#include "blaswrap.h" /* zstt21.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__1 = 1; /* Subroutine */ int zstt21_(integer *n, integer *kband, doublereal *ad, doublereal *ae, doublereal *sd, doublereal *se, doublecomplex *u, integer *ldu, doublecomplex *work, doublereal *rwork, doublereal * result) { /* System generated locals */ integer u_dim1, u_offset, i__1, i__2, i__3; doublereal d__1, d__2, d__3; doublecomplex z__1, z__2; /* Local variables */ static integer j; static doublereal ulp, unfl; extern /* Subroutine */ int zher_(char *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *); static doublereal temp1, temp2; extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); static doublereal anorm; extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); static doublereal wnorm; extern doublereal dlamch_(char *), zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *), zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZSTT21 checks a decomposition of the form A = U S U* where * means conjugate transpose, A is real symmetric tridiagonal, U is unitary, and S is real and diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Two tests are performed: RESULT(1) = | A - U S U* | / ( |A| n ulp ) RESULT(2) = | I - UU* | / ( n ulp ) Arguments ========= N (input) INTEGER The size of the matrix. If it is zero, ZSTT21 does nothing. It must be at least zero. KBAND (input) INTEGER The bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and SE is not referenced. If one, then S is symmetric tri-diagonal. AD (input) DOUBLE PRECISION array, dimension (N) The diagonal of the original (unfactored) matrix A. A is assumed to be real symmetric tridiagonal. AE (input) DOUBLE PRECISION array, dimension (N-1) The off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc. SD (input) DOUBLE PRECISION array, dimension (N) The diagonal of the real (symmetric tri-) diagonal matrix S. SE (input) DOUBLE PRECISION array, dimension (N-1) The off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc. U (input) COMPLEX*16 array, dimension (LDU, N) The unitary matrix in the decomposition. LDU (input) INTEGER The leading dimension of U. LDU must be at least N. WORK (workspace) COMPLEX*16 array, dimension (N**2) RWORK (workspace) DOUBLE PRECISION array, dimension (N) RESULT (output) DOUBLE PRECISION array, dimension (2) The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow. RESULT(1) is always modified. ===================================================================== 1) Constants Parameter adjustments */ --ad; --ae; --sd; --se; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; --work; --rwork; --result; /* Function Body */ result[1] = 0.; result[2] = 0.; if (*n <= 0) { return 0; } unfl = dlamch_("Safe minimum"); ulp = dlamch_("Precision"); /* Do Test 1 Copy A & Compute its 1-Norm: */ zlaset_("Full", n, n, &c_b1, &c_b1, &work[1], n); anorm = 0.; temp1 = 0.; i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = (*n + 1) * (j - 1) + 1; i__3 = j; work[i__2].r = ad[i__3], work[i__2].i = 0.; i__2 = (*n + 1) * (j - 1) + 2; i__3 = j; work[i__2].r = ae[i__3], work[i__2].i = 0.; temp2 = (d__1 = ae[j], abs(d__1)); /* Computing MAX */ d__2 = anorm, d__3 = (d__1 = ad[j], abs(d__1)) + temp1 + temp2; anorm = max(d__2,d__3); temp1 = temp2; /* L10: */ } /* Computing 2nd power */ i__2 = *n; i__1 = i__2 * i__2; i__3 = *n; work[i__1].r = ad[i__3], work[i__1].i = 0.; /* Computing MAX */ d__2 = anorm, d__3 = (d__1 = ad[*n], abs(d__1)) + temp1, d__2 = max(d__2, d__3); anorm = max(d__2,unfl); /* Norm of A - USU* */ i__1 = *n; for (j = 1; j <= i__1; ++j) { d__1 = -sd[j]; zher_("L", n, &d__1, &u[j * u_dim1 + 1], &c__1, &work[1], n); /* L20: */ } if (*n > 1 && *kband == 1) { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = j; z__2.r = se[i__2], z__2.i = 0.; z__1.r = -z__2.r, z__1.i = -z__2.i; zher2_("L", n, &z__1, &u[j * u_dim1 + 1], &c__1, &u[(j + 1) * u_dim1 + 1], &c__1, &work[1], n); /* L30: */ } } wnorm = zlanhe_("1", "L", n, &work[1], n, &rwork[1]) ; if (anorm > wnorm) { result[1] = wnorm / anorm / (*n * ulp); } else { if (anorm < 1.) { /* Computing MIN */ d__1 = wnorm, d__2 = *n * anorm; result[1] = min(d__1,d__2) / anorm / (*n * ulp); } else { /* Computing MIN */ d__1 = wnorm / anorm, d__2 = (doublereal) (*n); result[1] = min(d__1,d__2) / (*n * ulp); } } /* Do Test 2 Compute UU* - I */ zgemm_("N", "C", n, n, n, &c_b2, &u[u_offset], ldu, &u[u_offset], ldu, & c_b1, &work[1], n); i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = (*n + 1) * (j - 1) + 1; i__3 = (*n + 1) * (j - 1) + 1; z__1.r = work[i__3].r - 1., z__1.i = work[i__3].i - 0.; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L40: */ } /* Computing MIN */ d__1 = (doublereal) (*n), d__2 = zlange_("1", n, n, &work[1], n, &rwork[1] ); result[2] = min(d__1,d__2) / (*n * ulp); return 0; /* End of ZSTT21 */ } /* zstt21_ */