#include "f2c.h" #include "blaswrap.h" /* 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; /* 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) { /* 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 */ real f, g; integer i__, m; 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; logical weak; real ddum; integer idum; 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 *); real scale, bqra21, brqa21; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); real licop[16] /* was [4][4] */; integer linfo; extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); real ircop[16] /* was [4][4] */, dnorm; 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 *); 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 *); real thresh; extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slassq_(integer *, real *, integer *, real *, real *); real smlnum; logical strong; /* -- LAPACK auxiliary routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* 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. */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ 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_ */