table of constant values */ static integer c__4 = 4; static real c_b5 = 0.f; static integer c__1 = 1; static integer c__2 = 2; static real c_b42 = 1.f; static real c_b48 = -1.f; static integer c__0 = 0; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, i__2; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static real f, g; static integer i__, m; static real s[16] /* was [4][4] */, t[16] /* was [4][4] */, be[2], ai[2] , ar[2], sa, sb, li[16] /* was [4][4] */, ir[16] /* was [4][4] */, ss, ws, eps; static logical weak; static real ddum; static integer idum; static real taul[4], dsum, taur[4], scpy[16] /* was [4][4] */, tcpy[16] /* was [4][4] */; extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, integer *, real *, real *); static real scale, bqra21, brqa21; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static real licop[16] /* was [4][4] */; static integer linfo; extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static real ircop[16] /* was [4][4] */, dnorm; static integer iwork[4]; extern /* Subroutine */ int slagv2_(real *, integer *, real *, integer *, real *, real *, real *, real *, real *, real *, real *), sgeqr2_( integer *, integer *, real *, integer *, real *, real *, integer * ), sgerq2_(integer *, integer *, real *, integer *, real *, real * , integer *), sorg2r_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *), sorgr2_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *), sorm2r_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *), sormr2_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *); static real dscale; extern /* Subroutine */ int stgsy2_(char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real * , integer *, real *, integer *, real *, integer *, real *, real *, real *, integer *, integer *, integer *); extern doublereal slamch_(char *); extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slartg_(real *, real *, real *, real *, real *); static real thresh; extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slassq_(integer *, real *, integer *, real *, real *); static real smlnum; static logical strong; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; /* Function Body */ *info = 0; /* Quick return if possible */ if (*n <= 1 || *n1 <= 0 || *n2 <= 0) { return 0; } if (*n1 > *n || *j1 + *n1 > *n) { return 0; } m = *n1 + *n2; /* Computing MAX */ i__1 = *n * m, i__2 = m * m << 1; if (*lwork < max(i__1,i__2)) { *info = -16; /* Computing MAX */ i__1 = *n * m, i__2 = m * m << 1; work[1] = (real) max(i__1,i__2); return 0; } weak = FALSE_; strong = FALSE_; /* Make a local copy of selected block */ slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, li, &c__4); slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, ir, &c__4); slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__4); slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__4); /* Compute threshold for testing acceptance of swapping. */ eps = slamch_("P"); smlnum = slamch_("S") / eps; dscale = 0.f; dsum = 1.f; slacpy_("Full", &m, &m, s, &c__4, &work[1], &m); i__1 = m * m; slassq_(&i__1, &work[1], &c__1, &dscale, &dsum); slacpy_("Full", &m, &m, t, &c__4, &work[1], &m); i__1 = m * m; slassq_(&i__1, &work[1], &c__1, &dscale, &dsum); dnorm = dscale * sqrt(dsum); /* Computing MAX */ r__1 = eps * 10.f * dnorm; thresh = dmax(r__1,smlnum); if (m == 2) { /* CASE 1: Swap 1-by-1 and 1-by-1 blocks. Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks using Givens rotations and perform the swap tentatively. */ f = s[5] * t[0] - t[5] * s[0]; g = s[5] * t[4] - t[5] * s[4]; sb = dabs(t[5]); sa = dabs(s[5]); slartg_(&f, &g, &ir[4], ir, &ddum); ir[1] = -ir[4]; ir[5] = ir[0]; srot_(&c__2, s, &c__1, &s[4], &c__1, ir, &ir[1]); srot_(&c__2, t, &c__1, &t[4], &c__1, ir, &ir[1]); if (sa >= sb) { slartg_(s, &s[1], li, &li[1], &ddum); } else { slartg_(t, &t[1], li, &li[1], &ddum); } srot_(&c__2, s, &c__4, &s[1], &c__4, li, &li[1]); srot_(&c__2, t, &c__4, &t[1], &c__4, li, &li[1]); li[5] = li[0]; li[4] = -li[1]; /* Weak stability test: |S21| + |T21| <= O(EPS * F-norm((S, T))) */ ws = dabs(s[1]) + dabs(t[1]); weak = ws <= thresh; if (! weak) { goto L70; } if (TRUE_) { /* Strong stability test: F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B))) */ slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m + 1], &m); sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, & work[1], &m); sgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, & c_b42, &work[m * m + 1], &m); dscale = 0.f; dsum = 1.f; i__1 = m * m; slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum); slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m + 1], &m); sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, & work[1], &m); sgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, & c_b42, &work[m * m + 1], &m); i__1 = m * m; slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum); ss = dscale * sqrt(dsum); strong = ss <= thresh; if (! strong) { goto L70; } } /* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */ i__1 = *j1 + 1; srot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1], &c__1, ir, &ir[1]); i__1 = *j1 + 1; srot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1], &c__1, ir, &ir[1]); i__1 = *n - *j1 + 1; srot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1], lda, li, &li[1]); i__1 = *n - *j1 + 1; srot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1], ldb, li, &li[1]); /* Set N1-by-N2 (2,1) - blocks to ZERO. */ a[*j1 + 1 + *j1 * a_dim1] = 0.f; b[*j1 + 1 + *j1 * b_dim1] = 0.f; /* Accumulate transformations into Q and Z if requested. */ if (*wantz) { srot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 + 1], &c__1, ir, &ir[1]); } if (*wantq) { srot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1], &c__1, li, &li[1]); } /* Exit with INFO = 0 if swap was successfully performed. */ return 0; } else { /* CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 and 2-by-2 blocks. Solve the generalized Sylvester equation S11 * R - L * S22 = SCALE * S12 T11 * R - L * T22 = SCALE * T12 for R and L. Solutions in LI and IR. */ slacpy_("Full", n1, n2, &t[(*n1 + 1 << 2) - 4], &c__4, li, &c__4); slacpy_("Full", n1, n2, &s[(*n1 + 1 << 2) - 4], &c__4, &ir[*n2 + 1 + ( *n1 + 1 << 2) - 5], &c__4); stgsy2_("N", &c__0, n1, n2, s, &c__4, &s[*n1 + 1 + (*n1 + 1 << 2) - 5] , &c__4, &ir[*n2 + 1 + (*n1 + 1 << 2) - 5], &c__4, t, &c__4, & t[*n1 + 1 + (*n1 + 1 << 2) - 5], &c__4, li, &c__4, &scale, & dsum, &dscale, iwork, &idum, &linfo); /* Compute orthogonal matrix QL: QL' * LI = [ TL ] [ 0 ] where LI = [ -L ] [ SCALE * identity(N2) ] */ i__1 = *n2; for (i__ = 1; i__ <= i__1; ++i__) { sscal_(n1, &c_b48, &li[(i__ << 2) - 4], &c__1); li[*n1 + i__ + (i__ << 2) - 5] = scale; /* L10: */ } sgeqr2_(&m, n2, li, &c__4, taul, &work[1], &linfo); if (linfo != 0) { goto L70; } sorg2r_(&m, &m, n2, li, &c__4, taul, &work[1], &linfo); if (linfo != 0) { goto L70; } /* Compute orthogonal matrix RQ: IR * RQ' = [ 0 TR], where IR = [ SCALE * identity(N1), R ] */ i__1 = *n1; for (i__ = 1; i__ <= i__1; ++i__) { ir[*n2 + i__ + (i__ << 2) - 5] = scale; /* L20: */ } sgerq2_(n1, &m, &ir[*n2], &c__4, taur, &work[1], &linfo); if (linfo != 0) { goto L70; } sorgr2_(&m, &m, n1, ir, &c__4, taur, &work[1], &linfo); if (linfo != 0) { goto L70; } /* Perform the swapping tentatively: */ sgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, & work[1], &m); sgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5, s, &c__4); sgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, & work[1], &m); sgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5, t, &c__4); slacpy_("F", &m, &m, s, &c__4, scpy, &c__4); slacpy_("F", &m, &m, t, &c__4, tcpy, &c__4); slacpy_("F", &m, &m, ir, &c__4, ircop, &c__4); slacpy_("F", &m, &m, li, &c__4, licop, &c__4); /* Triangularize the B-part by an RQ factorization. Apply transformation (from left) to A-part, giving S. */ sgerq2_(&m, &m, t, &c__4, taur, &work[1], &linfo); if (linfo != 0) { goto L70; } sormr2_("R", "T", &m, &m, &m, t, &c__4, taur, s, &c__4, &work[1], & linfo); if (linfo != 0) { goto L70; } sormr2_("L", "N", &m, &m, &m, t, &c__4, taur, ir, &c__4, &work[1], & linfo); if (linfo != 0) { goto L70; } /* Compute F-norm(S21) in BRQA21. (T21 is 0.) */ dscale = 0.f; dsum = 1.f; i__1 = *n2; for (i__ = 1; i__ <= i__1; ++i__) { slassq_(n1, &s[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &dsum); /* L30: */ } brqa21 = dscale * sqrt(dsum); /* Triangularize the B-part by a QR factorization. Apply transformation (from right) to A-part, giving S. */ sgeqr2_(&m, &m, tcpy, &c__4, taul, &work[1], &linfo); if (linfo != 0) { goto L70; } sorm2r_("L", "T", &m, &m, &m, tcpy, &c__4, taul, scpy, &c__4, &work[1] , info); sorm2r_("R", "N", &m, &m, &m, tcpy, &c__4, taul, licop, &c__4, &work[ 1], info); if (linfo != 0) { goto L70; } /* Compute F-norm(S21) in BQRA21. (T21 is 0.) */ dscale = 0.f; dsum = 1.f; i__1 = *n2; for (i__ = 1; i__ <= i__1; ++i__) { slassq_(n1, &scpy[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, & dsum); /* L40: */ } bqra21 = dscale * sqrt(dsum); /* Decide which method to use. Weak stability test: F-norm(S21) <= O(EPS * F-norm((S, T))) */ if (bqra21 <= brqa21 && bqra21 <= thresh) { slacpy_("F", &m, &m, scpy, &c__4, s, &c__4); slacpy_("F", &m, &m, tcpy, &c__4, t, &c__4); slacpy_("F", &m, &m, ircop, &c__4, ir, &c__4); slacpy_("F", &m, &m, licop, &c__4, li, &c__4); } else if (brqa21 >= thresh) { goto L70; } /* Set lower triangle of B-part to zero */ i__1 = m - 1; i__2 = m - 1; slaset_("Lower", &i__1, &i__2, &c_b5, &c_b5, &t[1], &c__4); if (TRUE_) { /* Strong stability test: F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B))) */ slacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m + 1], &m); sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, & work[1], &m); sgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, & c_b42, &work[m * m + 1], &m); dscale = 0.f; dsum = 1.f; i__1 = m * m; slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum); slacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m + 1], &m); sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, & work[1], &m); sgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, & c_b42, &work[m * m + 1], &m); i__1 = m * m; slassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum); ss = dscale * sqrt(dsum); strong = ss <= thresh; if (! strong) { goto L70; } } /* If the swap is accepted ("weakly" and "strongly"), apply the transformations and set N1-by-N2 (2,1)-block to zero. */ slaset_("Full", n1, n2, &c_b5, &c_b5, &s[*n2], &c__4); /* copy back M-by-M diagonal block starting at index J1 of (A, B) */ slacpy_("F", &m, &m, s, &c__4, &a[*j1 + *j1 * a_dim1], lda) ; slacpy_("F", &m, &m, t, &c__4, &b[*j1 + *j1 * b_dim1], ldb) ; slaset_("Full", &c__4, &c__4, &c_b5, &c_b5, t, &c__4); /* Standardize existing 2-by-2 blocks. */ i__1 = m * m; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.f; /* L50: */ } work[1] = 1.f; t[0] = 1.f; idum = *lwork - m * m - 2; if (*n2 > 1) { slagv2_(&a[*j1 + *j1 * a_dim1], lda, &b[*j1 + *j1 * b_dim1], ldb, ar, ai, be, &work[1], &work[2], t, &t[1]); work[m + 1] = -work[2]; work[m + 2] = work[1]; t[*n2 + (*n2 << 2) - 5] = t[0]; t[4] = -t[1]; } work[m * m] = 1.f; t[m + (m << 2) - 5] = 1.f; if (*n1 > 1) { slagv2_(&a[*j1 + *n2 + (*j1 + *n2) * a_dim1], lda, &b[*j1 + *n2 + (*j1 + *n2) * b_dim1], ldb, taur, taul, &work[m * m + 1], &work[*n2 * m + *n2 + 1], &work[*n2 * m + *n2 + 2], &t[* n2 + 1 + (*n2 + 1 << 2) - 5], &t[m + (m - 1 << 2) - 5]); work[m * m] = work[*n2 * m + *n2 + 1]; work[m * m - 1] = -work[*n2 * m + *n2 + 2]; t[m + (m << 2) - 5] = t[*n2 + 1 + (*n2 + 1 << 2) - 5]; t[m - 1 + (m << 2) - 5] = -t[m + (m - 1 << 2) - 5]; } sgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &a[*j1 + (*j1 + * n2) * a_dim1], lda, &c_b5, &work[m * m + 1], n2); slacpy_("Full", n2, n1, &work[m * m + 1], n2, &a[*j1 + (*j1 + *n2) * a_dim1], lda); sgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &b[*j1 + (*j1 + * n2) * b_dim1], ldb, &c_b5, &work[m * m + 1], n2); slacpy_("Full", n2, n1, &work[m * m + 1], n2, &b[*j1 + (*j1 + *n2) * b_dim1], ldb); sgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, &work[1], &m, &c_b5, & work[m * m + 1], &m); slacpy_("Full", &m, &m, &work[m * m + 1], &m, li, &c__4); sgemm_("N", "N", n2, n1, n1, &c_b42, &a[*j1 + (*j1 + *n2) * a_dim1], lda, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1], n2); slacpy_("Full", n2, n1, &work[1], n2, &a[*j1 + (*j1 + *n2) * a_dim1], lda); sgemm_("N", "N", n2, n1, n1, &c_b42, &b[*j1 + (*j1 + *n2) * b_dim1], ldb, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1], n2); slacpy_("Full", n2, n1, &work[1], n2, &b[*j1 + (*j1 + *n2) * b_dim1], ldb); sgemm_("T", "N", &m, &m, &m, &c_b42, ir, &c__4, t, &c__4, &c_b5, & work[1], &m); slacpy_("Full", &m, &m, &work[1], &m, ir, &c__4); /* Accumulate transformations into Q and Z if requested. */ if (*wantq) { sgemm_("N", "N", n, &m, &m, &c_b42, &q[*j1 * q_dim1 + 1], ldq, li, &c__4, &c_b5, &work[1], n); slacpy_("Full", n, &m, &work[1], n, &q[*j1 * q_dim1 + 1], ldq); } if (*wantz) { sgemm_("N", "N", n, &m, &m, &c_b42, &z__[*j1 * z_dim1 + 1], ldz, ir, &c__4, &c_b5, &work[1], n); slacpy_("Full", n, &m, &work[1], n, &z__[*j1 * z_dim1 + 1], ldz); } /* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */ i__ = *j1 + m; if (i__ <= *n) { i__1 = *n - i__ + 1; sgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &a[*j1 + i__ * a_dim1], lda, &c_b5, &work[1], &m); i__1 = *n - i__ + 1; slacpy_("Full", &m, &i__1, &work[1], &m, &a[*j1 + i__ * a_dim1], lda); i__1 = *n - i__ + 1; sgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &b[*j1 + i__ * b_dim1], ldb, &c_b5, &work[1], &m); i__1 = *n - i__ + 1; slacpy_("Full", &m, &i__1, &work[1], &m, &b[*j1 + i__ * b_dim1], ldb); } i__ = *j1 - 1; if (i__ > 0) { sgemm_("N", "N", &i__, &m, &m, &c_b42, &a[*j1 * a_dim1 + 1], lda, ir, &c__4, &c_b5, &work[1], &i__); slacpy_("Full", &i__, &m, &work[1], &i__, &a[*j1 * a_dim1 + 1], lda); sgemm_("N", "N", &i__, &m, &m, &c_b42, &b[*j1 * b_dim1 + 1], ldb, ir, &c__4, &c_b5, &work[1], &i__); slacpy_("Full", &i__, &m, &work[1], &i__, &b[*j1 * b_dim1 + 1], ldb); } /* Exit with INFO = 0 if swap was successfully performed. */ return 0; } /* Exit with INFO = 1 if swap was rejected. */ L70: *info = 1; return 0; /* End of STGEX2 */ } /* stgex2_ */