#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dtrsyl_(char *trana, char *tranb, integer *isgn, integer *m, integer *n, doublereal *a, integer *lda, doublereal *b, integer * ldb, doublereal *c__, integer *ldc, doublereal *scale, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= DTRSYL solves the real Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**T, and A and B are both upper quasi- triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X. A and B must be in Schur canonical form (as returned by DHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign. Arguments ========= TRANA (input) CHARACTER*1 Specifies the option op(A): = 'N': op(A) = A (No transpose) = 'T': op(A) = A**T (Transpose) = 'C': op(A) = A**H (Conjugate transpose = Transpose) TRANB (input) CHARACTER*1 Specifies the option op(B): = 'N': op(B) = B (No transpose) = 'T': op(B) = B**T (Transpose) = 'C': op(B) = B**H (Conjugate transpose = Transpose) ISGN (input) INTEGER Specifies the sign in the equation: = +1: solve op(A)*X + X*op(B) = scale*C = -1: solve op(A)*X - X*op(B) = scale*C M (input) INTEGER The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. N (input) INTEGER The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,M) The upper quasi-triangular matrix A, in Schur canonical form. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). B (input) DOUBLE PRECISION array, dimension (LDB,N) The upper quasi-triangular matrix B, in Schur canonical form. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). C (input/output) DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M) SCALE (output) DOUBLE PRECISION The scale factor, scale, set <= 1 to avoid overflow in X. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged). ===================================================================== Decode and Test input parameters Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static logical c_false = FALSE_; static integer c__2 = 2; static doublereal c_b26 = 1.; static doublereal c_b30 = 0.; static logical c_true = TRUE_; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; /* Local variables */ extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); static integer ierr; static doublereal smin, suml, sumr; static integer j, k, l; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static doublereal x[4] /* was [2][2] */; extern logical lsame_(char *, char *); static integer knext, lnext, k1, k2, l1, l2; static doublereal xnorm; extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal * , doublereal *, integer *, doublereal *, doublereal *, integer *), dlasy2_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); static doublereal a11, db; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); static doublereal scaloc; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal bignum; static logical notrna, notrnb; static doublereal smlnum, da11, vec[4] /* was [2][2] */, dum[1], eps, sgn; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] #define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1] #define x_ref(a_1,a_2) x[(a_2)*2 + a_1 - 3] #define vec_ref(a_1,a_2) vec[(a_2)*2 + a_1 - 3] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ notrna = lsame_(trana, "N"); notrnb = lsame_(tranb, "N"); *info = 0; if (! notrna && ! lsame_(trana, "T") && ! lsame_( trana, "C")) { *info = -1; } else if (! notrnb && ! lsame_(tranb, "T") && ! lsame_(tranb, "C")) { *info = -2; } else if (*isgn != 1 && *isgn != -1) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*lda < max(1,*m)) { *info = -7; } else if (*ldb < max(1,*n)) { *info = -9; } else if (*ldc < max(1,*m)) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("DTRSYL", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } /* Set constants to control overflow */ eps = dlamch_("P"); smlnum = dlamch_("S"); bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); smlnum = smlnum * (doublereal) (*m * *n) / eps; bignum = 1. / smlnum; /* Computing MAX */ d__1 = smlnum, d__2 = eps * dlange_("M", m, m, &a[a_offset], lda, dum), d__1 = max(d__1,d__2), d__2 = eps * dlange_("M", n, n, &b[b_offset], ldb, dum); smin = max(d__1,d__2); *scale = 1.; sgn = (doublereal) (*isgn); if (notrna && notrnb) { /* Solve A*X + ISGN*X*B = scale*C. The (K,L)th block of X is determined starting from bottom-left corner column by column by A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) Where M L-1 R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]. I=K+1 J=1 Start column loop (index = L) L1 (L2) : column index of the first (first) row of X(K,L). */ lnext = 1; i__1 = *n; for (l = 1; l <= i__1; ++l) { if (l < lnext) { goto L60; } if (l == *n) { l1 = l; l2 = l; } else { if (b_ref(l + 1, l) != 0.) { l1 = l; l2 = l + 1; lnext = l + 2; } else { l1 = l; l2 = l; lnext = l + 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L). */ knext = *m; for (k = *m; k >= 1; --k) { if (k > knext) { goto L50; } if (k == 1) { k1 = k; k2 = k; } else { if (a_ref(k, k - 1) != 0.) { k1 = k - 1; k2 = k; knext = k - 2; } else { k1 = k; k2 = k; knext = k - 1; } } if (l1 == l2 && k1 == k2) { /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; i__4 = *m - k1; suml = ddot_(&i__4, &a_ref(k1, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l1), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); scaloc = 1.; a11 = a_ref(k1, k1) + sgn * b_ref(l1, l1); da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = (d__1 = vec_ref(1, 1), abs(d__1)); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x_ref(1, 1) = vec_ref(1, 1) * scaloc / a11; if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L10: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); } else if (l1 == l2 && k1 != k2) { /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; i__4 = *m - k2; suml = ddot_(&i__4, &a_ref(k1, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l1), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; i__4 = *m - k2; suml = ddot_(&i__4, &a_ref(k2, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l1), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k2, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); d__1 = -sgn * b_ref(l1, l1); dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a_ref(k1, k1), lda, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L20: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k2, l1) = x_ref(2, 1); } else if (l1 != l2 && k1 == k2) { /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; i__4 = *m - k1; suml = ddot_(&i__4, &a_ref(k1, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l1), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = sgn * (c___ref(k1, l1) - (suml + sgn * sumr)); /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; i__4 = *m - k1; suml = ddot_(&i__4, &a_ref(k1, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l2), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k1, 1), ldc, &b_ref(1, l2), & c__1); vec_ref(2, 1) = sgn * (c___ref(k1, l2) - (suml + sgn * sumr)); d__1 = -sgn * a_ref(k1, k1); dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b_ref(l1, l1), ldb, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L30: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(2, 1); } else if (l1 != l2 && k1 != k2) { /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; i__4 = *m - k2; suml = ddot_(&i__4, &a_ref(k1, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l1), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; i__4 = *m - k2; suml = ddot_(&i__4, &a_ref(k1, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l2), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k1, 1), ldc, &b_ref(1, l2), & c__1); vec_ref(1, 2) = c___ref(k1, l2) - (suml + sgn * sumr); /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; i__4 = *m - k2; suml = ddot_(&i__4, &a_ref(k2, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l1), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k2, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; i__4 = *m - k2; suml = ddot_(&i__4, &a_ref(k2, min(i__2,*m)), lda, & c___ref(min(i__3,*m), l2), &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c___ref(k2, 1), ldc, &b_ref(1, l2), & c__1); vec_ref(2, 2) = c___ref(k2, l2) - (suml + sgn * sumr); dlasy2_(&c_false, &c_false, isgn, &c__2, &c__2, &a_ref(k1, k1), lda, &b_ref(l1, l1), ldb, vec, &c__2, & scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L40: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(1, 2); c___ref(k2, l1) = x_ref(2, 1); c___ref(k2, l2) = x_ref(2, 2); } L50: ; } L60: ; } } else if (! notrna && notrnb) { /* Solve A' *X + ISGN*X*B = scale*C. The (K,L)th block of X is determined starting from upper-left corner column by column by A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) Where K-1 L-1 R(K,L) = SUM [A(I,K)'*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)] I=1 J=1 Start column loop (index = L) L1 (L2): column index of the first (last) row of X(K,L) */ lnext = 1; i__1 = *n; for (l = 1; l <= i__1; ++l) { if (l < lnext) { goto L120; } if (l == *n) { l1 = l; l2 = l; } else { if (b_ref(l + 1, l) != 0.) { l1 = l; l2 = l + 1; lnext = l + 2; } else { l1 = l; l2 = l; lnext = l + 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L) */ knext = 1; i__2 = *m; for (k = 1; k <= i__2; ++k) { if (k < knext) { goto L110; } if (k == *m) { k1 = k; k2 = k; } else { if (a_ref(k + 1, k) != 0.) { k1 = k; k2 = k + 1; knext = k + 2; } else { k1 = k; k2 = k; knext = k + 1; } } if (l1 == l2 && k1 == k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); scaloc = 1.; a11 = a_ref(k1, k1) + sgn * b_ref(l1, l1); da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = (d__1 = vec_ref(1, 1), abs(d__1)); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x_ref(1, 1) = vec_ref(1, 1) * scaloc / a11; if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L70: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); } else if (l1 == l2 && k1 != k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k2), &c__1, &c___ref(1, l1), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k2, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); d__1 = -sgn * b_ref(l1, l1); dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a_ref(k1, k1), lda, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L80: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k2, l1) = x_ref(2, 1); } else if (l1 != l2 && k1 == k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = sgn * (c___ref(k1, l1) - (suml + sgn * sumr)); i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k1), &c__1, &c___ref(1, l2), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k1, 1), ldc, &b_ref(1, l2), & c__1); vec_ref(2, 1) = sgn * (c___ref(k1, l2) - (suml + sgn * sumr)); d__1 = -sgn * a_ref(k1, k1); dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b_ref(l1, l1), ldb, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L90: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(2, 1); } else if (l1 != l2 && k1 != k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k1, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k1), &c__1, &c___ref(1, l2), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k1, 1), ldc, &b_ref(1, l2), & c__1); vec_ref(1, 2) = c___ref(k1, l2) - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k2), &c__1, &c___ref(1, l1), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k2, 1), ldc, &b_ref(1, l1), & c__1); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a_ref(1, k2), &c__1, &c___ref(1, l2), &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c___ref(k2, 1), ldc, &b_ref(1, l2), & c__1); vec_ref(2, 2) = c___ref(k2, l2) - (suml + sgn * sumr); dlasy2_(&c_true, &c_false, isgn, &c__2, &c__2, &a_ref(k1, k1), lda, &b_ref(l1, l1), ldb, vec, &c__2, & scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L100: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(1, 2); c___ref(k2, l1) = x_ref(2, 1); c___ref(k2, l2) = x_ref(2, 2); } L110: ; } L120: ; } } else if (! notrna && ! notrnb) { /* Solve A'*X + ISGN*X*B' = scale*C. The (K,L)th block of X is determined starting from top-right corner column by column by A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L) Where K-1 N R(K,L) = SUM [A(I,K)'*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)']. I=1 J=L+1 Start column loop (index = L) L1 (L2): column index of the first (last) row of X(K,L) */ lnext = *n; for (l = *n; l >= 1; --l) { if (l > lnext) { goto L180; } if (l == 1) { l1 = l; l2 = l; } else { if (b_ref(l, l - 1) != 0.) { l1 = l - 1; l2 = l; lnext = l - 2; } else { l1 = l; l2 = l; lnext = l - 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L) */ knext = 1; i__1 = *m; for (k = 1; k <= i__1; ++k) { if (k < knext) { goto L170; } if (k == *m) { k1 = k; k2 = k; } else { if (a_ref(k + 1, k) != 0.) { k1 = k; k2 = k + 1; knext = k + 2; } else { k1 = k; k2 = k; knext = k + 1; } } if (l1 == l2 && k1 == k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); /* Computing MIN */ i__2 = l1 + 1; /* Computing MIN */ i__3 = l1 + 1; i__4 = *n - l1; sumr = ddot_(&i__4, &c___ref(k1, min(i__2,*n)), ldc, & b_ref(l1, min(i__3,*n)), ldb); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); scaloc = 1.; a11 = a_ref(k1, k1) + sgn * b_ref(l1, l1); da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = (d__1 = vec_ref(1, 1), abs(d__1)); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x_ref(1, 1) = vec_ref(1, 1) * scaloc / a11; if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L130: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); } else if (l1 == l2 && k1 != k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k1, min(i__2,*n)), ldc, & b_ref(l1, min(i__3,*n)), ldb); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k2), &c__1, &c___ref(1, l1), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k2, min(i__2,*n)), ldc, & b_ref(l1, min(i__3,*n)), ldb); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); d__1 = -sgn * b_ref(l1, l1); dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a_ref(k1, k1), lda, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L140: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k2, l1) = x_ref(2, 1); } else if (l1 != l2 && k1 == k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k1, min(i__2,*n)), ldc, & b_ref(l1, min(i__3,*n)), ldb); vec_ref(1, 1) = sgn * (c___ref(k1, l1) - (suml + sgn * sumr)); i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k1), &c__1, &c___ref(1, l2), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k1, min(i__2,*n)), ldc, & b_ref(l2, min(i__3,*n)), ldb); vec_ref(2, 1) = sgn * (c___ref(k1, l2) - (suml + sgn * sumr)); d__1 = -sgn * a_ref(k1, k1); dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b_ref(l1, l1), ldb, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L150: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(2, 1); } else if (l1 != l2 && k1 != k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k1), &c__1, &c___ref(1, l1), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k1, min(i__2,*n)), ldc, & b_ref(l1, min(i__3,*n)), ldb); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k1), &c__1, &c___ref(1, l2), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k1, min(i__2,*n)), ldc, & b_ref(l2, min(i__3,*n)), ldb); vec_ref(1, 2) = c___ref(k1, l2) - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k2), &c__1, &c___ref(1, l1), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k2, min(i__2,*n)), ldc, & b_ref(l1, min(i__3,*n)), ldb); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a_ref(1, k2), &c__1, &c___ref(1, l2), &c__1); /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; i__4 = *n - l2; sumr = ddot_(&i__4, &c___ref(k2, min(i__2,*n)), ldc, & b_ref(l2, min(i__3,*n)), ldb); vec_ref(2, 2) = c___ref(k2, l2) - (suml + sgn * sumr); dlasy2_(&c_true, &c_true, isgn, &c__2, &c__2, &a_ref(k1, k1), lda, &b_ref(l1, l1), ldb, vec, &c__2, & scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L160: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(1, 2); c___ref(k2, l1) = x_ref(2, 1); c___ref(k2, l2) = x_ref(2, 2); } L170: ; } L180: ; } } else if (notrna && ! notrnb) { /* Solve A*X + ISGN*X*B' = scale*C. The (K,L)th block of X is determined starting from bottom-right corner column by column by A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L) Where M N R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)']. I=K+1 J=L+1 Start column loop (index = L) L1 (L2): column index of the first (last) row of X(K,L) */ lnext = *n; for (l = *n; l >= 1; --l) { if (l > lnext) { goto L240; } if (l == 1) { l1 = l; l2 = l; } else { if (b_ref(l, l - 1) != 0.) { l1 = l - 1; l2 = l; lnext = l - 2; } else { l1 = l; l2 = l; lnext = l - 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L) */ knext = *m; for (k = *m; k >= 1; --k) { if (k > knext) { goto L230; } if (k == 1) { k1 = k; k2 = k; } else { if (a_ref(k, k - 1) != 0.) { k1 = k - 1; k2 = k; knext = k - 2; } else { k1 = k; k2 = k; knext = k - 1; } } if (l1 == l2 && k1 == k2) { /* Computing MIN */ i__1 = k1 + 1; /* Computing MIN */ i__2 = k1 + 1; i__3 = *m - k1; suml = ddot_(&i__3, &a_ref(k1, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l1), &c__1); /* Computing MIN */ i__1 = l1 + 1; /* Computing MIN */ i__2 = l1 + 1; i__3 = *n - l1; sumr = ddot_(&i__3, &c___ref(k1, min(i__1,*n)), ldc, & b_ref(l1, min(i__2,*n)), ldb); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); scaloc = 1.; a11 = a_ref(k1, k1) + sgn * b_ref(l1, l1); da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = (d__1 = vec_ref(1, 1), abs(d__1)); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x_ref(1, 1) = vec_ref(1, 1) * scaloc / a11; if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L190: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); } else if (l1 == l2 && k1 != k2) { /* Computing MIN */ i__1 = k2 + 1; /* Computing MIN */ i__2 = k2 + 1; i__3 = *m - k2; suml = ddot_(&i__3, &a_ref(k1, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l1), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k1, min(i__1,*n)), ldc, & b_ref(l1, min(i__2,*n)), ldb); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); /* Computing MIN */ i__1 = k2 + 1; /* Computing MIN */ i__2 = k2 + 1; i__3 = *m - k2; suml = ddot_(&i__3, &a_ref(k2, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l1), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k2, min(i__1,*n)), ldc, & b_ref(l1, min(i__2,*n)), ldb); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); d__1 = -sgn * b_ref(l1, l1); dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a_ref(k1, k1), lda, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L200: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k2, l1) = x_ref(2, 1); } else if (l1 != l2 && k1 == k2) { /* Computing MIN */ i__1 = k1 + 1; /* Computing MIN */ i__2 = k1 + 1; i__3 = *m - k1; suml = ddot_(&i__3, &a_ref(k1, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l1), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k1, min(i__1,*n)), ldc, & b_ref(l1, min(i__2,*n)), ldb); vec_ref(1, 1) = sgn * (c___ref(k1, l1) - (suml + sgn * sumr)); /* Computing MIN */ i__1 = k1 + 1; /* Computing MIN */ i__2 = k1 + 1; i__3 = *m - k1; suml = ddot_(&i__3, &a_ref(k1, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l2), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k1, min(i__1,*n)), ldc, & b_ref(l2, min(i__2,*n)), ldb); vec_ref(2, 1) = sgn * (c___ref(k1, l2) - (suml + sgn * sumr)); d__1 = -sgn * a_ref(k1, k1); dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b_ref(l1, l1), ldb, &c_b26, &c_b26, vec, &c__2, &d__1, & c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L210: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(2, 1); } else if (l1 != l2 && k1 != k2) { /* Computing MIN */ i__1 = k2 + 1; /* Computing MIN */ i__2 = k2 + 1; i__3 = *m - k2; suml = ddot_(&i__3, &a_ref(k1, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l1), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k1, min(i__1,*n)), ldc, & b_ref(l1, min(i__2,*n)), ldb); vec_ref(1, 1) = c___ref(k1, l1) - (suml + sgn * sumr); /* Computing MIN */ i__1 = k2 + 1; /* Computing MIN */ i__2 = k2 + 1; i__3 = *m - k2; suml = ddot_(&i__3, &a_ref(k1, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l2), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k1, min(i__1,*n)), ldc, & b_ref(l2, min(i__2,*n)), ldb); vec_ref(1, 2) = c___ref(k1, l2) - (suml + sgn * sumr); /* Computing MIN */ i__1 = k2 + 1; /* Computing MIN */ i__2 = k2 + 1; i__3 = *m - k2; suml = ddot_(&i__3, &a_ref(k2, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l1), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k2, min(i__1,*n)), ldc, & b_ref(l1, min(i__2,*n)), ldb); vec_ref(2, 1) = c___ref(k2, l1) - (suml + sgn * sumr); /* Computing MIN */ i__1 = k2 + 1; /* Computing MIN */ i__2 = k2 + 1; i__3 = *m - k2; suml = ddot_(&i__3, &a_ref(k2, min(i__1,*m)), lda, & c___ref(min(i__2,*m), l2), &c__1); /* Computing MIN */ i__1 = l2 + 1; /* Computing MIN */ i__2 = l2 + 1; i__3 = *n - l2; sumr = ddot_(&i__3, &c___ref(k2, min(i__1,*n)), ldc, & b_ref(l2, min(i__2,*n)), ldb); vec_ref(2, 2) = c___ref(k2, l2) - (suml + sgn * sumr); dlasy2_(&c_false, &c_true, isgn, &c__2, &c__2, &a_ref(k1, k1), lda, &b_ref(l1, l1), ldb, vec, &c__2, & scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c___ref(1, j), &c__1); /* L220: */ } *scale *= scaloc; } c___ref(k1, l1) = x_ref(1, 1); c___ref(k1, l2) = x_ref(1, 2); c___ref(k2, l1) = x_ref(2, 1); c___ref(k2, l2) = x_ref(2, 2); } L230: ; } L240: ; } } return 0; /* End of DTRSYL */ } /* dtrsyl_ */ #undef vec_ref #undef x_ref #undef c___ref #undef b_ref #undef a_ref