/* slatrd.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 "clapack.h" /* Table of constant values */ static real c_b5 = -1.f; static real c_b6 = 1.f; static integer c__1 = 1; static real c_b16 = 0.f; /* Subroutine */ int slatrd_(char *uplo, integer *n, integer *nb, real *a, integer *lda, real *e, real *tau, real *w, integer *ldw) { /* System generated locals */ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; /* Local variables */ integer i__, iw; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); real alpha; extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), saxpy_( integer *, real *, real *, integer *, real *, integer *), ssymv_( char *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), slarfg_(integer *, real *, real *, integer *, real *); /* -- LAPACK auxiliary routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SLATRD reduces NB rows and columns of a real symmetric matrix A to */ /* symmetric tridiagonal form by an orthogonal similarity */ /* transformation Q' * A * Q, and returns the matrices V and W which are */ /* needed to apply the transformation to the unreduced part of A. */ /* If UPLO = 'U', SLATRD reduces the last NB rows and columns of a */ /* matrix, of which the upper triangle is supplied; */ /* if UPLO = 'L', SLATRD reduces the first NB rows and columns of a */ /* matrix, of which the lower triangle is supplied. */ /* This is an auxiliary routine called by SSYTRD. */ /* 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. */ /* NB (input) INTEGER */ /* The number of rows and columns to be reduced. */ /* 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 last NB columns have been reduced to */ /* tridiagonal form, with the diagonal elements overwriting */ /* the diagonal elements of A; the elements above the diagonal */ /* with the array TAU, represent the orthogonal matrix Q as a */ /* product of elementary reflectors; */ /* if UPLO = 'L', the first NB columns have been reduced to */ /* tridiagonal form, with the diagonal elements overwriting */ /* the diagonal elements of A; the elements below the diagonal */ /* 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 >= (1,N). */ /* E (output) REAL array, dimension (N-1) */ /* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */ /* elements of the last NB columns of the reduced matrix; */ /* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */ /* the first NB columns of the reduced matrix. */ /* TAU (output) REAL array, dimension (N-1) */ /* The scalar factors of the elementary reflectors, stored in */ /* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */ /* See Further Details. */ /* W (output) REAL array, dimension (LDW,NB) */ /* The n-by-nb matrix W required to update the unreduced part */ /* of A. */ /* LDW (input) INTEGER */ /* The leading dimension of the array W. LDW >= max(1,N). */ /* Further Details */ /* =============== */ /* If UPLO = 'U', the matrix Q is represented as a product of elementary */ /* reflectors */ /* Q = H(n) H(n-1) . . . H(n-nb+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:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */ /* and tau in TAU(i-1). */ /* If UPLO = 'L', the matrix Q is represented as a product of elementary */ /* reflectors */ /* Q = H(1) H(2) . . . H(nb). */ /* 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+1:n) is stored on exit in A(i+1:n,i), */ /* and tau in TAU(i). */ /* The elements of the vectors v together form the n-by-nb matrix V */ /* which is needed, with W, to apply the transformation to the unreduced */ /* part of the matrix, using a symmetric rank-2k update of the form: */ /* A := A - V*W' - W*V'. */ /* The contents of A on exit are illustrated by the following examples */ /* with n = 5 and nb = 2: */ /* if UPLO = 'U': if UPLO = 'L': */ /* ( a a a v4 v5 ) ( d ) */ /* ( a a v4 v5 ) ( 1 d ) */ /* ( a 1 v5 ) ( v1 1 a ) */ /* ( d 1 ) ( v1 v2 a a ) */ /* ( d ) ( v1 v2 a a a ) */ /* where d denotes a diagonal element of the reduced matrix, a denotes */ /* an element of the original matrix that is unchanged, and vi denotes */ /* an element of the vector defining H(i). */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick return if possible */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --e; --tau; w_dim1 = *ldw; w_offset = 1 + w_dim1; w -= w_offset; /* Function Body */ if (*n <= 0) { return 0; } if (lsame_(uplo, "U")) { /* Reduce last NB columns of upper triangle */ i__1 = *n - *nb + 1; for (i__ = *n; i__ >= i__1; --i__) { iw = i__ - *n + *nb; if (i__ < *n) { /* Update A(1:i,i) */ i__2 = *n - i__; sgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & c_b6, &a[i__ * a_dim1 + 1], &c__1); i__2 = *n - i__; sgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & c_b6, &a[i__ * a_dim1 + 1], &c__1); } if (i__ > 1) { /* Generate elementary reflector H(i) to annihilate */ /* A(1:i-2,i) */ i__2 = i__ - 1; slarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + 1], &c__1, &tau[i__ - 1]); e[i__ - 1] = a[i__ - 1 + i__ * a_dim1]; a[i__ - 1 + i__ * a_dim1] = 1.f; /* Compute W(1:i-1,i) */ i__2 = i__ - 1; ssymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], & c__1); if (i__ < *n) { i__2 = i__ - 1; i__3 = *n - i__; sgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, & c_b16, &w[i__ + 1 + iw * w_dim1], &c__1); i__2 = i__ - 1; i__3 = *n - i__; sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1); i__2 = i__ - 1; i__3 = *n - i__; sgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, & c_b16, &w[i__ + 1 + iw * w_dim1], &c__1); i__2 = i__ - 1; i__3 = *n - i__; sgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1); } i__2 = i__ - 1; sscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); i__2 = i__ - 1; alpha = tau[i__ - 1] * -.5f * sdot_(&i__2, &w[iw * w_dim1 + 1] , &c__1, &a[i__ * a_dim1 + 1], &c__1); i__2 = i__ - 1; saxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * w_dim1 + 1], &c__1); } /* L10: */ } } else { /* Reduce first NB columns of lower triangle */ i__1 = *nb; for (i__ = 1; i__ <= i__1; ++i__) { /* Update A(i:n,i) */ i__2 = *n - i__ + 1; i__3 = i__ - 1; sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], & c__1); i__2 = *n - i__ + 1; i__3 = i__ - 1; sgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], & c__1); if (i__ < *n) { /* Generate elementary reflector H(i) 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, &tau[i__]); e[i__] = a[i__ + 1 + i__ * a_dim1]; a[i__ + 1 + i__ * a_dim1] = 1.f; /* Compute W(i+1:n,i) */ i__2 = *n - i__; ssymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1] , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ i__ + 1 + i__ * w_dim1], &c__1); i__2 = *n - i__; i__3 = i__ - 1; sgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ i__ * w_dim1 + 1], &c__1); i__2 = *n - i__; i__3 = i__ - 1; sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ i__ + 1 + i__ * w_dim1], &c__1); i__2 = *n - i__; i__3 = i__ - 1; sgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ i__ * w_dim1 + 1], &c__1); i__2 = *n - i__; i__3 = i__ - 1; sgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ i__ + 1 + i__ * w_dim1], &c__1); i__2 = *n - i__; sscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); i__2 = *n - i__; alpha = tau[i__] * -.5f * sdot_(&i__2, &w[i__ + 1 + i__ * w_dim1], &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, &w[ i__ + 1 + i__ * w_dim1], &c__1); } /* L20: */ } } return 0; /* End of SLATRD */ } /* slatrd_ */