/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static complex c_b1 = {0.f,0.f}; static complex c_b2 = {1.f,0.f}; static integer c__3 = 3; static integer c__1 = 1; /* Subroutine */ int clagsy_(integer *n, integer *k, real *d, complex *a, integer *lda, integer *iseed, complex *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; complex q__1, q__2, q__3, q__4; /* Builtin functions */ double c_abs(complex *); void c_div(complex *, complex *, complex *); /* Local variables */ static integer i, j; extern /* Subroutine */ int cgerc_(integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, integer *); static complex alpha; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *); extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *), caxpy_(integer *, complex *, complex *, integer *, complex *, integer *), csymv_(char *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); extern real scnrm2_(integer *, complex *, integer *); static integer ii, jj; static complex wa, wb; extern /* Subroutine */ int clacgv_(integer *, complex *, integer *); static real wn; extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_( integer *, integer *, integer *, complex *); static complex tau; /* -- LAPACK auxiliary test routine (version 2.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= CLAGSY 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) REAL array, dimension (N) The diagonal elements of the diagonal matrix D. A (output) COMPLEX 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 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 = 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_("CLAGSY", &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 = i + j * a_dim1; a[i__3].r = 0.f, a[i__3].i = 0.f; /* L10: */ } /* L20: */ } i__1 = *n; for (i = 1; i <= i__1; ++i) { i__2 = i + i * a_dim1; i__3 = i; a[i__2].r = d[i__3], a[i__2].i = 0.f; /* L30: */ } /* Generate lower triangle of symmetric matrix */ for (i = *n - 1; i >= 1; --i) { /* generate random reflection */ i__1 = *n - i + 1; clarnv_(&c__3, &iseed[1], &i__1, &work[1]); i__1 = *n - i + 1; wn = scnrm2_(&i__1, &work[1], &c__1); d__1 = wn / c_abs(&work[1]); q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i; wa.r = q__1.r, wa.i = q__1.i; if (wn == 0.f) { tau.r = 0.f, tau.i = 0.f; } else { q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i; wb.r = q__1.r, wb.i = q__1.i; i__1 = *n - i; c_div(&q__1, &c_b2, &wb); cscal_(&i__1, &q__1, &work[2], &c__1); work[1].r = 1.f, work[1].i = 0.f; c_div(&q__1, &wb, &wa); d__1 = q__1.r; tau.r = d__1, tau.i = 0.f; } /* 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; clacgv_(&i__1, &work[1], &c__1); i__1 = *n - i + 1; csymv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1); i__1 = *n - i + 1; clacgv_(&i__1, &work[1], &c__1); /* compute v := y - 1/2 * tau * ( u, y ) * u */ q__3.r = -.5f, q__3.i = 0.f; q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i + q__3.i * tau.r; i__1 = *n - i + 1; cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1); q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i + q__2.i * q__4.r; alpha.r = q__1.r, alpha.i = q__1.i; i__1 = *n - i + 1; caxpy_(&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 CSYR2( '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 = ii + jj * a_dim1; i__4 = ii + jj * a_dim1; i__5 = ii - i + 1; i__6 = *n + jj - i + 1; q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[ i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[ i__5].i * work[i__6].r; q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i; i__7 = *n + ii - i + 1; i__8 = jj - i + 1; q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[ i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[ i__7].i * work[i__8].r; q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i; a[i__3].r = q__1.r, a[i__3].i = q__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 = scnrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1); d__1 = wn / c_abs(&a[*k + i + i * a_dim1]); i__2 = *k + i + i * a_dim1; q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i; wa.r = q__1.r, wa.i = q__1.i; if (wn == 0.f) { tau.r = 0.f, tau.i = 0.f; } else { i__2 = *k + i + i * a_dim1; q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i; wb.r = q__1.r, wb.i = q__1.i; i__2 = *n - *k - i; c_div(&q__1, &c_b2, &wb); cscal_(&i__2, &q__1, &a[*k + i + 1 + i * a_dim1], &c__1); i__2 = *k + i + i * a_dim1; a[i__2].r = 1.f, a[i__2].i = 0.f; c_div(&q__1, &wb, &wa); d__1 = q__1.r; tau.r = d__1, tau.i = 0.f; } /* 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; cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i + (i + 1) * a_dim1], lda, &a[*k + i + i * a_dim1], &c__1, &c_b1, &work[ 1], &c__1); i__2 = *n - *k - i + 1; i__3 = *k - 1; q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i; cgerc_(&i__2, &i__3, &q__1, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1, &a[*k + i + (i + 1) * a_dim1], lda); /* apply reflection to A(k+i:n,k+i:n) from the left and the rig ht compute y := tau * A * conjg(u) */ i__2 = *n - *k - i + 1; clacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1); i__2 = *n - *k - i + 1; csymv_("Lower", &i__2, &tau, &a[*k + i + (*k + i) * a_dim1], lda, &a[* k + i + i * a_dim1], &c__1, &c_b1, &work[1], &c__1); i__2 = *n - *k - i + 1; clacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1); /* compute v := y - 1/2 * tau * ( u, y ) * u */ q__3.r = -.5f, q__3.i = 0.f; q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i + q__3.i * tau.r; i__2 = *n - *k - i + 1; cdotc_(&q__4, &i__2, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1); q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i + q__2.i * q__4.r; alpha.r = q__1.r, alpha.i = q__1.i; i__2 = *n - *k - i + 1; caxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1) ; /* apply symmetric rank-2 update to A(k+i:n,k+i:n) CALL CSYR2( '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 = ii + jj * a_dim1; i__5 = ii + jj * a_dim1; i__6 = ii + i * a_dim1; i__7 = jj - *k - i + 1; q__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i, q__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[ i__7].r; q__2.r = a[i__5].r - q__3.r, q__2.i = a[i__5].i - q__3.i; i__8 = ii - *k - i + 1; i__9 = jj + i * a_dim1; q__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i, q__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[ i__9].r; q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i; a[i__4].r = q__1.r, a[i__4].i = q__1.i; /* L70: */ } /* L80: */ } i__2 = *k + i + i * a_dim1; q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i; a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = *n; for (j = *k + i + 1; j <= i__2; ++j) { i__3 = j + i * a_dim1; a[i__3].r = 0.f, a[i__3].i = 0.f; /* 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 = j + i * a_dim1; i__4 = i + j * a_dim1; a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i; /* L110: */ } /* L120: */ } return 0; /* End of CLAGSY */ } /* clagsy_ */