/* ssytd2.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" #include "blaswrap.h" /* Table of constant values */ static integer c__1 = 1; static real c_b8 = 0.f; static real c_b14 = -1.f; /* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda, real *d__, real *e, real *tau, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ integer i__; real taui; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *, integer *, real *, integer *, real *, integer *); real alpha; extern logical lsame_(char *, char *); logical upper; extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, real *, integer *), ssymv_(char *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), xerbla_(char *, integer *), slarfg_(integer *, real *, real *, integer *, real *); /* -- LAPACK routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */ /* form T by an orthogonal similarity transformation: Q' * A * Q = T. */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* Specifies whether the upper or lower triangular part of the */ /* symmetric matrix A is stored: */ /* = 'U': Upper triangular */ /* = 'L': Lower triangular */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* A (input/output) REAL array, dimension (LDA,N) */ /* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ /* n-by-n upper triangular part of A contains the upper */ /* triangular part of the matrix A, and the strictly lower */ /* triangular part of A is not referenced. If UPLO = 'L', the */ /* leading n-by-n lower triangular part of A contains the lower */ /* triangular part of the matrix A, and the strictly upper */ /* triangular part of A is not referenced. */ /* On exit, if UPLO = 'U', the diagonal and first superdiagonal */ /* of A are overwritten by the corresponding elements of the */ /* tridiagonal matrix T, and the elements above the first */ /* superdiagonal, with the array TAU, represent the orthogonal */ /* matrix Q as a product of elementary reflectors; if UPLO */ /* = 'L', the diagonal and first subdiagonal of A are over- */ /* written by the corresponding elements of the tridiagonal */ /* matrix T, and the elements below the first subdiagonal, with */ /* the array TAU, represent the orthogonal matrix Q as a product */ /* of elementary reflectors. See Further Details. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* D (output) REAL array, dimension (N) */ /* The diagonal elements of the tridiagonal matrix T: */ /* D(i) = A(i,i). */ /* E (output) REAL array, dimension (N-1) */ /* The off-diagonal elements of the tridiagonal matrix T: */ /* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ /* TAU (output) REAL array, dimension (N-1) */ /* The scalar factors of the elementary reflectors (see Further */ /* Details). */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* Further Details */ /* =============== */ /* If UPLO = 'U', the matrix Q is represented as a product of elementary */ /* reflectors */ /* Q = H(n-1) . . . H(2) H(1). */ /* Each H(i) has the form */ /* H(i) = I - tau * v * v' */ /* where tau is a real scalar, and v is a real vector with */ /* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ /* A(1:i-1,i+1), and tau in TAU(i). */ /* If UPLO = 'L', the matrix Q is represented as a product of elementary */ /* reflectors */ /* Q = H(1) H(2) . . . H(n-1). */ /* Each H(i) has the form */ /* H(i) = I - tau * v * v' */ /* where tau is a real scalar, and v is a real vector with */ /* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ /* and tau in TAU(i). */ /* The contents of A on exit are illustrated by the following examples */ /* with n = 5: */ /* if UPLO = 'U': if UPLO = 'L': */ /* ( d e v2 v3 v4 ) ( d ) */ /* ( d e v3 v4 ) ( e d ) */ /* ( d e v4 ) ( v1 e d ) */ /* ( d e ) ( v1 v2 e d ) */ /* ( d ) ( v1 v2 v3 e d ) */ /* where d and e denote diagonal and off-diagonal elements of T, and vi */ /* denotes an element of the vector defining H(i). */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --d__; --e; --tau; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*n)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("SSYTD2", &i__1); return 0; } /* Quick return if possible */ if (*n <= 0) { return 0; } if (upper) { /* Reduce the upper triangle of A */ for (i__ = *n - 1; i__ >= 1; --i__) { /* Generate elementary reflector H(i) = I - tau * v * v' */ /* to annihilate A(1:i-1,i+1) */ slarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui); e[i__] = a[i__ + (i__ + 1) * a_dim1]; if (taui != 0.f) { /* Apply H(i) from both sides to A(1:i,1:i) */ a[i__ + (i__ + 1) * a_dim1] = 1.f; /* Compute x := tau * A * v storing x in TAU(1:i) */ ssymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1); /* Compute w := x - 1/2 * tau * (x'*v) * v */ alpha = taui * -.5f * sdot_(&i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1], &c__1); saxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ 1], &c__1); /* Apply the transformation as a rank-2 update: */ /* A := A - v * w' - w * v' */ ssyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[1], &c__1, &a[a_offset], lda); a[i__ + (i__ + 1) * a_dim1] = e[i__]; } d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; tau[i__] = taui; /* L10: */ } d__[1] = a[a_dim1 + 1]; } else { /* Reduce the lower triangle of A */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { /* Generate elementary reflector H(i) = I - tau * v * v' */ /* to annihilate A(i+2:n,i) */ i__2 = *n - i__; /* Computing MIN */ i__3 = i__ + 2; slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+ i__ * a_dim1], &c__1, &taui); e[i__] = a[i__ + 1 + i__ * a_dim1]; if (taui != 0.f) { /* Apply H(i) from both sides to A(i+1:n,i+1:n) */ a[i__ + 1 + i__ * a_dim1] = 1.f; /* Compute x := tau * A * v storing y in TAU(i:n-1) */ i__2 = *n - i__; ssymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ i__], &c__1); /* Compute w := x - 1/2 * tau * (x'*v) * v */ i__2 = *n - i__; alpha = taui * -.5f * sdot_(&i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); i__2 = *n - i__; saxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ i__], &c__1); /* Apply the transformation as a rank-2 update: */ /* A := A - v * w' - w * v' */ i__2 = *n - i__; ssyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], lda); a[i__ + 1 + i__ * a_dim1] = e[i__]; } d__[i__] = a[i__ + i__ * a_dim1]; tau[i__] = taui; /* L20: */ } d__[*n] = a[*n + *n * a_dim1]; } return 0; /* End of SSYTD2 */ } /* ssytd2_ */