#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__3 = 3; static integer c__1 = 1; /* Subroutine */ int zlagsy_(integer *n, integer *k, doublereal *d__, doublecomplex *a, integer *lda, integer *iseed, doublecomplex *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ double z_abs(doublecomplex *); void z_div(doublecomplex *, doublecomplex *, doublecomplex *); /* Local variables */ static integer i__, j; static doublecomplex alpha; extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zscal_(integer *, doublecomplex *, doublecomplex *, integer *); extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern /* Subroutine */ int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), zsymv_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); extern doublereal dznrm2_(integer *, doublecomplex *, integer *); static integer ii, jj; static doublecomplex wa, wb; static doublereal wn; extern /* Subroutine */ int xerbla_(char *, integer *), zlacgv_( integer *, doublecomplex *, integer *), zlarnv_(integer *, integer *, integer *, doublecomplex *); static doublecomplex tau; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* -- LAPACK auxiliary test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= ZLAGSY generates a complex symmetric matrix A, by pre- and post- multiplying a real diagonal matrix D with a random unitary matrix: A = U*D*U**T. The semi-bandwidth may then be reduced to k by additional unitary transformations. Arguments ========= N (input) INTEGER The order of the matrix A. N >= 0. K (input) INTEGER The number of nonzero subdiagonals within the band of A. 0 <= K <= N-1. D (input) DOUBLE PRECISION array, dimension (N) The diagonal elements of the diagonal matrix D. A (output) COMPLEX*16 array, dimension (LDA,N) The generated n by n symmetric matrix A (the full matrix is stored). LDA (input) INTEGER The leading dimension of the array A. LDA >= N. ISEED (input/output) INTEGER array, dimension (4) On entry, the seed of the random number generator; the array elements must be between 0 and 4095, and ISEED(4) must be odd. On exit, the seed is updated. WORK (workspace) COMPLEX*16 array, dimension (2*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input arguments Parameter adjustments */ --d__; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --iseed; --work; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } else if (*k < 0 || *k > *n - 1) { *info = -2; } else if (*lda < max(1,*n)) { *info = -5; } if (*info < 0) { i__1 = -(*info); xerbla_("ZLAGSY", &i__1); return 0; } /* initialize lower triangle of A to diagonal matrix */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ } /* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = a_subscr(i__, i__); i__3 = i__; a[i__2].r = d__[i__3], a[i__2].i = 0.; /* L30: */ } /* Generate lower triangle of symmetric matrix */ for (i__ = *n - 1; i__ >= 1; --i__) { /* generate random reflection */ i__1 = *n - i__ + 1; zlarnv_(&c__3, &iseed[1], &i__1, &work[1]); i__1 = *n - i__ + 1; wn = dznrm2_(&i__1, &work[1], &c__1); d__1 = wn / z_abs(&work[1]); z__1.r = d__1 * work[1].r, z__1.i = d__1 * work[1].i; wa.r = z__1.r, wa.i = z__1.i; if (wn == 0.) { tau.r = 0., tau.i = 0.; } else { z__1.r = work[1].r + wa.r, z__1.i = work[1].i + wa.i; wb.r = z__1.r, wb.i = z__1.i; i__1 = *n - i__; z_div(&z__1, &c_b2, &wb); zscal_(&i__1, &z__1, &work[2], &c__1); work[1].r = 1., work[1].i = 0.; z_div(&z__1, &wb, &wa); d__1 = z__1.r; tau.r = d__1, tau.i = 0.; } /* apply random reflection to A(i:n,i:n) from the left and the right compute y := tau * A * conjg(u) */ i__1 = *n - i__ + 1; zlacgv_(&i__1, &work[1], &c__1); i__1 = *n - i__ + 1; zsymv_("Lower", &i__1, &tau, &a_ref(i__, i__), lda, &work[1], &c__1, & c_b1, &work[*n + 1], &c__1); i__1 = *n - i__ + 1; zlacgv_(&i__1, &work[1], &c__1); /* compute v := y - 1/2 * tau * ( u, y ) * u */ z__3.r = -.5, z__3.i = 0.; z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i + z__3.i * tau.r; i__1 = *n - i__ + 1; zdotc_(&z__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1); z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__1 = *n - i__ + 1; zaxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1); /* apply the transformation as a rank-2 update to A(i:n,i:n) CALL ZSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, $ A( I, I ), LDA ) */ i__1 = *n; for (jj = i__; jj <= i__1; ++jj) { i__2 = *n; for (ii = jj; ii <= i__2; ++ii) { i__3 = a_subscr(ii, jj); i__4 = a_subscr(ii, jj); i__5 = ii - i__ + 1; i__6 = *n + jj - i__ + 1; z__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[ i__6].i, z__3.i = work[i__5].r * work[i__6].i + work[ i__5].i * work[i__6].r; z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i - z__3.i; i__7 = *n + ii - i__ + 1; i__8 = jj - i__ + 1; z__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[ i__8].i, z__4.i = work[i__7].r * work[i__8].i + work[ i__7].i * work[i__8].r; z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L40: */ } /* L50: */ } /* L60: */ } /* Reduce number of subdiagonals to K */ i__1 = *n - 1 - *k; for (i__ = 1; i__ <= i__1; ++i__) { /* generate reflection to annihilate A(k+i+1:n,i) */ i__2 = *n - *k - i__ + 1; wn = dznrm2_(&i__2, &a_ref(*k + i__, i__), &c__1); d__1 = wn / z_abs(&a_ref(*k + i__, i__)); i__2 = a_subscr(*k + i__, i__); z__1.r = d__1 * a[i__2].r, z__1.i = d__1 * a[i__2].i; wa.r = z__1.r, wa.i = z__1.i; if (wn == 0.) { tau.r = 0., tau.i = 0.; } else { i__2 = a_subscr(*k + i__, i__); z__1.r = a[i__2].r + wa.r, z__1.i = a[i__2].i + wa.i; wb.r = z__1.r, wb.i = z__1.i; i__2 = *n - *k - i__; z_div(&z__1, &c_b2, &wb); zscal_(&i__2, &z__1, &a_ref(*k + i__ + 1, i__), &c__1); i__2 = a_subscr(*k + i__, i__); a[i__2].r = 1., a[i__2].i = 0.; z_div(&z__1, &wb, &wa); d__1 = z__1.r; tau.r = d__1, tau.i = 0.; } /* apply reflection to A(k+i:n,i+1:k+i-1) from the left */ i__2 = *n - *k - i__ + 1; i__3 = *k - 1; zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a_ref(*k + i__, i__ + 1), lda, &a_ref(*k + i__, i__), &c__1, &c_b1, &work[1], &c__1); i__2 = *n - *k - i__ + 1; i__3 = *k - 1; z__1.r = -tau.r, z__1.i = -tau.i; zgerc_(&i__2, &i__3, &z__1, &a_ref(*k + i__, i__), &c__1, &work[1], & c__1, &a_ref(*k + i__, i__ + 1), lda); /* apply reflection to A(k+i:n,k+i:n) from the left and the right compute y := tau * A * conjg(u) */ i__2 = *n - *k - i__ + 1; zlacgv_(&i__2, &a_ref(*k + i__, i__), &c__1); i__2 = *n - *k - i__ + 1; zsymv_("Lower", &i__2, &tau, &a_ref(*k + i__, *k + i__), lda, &a_ref(* k + i__, i__), &c__1, &c_b1, &work[1], &c__1); i__2 = *n - *k - i__ + 1; zlacgv_(&i__2, &a_ref(*k + i__, i__), &c__1); /* compute v := y - 1/2 * tau * ( u, y ) * u */ z__3.r = -.5, z__3.i = 0.; z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i + z__3.i * tau.r; i__2 = *n - *k - i__ + 1; zdotc_(&z__4, &i__2, &a_ref(*k + i__, i__), &c__1, &work[1], &c__1); z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__2 = *n - *k - i__ + 1; zaxpy_(&i__2, &alpha, &a_ref(*k + i__, i__), &c__1, &work[1], &c__1); /* apply symmetric rank-2 update to A(k+i:n,k+i:n) CALL ZSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, $ A( K+I, K+I ), LDA ) */ i__2 = *n; for (jj = *k + i__; jj <= i__2; ++jj) { i__3 = *n; for (ii = jj; ii <= i__3; ++ii) { i__4 = a_subscr(ii, jj); i__5 = a_subscr(ii, jj); i__6 = a_subscr(ii, i__); i__7 = jj - *k - i__ + 1; z__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i, z__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[ i__7].r; z__2.r = a[i__5].r - z__3.r, z__2.i = a[i__5].i - z__3.i; i__8 = ii - *k - i__ + 1; i__9 = a_subscr(jj, i__); z__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i, z__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[ i__9].r; z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i; a[i__4].r = z__1.r, a[i__4].i = z__1.i; /* L70: */ } /* L80: */ } i__2 = a_subscr(*k + i__, i__); z__1.r = -wa.r, z__1.i = -wa.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = *n; for (j = *k + i__ + 1; j <= i__2; ++j) { i__3 = a_subscr(j, i__); a[i__3].r = 0., a[i__3].i = 0.; /* L90: */ } /* L100: */ } /* Store full symmetric matrix */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = a_subscr(j, i__); i__4 = a_subscr(i__, j); a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i; /* L110: */ } /* L120: */ } return 0; /* End of ZLAGSY */ } /* zlagsy_ */ #undef a_ref #undef a_subscr