#include "blaswrap.h" /* dsyt22.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_b6 = 1.; static doublereal c_b7 = 0.; /* Subroutine */ int dsyt22_(integer *itype, char *uplo, integer *n, integer * m, integer *kband, doublereal *a, integer *lda, doublereal *d__, doublereal *e, doublereal *u, integer *ldu, doublereal *v, integer * ldv, doublereal *tau, doublereal *work, doublereal *result ) { /* System generated locals */ integer a_dim1, a_offset, u_dim1, u_offset, v_dim1, v_offset, i__1; doublereal d__1, d__2; /* Local variables */ static integer j, jj, nn, jj1, jj2; static doublereal ulp; static integer nnp1; static doublereal unfl; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dort01_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *); static doublereal anorm; extern /* Subroutine */ int dsymm_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); static doublereal wnorm; extern doublereal dlamch_(char *), 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 ======= DSYT22 generally checks a decomposition of the form A U = U S where A is symmetric, the columns of U are orthonormal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as a dense matrix, otherwise the U is expressed as a product of Householder transformations, whose vectors are stored in the array "V" and whose scaling constants are in "TAU"; we shall use the letter "V" to refer to the product of Householder transformations (which should be equal to U). Specifically, if ITYPE=1, then: RESULT(1) = | U' A U - S | / ( |A| m ulp ) *and* RESULT(2) = | I - U'U | / ( m ulp ) Arguments ========= ITYPE INTEGER Specifies the type of tests to be performed. 1: U expressed as a dense orthogonal matrix: RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* RESULT(2) = | I - UU' | / ( n ulp ) UPLO CHARACTER If UPLO='U', the upper triangle of A will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A will be used and the (strictly) upper triangle will not be referenced. Not modified. N INTEGER The size of the matrix. If it is zero, DSYT22 does nothing. It must be at least zero. Not modified. M INTEGER The number of columns of U. If it is zero, DSYT22 does nothing. It must be at least zero. Not modified. KBAND INTEGER The bandwidth of the matrix. It may only be zero or one. If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal. Not modified. A DOUBLE PRECISION array, dimension (LDA , N) The original (unfactored) matrix. It is assumed to be symmetric, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced. Not modified. LDA INTEGER The leading dimension of A. It must be at least 1 and at least N. Not modified. D DOUBLE PRECISION array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix. Not modified. E DOUBLE PRECISION array, dimension (N) The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. Not referenced if KBAND=0. Not modified. U DOUBLE PRECISION array, dimension (LDU, N) If ITYPE=1 or 3, this contains the orthogonal matrix in the decomposition, expressed as a dense matrix. If ITYPE=2, then it is not referenced. Not modified. LDU INTEGER The leading dimension of U. LDU must be at least N and at least 1. Not modified. V DOUBLE PRECISION array, dimension (LDV, N) If ITYPE=2 or 3, the lower triangle of this array contains the Householder vectors used to describe the orthogonal matrix in the decomposition. If ITYPE=1, then it is not referenced. Not modified. LDV INTEGER The leading dimension of V. LDV must be at least N and at least 1. Not modified. TAU DOUBLE PRECISION array, dimension (N) If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)' in the Householder transformation H(j) of the product U = H(1)...H(n-2) If ITYPE < 2, then TAU is not referenced. Not modified. WORK DOUBLE PRECISION array, dimension (2*N**2) Workspace. Modified. RESULT 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. RESULT(2) is modified only if LDU is at least N. Modified. ===================================================================== Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --d__; --e; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; --tau; --work; --result; /* Function Body */ result[1] = 0.; result[2] = 0.; if (*n <= 0 || *m <= 0) { return 0; } unfl = dlamch_("Safe minimum"); ulp = dlamch_("Precision"); /* Do Test 1 Norm of A: Computing MAX */ d__1 = dlansy_("1", uplo, n, &a[a_offset], lda, &work[1]); anorm = max(d__1,unfl); /* Compute error matrix: ITYPE=1: error = U' A U - S */ dsymm_("L", uplo, n, m, &c_b6, &a[a_offset], lda, &u[u_offset], ldu, & c_b7, &work[1], n); nn = *n * *n; nnp1 = nn + 1; dgemm_("T", "N", m, m, n, &c_b6, &u[u_offset], ldu, &work[1], n, &c_b7, & work[nnp1], n); i__1 = *m; for (j = 1; j <= i__1; ++j) { jj = nn + (j - 1) * *n + j; work[jj] -= d__[j]; /* L10: */ } if (*kband == 1 && *n > 1) { i__1 = *m; for (j = 2; j <= i__1; ++j) { jj1 = nn + (j - 1) * *n + j - 1; jj2 = nn + (j - 2) * *n + j; work[jj1] -= e[j - 1]; work[jj2] -= e[j - 1]; /* L20: */ } } wnorm = dlansy_("1", uplo, m, &work[nnp1], n, &work[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 */ if (*itype == 1) { i__1 = (*n << 1) * *n; dort01_("Columns", n, m, &u[u_offset], ldu, &work[1], &i__1, &result[ 2]); } return 0; /* End of DSYT22 */ } /* dsyt22_ */