#include "blaswrap.h" /* sstt21.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 real c_b5 = 0.f; static integer c__1 = 1; static real c_b19 = 1.f; /* Subroutine */ int sstt21_(integer *n, integer *kband, real *ad, real *ae, real *sd, real *se, real *u, integer *ldu, real *work, real *result) { /* System generated locals */ integer u_dim1, u_offset, i__1; real r__1, r__2, r__3; /* Local variables */ static integer j; static real ulp, unfl; extern /* Subroutine */ int ssyr_(char *, integer *, real *, real *, integer *, real *, integer *); static real temp1, temp2; extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *, integer *, real *, integer *, real *, integer *), sgemm_( char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static real anorm, wnorm; extern doublereal slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, real *, real *, integer *); extern doublereal slansy_(char *, char *, integer *, real *, integer *, real *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SSTT21 checks a decomposition of the form A = U S U' where ' means transpose, A is symmetric tridiagonal, U is orthogonal, and S is 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, SSTT21 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) REAL array, dimension (N) The diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE (input) REAL 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) REAL array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix S. SE (input) REAL 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) REAL 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) REAL array, dimension (N*(N+1)) RESULT (output) REAL 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; --result; /* Function Body */ result[1] = 0.f; result[2] = 0.f; if (*n <= 0) { return 0; } unfl = slamch_("Safe minimum"); ulp = slamch_("Precision"); /* Do Test 1 Copy A & Compute its 1-Norm: */ slaset_("Full", n, n, &c_b5, &c_b5, &work[1], n); anorm = 0.f; temp1 = 0.f; i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { work[(*n + 1) * (j - 1) + 1] = ad[j]; work[(*n + 1) * (j - 1) + 2] = ae[j]; temp2 = (r__1 = ae[j], dabs(r__1)); /* Computing MAX */ r__2 = anorm, r__3 = (r__1 = ad[j], dabs(r__1)) + temp1 + temp2; anorm = dmax(r__2,r__3); temp1 = temp2; /* L10: */ } /* Computing 2nd power */ i__1 = *n; work[i__1 * i__1] = ad[*n]; /* Computing MAX */ r__2 = anorm, r__3 = (r__1 = ad[*n], dabs(r__1)) + temp1, r__2 = max(r__2, r__3); anorm = dmax(r__2,unfl); /* Norm of A - USU' */ i__1 = *n; for (j = 1; j <= i__1; ++j) { r__1 = -sd[j]; ssyr_("L", n, &r__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) { r__1 = -se[j]; ssyr2_("L", n, &r__1, &u[j * u_dim1 + 1], &c__1, &u[(j + 1) * u_dim1 + 1], &c__1, &work[1], n); /* L30: */ } } /* Computing 2nd power */ i__1 = *n; wnorm = slansy_("1", "L", n, &work[1], n, &work[i__1 * i__1 + 1]); if (anorm > wnorm) { result[1] = wnorm / anorm / (*n * ulp); } else { if (anorm < 1.f) { /* Computing MIN */ r__1 = wnorm, r__2 = *n * anorm; result[1] = dmin(r__1,r__2) / anorm / (*n * ulp); } else { /* Computing MIN */ r__1 = wnorm / anorm, r__2 = (real) (*n); result[1] = dmin(r__1,r__2) / (*n * ulp); } } /* Do Test 2 Compute UU' - I */ sgemm_("N", "C", n, n, n, &c_b19, &u[u_offset], ldu, &u[u_offset], ldu, & c_b5, &work[1], n); i__1 = *n; for (j = 1; j <= i__1; ++j) { work[(*n + 1) * (j - 1) + 1] += -1.f; /* L40: */ } /* Computing MIN Computing 2nd power */ i__1 = *n; r__1 = (real) (*n), r__2 = slange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]); result[2] = dmin(r__1,r__2) / (*n * ulp); return 0; /* End of SSTT21 */ } /* sstt21_ */