#include "blaswrap.h" /* dstt22.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 doublereal c_b12 = 1.; static doublereal c_b13 = 0.; /* Subroutine */ int dstt22_(integer *n, integer *m, integer *kband, doublereal *ad, doublereal *ae, doublereal *sd, doublereal *se, doublereal *u, integer *ldu, doublereal *work, integer *ldwork, doublereal *result) { /* System generated locals */ integer u_dim1, u_offset, work_dim1, work_offset, i__1, i__2, i__3; doublereal d__1, d__2, d__3, d__4, d__5; /* Local variables */ static integer i__, j, k; static doublereal ulp, aukj, unfl; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); static doublereal anorm, wnorm; extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *), dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DSTT22 checks a set of M eigenvalues and eigenvectors, A U = U S where A is symmetric tridiagonal, the columns of U are orthogonal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Two tests are performed: RESULT(1) = | U' A U - S | / ( |A| m ulp ) RESULT(2) = | I - U'U | / ( m ulp ) Arguments ========= N (input) INTEGER The size of the matrix. If it is zero, DSTT22 does nothing. It must be at least zero. M (input) INTEGER The number of eigenpairs to check. If it is zero, DSTT22 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 symmetric tridiagonal. AE (input) DOUBLE PRECISION array, dimension (N) The off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is ignored, AE(2) is the (1,2) and (2,1) element, etc. SD (input) DOUBLE PRECISION array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix S. SE (input) DOUBLE PRECISION array, dimension (N) The off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is ignored, SE(2) is the (1,2) and (2,1) element, etc. U (input) DOUBLE PRECISION array, dimension (LDU, N) The orthogonal matrix in the decomposition. LDU (input) INTEGER The leading dimension of U. LDU must be at least N. WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK, M+1) LDWORK (input) INTEGER The leading dimension of WORK. LDWORK must be at least max(1,M). 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. ===================================================================== Parameter adjustments */ --ad; --ae; --sd; --se; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; work_dim1 = *ldwork; work_offset = 1 + work_dim1; work -= work_offset; --result; /* Function Body */ result[1] = 0.; result[2] = 0.; if (*n <= 0 || *m <= 0) { return 0; } unfl = dlamch_("Safe minimum"); ulp = dlamch_("Epsilon"); /* Do Test 1 Compute the 1-norm of A. */ if (*n > 1) { anorm = abs(ad[1]) + abs(ae[1]); i__1 = *n - 1; for (j = 2; j <= i__1; ++j) { /* Computing MAX */ d__4 = anorm, d__5 = (d__1 = ad[j], abs(d__1)) + (d__2 = ae[j], abs(d__2)) + (d__3 = ae[j - 1], abs(d__3)); anorm = max(d__4,d__5); /* L10: */ } /* Computing MAX */ d__3 = anorm, d__4 = (d__1 = ad[*n], abs(d__1)) + (d__2 = ae[*n - 1], abs(d__2)); anorm = max(d__3,d__4); } else { anorm = abs(ad[1]); } anorm = max(anorm,unfl); /* Norm of U'AU - S */ i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *m; for (j = 1; j <= i__2; ++j) { work[i__ + j * work_dim1] = 0.; i__3 = *n; for (k = 1; k <= i__3; ++k) { aukj = ad[k] * u[k + j * u_dim1]; if (k != *n) { aukj += ae[k] * u[k + 1 + j * u_dim1]; } if (k != 1) { aukj += ae[k - 1] * u[k - 1 + j * u_dim1]; } work[i__ + j * work_dim1] += u[k + i__ * u_dim1] * aukj; /* L20: */ } /* L30: */ } work[i__ + i__ * work_dim1] -= sd[i__]; if (*kband == 1) { if (i__ != 1) { work[i__ + (i__ - 1) * work_dim1] -= se[i__ - 1]; } if (i__ != *n) { work[i__ + (i__ + 1) * work_dim1] -= se[i__]; } } /* L40: */ } wnorm = dlansy_("1", "L", m, &work[work_offset], m, &work[(*m + 1) * work_dim1 + 1]); if (anorm > wnorm) { result[1] = wnorm / anorm / (*m * ulp); } else { if (anorm < 1.) { /* Computing MIN */ d__1 = wnorm, d__2 = *m * anorm; result[1] = min(d__1,d__2) / anorm / (*m * ulp); } else { /* Computing MIN */ d__1 = wnorm / anorm, d__2 = (doublereal) (*m); result[1] = min(d__1,d__2) / (*m * ulp); } } /* Do Test 2 Compute U'U - I */ dgemm_("T", "N", m, m, n, &c_b12, &u[u_offset], ldu, &u[u_offset], ldu, & c_b13, &work[work_offset], m); i__1 = *m; for (j = 1; j <= i__1; ++j) { work[j + j * work_dim1] += -1.; /* L50: */ } /* Computing MIN */ d__1 = (doublereal) (*m), d__2 = dlange_("1", m, m, &work[work_offset], m, &work[(*m + 1) * work_dim1 + 1]); result[2] = min(d__1,d__2) / (*m * ulp); return 0; /* End of DSTT22 */ } /* dstt22_ */