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322 lines
9.7 KiB
322 lines
9.7 KiB
#include "clapack.h" |
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/* Subroutine */ int dsytrf_(char *uplo, integer *n, doublereal *a, integer * |
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lda, integer *ipiv, doublereal *work, integer *lwork, integer *info) |
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{ |
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/* -- LAPACK routine (version 3.0) -- |
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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Courant Institute, Argonne National Lab, and Rice University |
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June 30, 1999 |
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Purpose |
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======= |
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DSYTRF computes the factorization of a real symmetric matrix A using |
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the Bunch-Kaufman diagonal pivoting method. The form of the |
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factorization is |
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A = U*D*U**T or A = L*D*L**T |
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where U (or L) is a product of permutation and unit upper (lower) |
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triangular matrices, and D is symmetric and block diagonal with |
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1-by-1 and 2-by-2 diagonal blocks. |
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This is the blocked version of the algorithm, calling Level 3 BLAS. |
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Arguments |
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========= |
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UPLO (input) CHARACTER*1 |
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= 'U': Upper triangle of A is stored; |
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= 'L': Lower triangle of A is stored. |
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N (input) INTEGER |
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The order of the matrix A. N >= 0. |
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A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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N-by-N upper triangular part of A contains the upper |
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triangular part of the matrix A, and the strictly lower |
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triangular part of A is not referenced. If UPLO = 'L', the |
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leading N-by-N lower triangular part of A contains the lower |
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triangular part of the matrix A, and the strictly upper |
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triangular part of A is not referenced. |
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On exit, the block diagonal matrix D and the multipliers used |
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to obtain the factor U or L (see below for further details). |
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LDA (input) INTEGER |
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The leading dimension of the array A. LDA >= max(1,N). |
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IPIV (output) INTEGER array, dimension (N) |
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Details of the interchanges and the block structure of D. |
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If IPIV(k) > 0, then rows and columns k and IPIV(k) were |
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interchanged and D(k,k) is a 1-by-1 diagonal block. |
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If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and |
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columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) |
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is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = |
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IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were |
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interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. |
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WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) |
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On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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LWORK (input) INTEGER |
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The length of WORK. LWORK >=1. For best performance |
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LWORK >= N*NB, where NB is the block size returned by ILAENV. |
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If LWORK = -1, then a workspace query is assumed; the routine |
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only calculates the optimal size of the WORK array, returns |
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this value as the first entry of the WORK array, and no error |
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message related to LWORK is issued by XERBLA. |
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INFO (output) INTEGER |
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= 0: successful exit |
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< 0: if INFO = -i, the i-th argument had an illegal value |
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> 0: if INFO = i, D(i,i) is exactly zero. The factorization |
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has been completed, but the block diagonal matrix D is |
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exactly singular, and division by zero will occur if it |
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is used to solve a system of equations. |
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Further Details |
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=============== |
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If UPLO = 'U', then A = U*D*U', where |
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U = P(n)*U(n)* ... *P(k)U(k)* ..., |
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i.e., U is a product of terms P(k)*U(k), where k decreases from n to |
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1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as |
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defined by IPIV(k), and U(k) is a unit upper triangular matrix, such |
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that if the diagonal block D(k) is of order s (s = 1 or 2), then |
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( I v 0 ) k-s |
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U(k) = ( 0 I 0 ) s |
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( 0 0 I ) n-k |
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k-s s n-k |
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If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). |
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If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), |
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and A(k,k), and v overwrites A(1:k-2,k-1:k). |
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If UPLO = 'L', then A = L*D*L', where |
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L = P(1)*L(1)* ... *P(k)*L(k)* ..., |
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i.e., L is a product of terms P(k)*L(k), where k increases from 1 to |
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n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as |
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defined by IPIV(k), and L(k) is a unit lower triangular matrix, such |
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that if the diagonal block D(k) is of order s (s = 1 or 2), then |
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( I 0 0 ) k-1 |
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L(k) = ( 0 I 0 ) s |
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( 0 v I ) n-k-s+1 |
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k-1 s n-k-s+1 |
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If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). |
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If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), |
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and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). |
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===================================================================== |
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Test the input parameters. |
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Parameter adjustments */ |
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/* Table of constant values */ |
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static integer c__1 = 1; |
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static integer c_n1 = -1; |
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static integer c__2 = 2; |
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/* System generated locals */ |
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integer a_dim1, a_offset, i__1, i__2; |
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/* Local variables */ |
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static integer j, k; |
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extern logical lsame_(char *, char *); |
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static integer nbmin, iinfo; |
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static logical upper; |
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extern /* Subroutine */ int dsytf2_(char *, integer *, doublereal *, |
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integer *, integer *, integer *); |
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static integer kb, nb; |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *, ftnlen, ftnlen); |
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extern /* Subroutine */ int dlasyf_(char *, integer *, integer *, integer |
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*, doublereal *, integer *, integer *, doublereal *, integer *, |
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integer *); |
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static integer ldwork, lwkopt; |
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static logical lquery; |
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static integer iws; |
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#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1 * 1; |
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a -= a_offset; |
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--ipiv; |
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--work; |
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/* Function Body */ |
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*info = 0; |
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upper = lsame_(uplo, "U"); |
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lquery = *lwork == -1; |
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if (! upper && ! lsame_(uplo, "L")) { |
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*info = -1; |
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} else if (*n < 0) { |
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*info = -2; |
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} else if (*lda < max(1,*n)) { |
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*info = -4; |
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} else if (*lwork < 1 && ! lquery) { |
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*info = -7; |
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} |
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if (*info == 0) { |
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/* Determine the block size */ |
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nb = ilaenv_(&c__1, "DSYTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, |
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(ftnlen)1); |
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lwkopt = *n * nb; |
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work[1] = (doublereal) lwkopt; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DSYTRF", &i__1); |
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return 0; |
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} else if (lquery) { |
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return 0; |
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} |
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nbmin = 2; |
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ldwork = *n; |
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if (nb > 1 && nb < *n) { |
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iws = ldwork * nb; |
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if (*lwork < iws) { |
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/* Computing MAX */ |
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i__1 = *lwork / ldwork; |
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nb = max(i__1,1); |
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/* Computing MAX */ |
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i__1 = 2, i__2 = ilaenv_(&c__2, "DSYTRF", uplo, n, &c_n1, &c_n1, & |
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c_n1, (ftnlen)6, (ftnlen)1); |
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nbmin = max(i__1,i__2); |
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} |
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} else { |
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iws = 1; |
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} |
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if (nb < nbmin) { |
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nb = *n; |
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} |
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if (upper) { |
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/* Factorize A as U*D*U' using the upper triangle of A |
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K is the main loop index, decreasing from N to 1 in steps of |
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KB, where KB is the number of columns factorized by DLASYF; |
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KB is either NB or NB-1, or K for the last block */ |
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k = *n; |
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L10: |
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/* If K < 1, exit from loop */ |
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if (k < 1) { |
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goto L40; |
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} |
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if (k > nb) { |
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/* Factorize columns k-kb+1:k of A and use blocked code to |
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update columns 1:k-kb */ |
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dlasyf_(uplo, &k, &nb, &kb, &a[a_offset], lda, &ipiv[1], &work[1], |
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&ldwork, &iinfo); |
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} else { |
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/* Use unblocked code to factorize columns 1:k of A */ |
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dsytf2_(uplo, &k, &a[a_offset], lda, &ipiv[1], &iinfo); |
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kb = k; |
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} |
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/* Set INFO on the first occurrence of a zero pivot */ |
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if (*info == 0 && iinfo > 0) { |
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*info = iinfo; |
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} |
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/* Decrease K and return to the start of the main loop */ |
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k -= kb; |
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goto L10; |
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} else { |
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/* Factorize A as L*D*L' using the lower triangle of A |
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K is the main loop index, increasing from 1 to N in steps of |
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KB, where KB is the number of columns factorized by DLASYF; |
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KB is either NB or NB-1, or N-K+1 for the last block */ |
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k = 1; |
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L20: |
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/* If K > N, exit from loop */ |
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if (k > *n) { |
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goto L40; |
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} |
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if (k <= *n - nb) { |
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/* Factorize columns k:k+kb-1 of A and use blocked code to |
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update columns k+kb:n */ |
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i__1 = *n - k + 1; |
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dlasyf_(uplo, &i__1, &nb, &kb, &a_ref(k, k), lda, &ipiv[k], &work[ |
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1], &ldwork, &iinfo); |
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} else { |
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/* Use unblocked code to factorize columns k:n of A */ |
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i__1 = *n - k + 1; |
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dsytf2_(uplo, &i__1, &a_ref(k, k), lda, &ipiv[k], &iinfo); |
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kb = *n - k + 1; |
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} |
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/* Set INFO on the first occurrence of a zero pivot */ |
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if (*info == 0 && iinfo > 0) { |
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*info = iinfo + k - 1; |
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} |
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/* Adjust IPIV */ |
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i__1 = k + kb - 1; |
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for (j = k; j <= i__1; ++j) { |
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if (ipiv[j] > 0) { |
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ipiv[j] = ipiv[j] + k - 1; |
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} else { |
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ipiv[j] = ipiv[j] - k + 1; |
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} |
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/* L30: */ |
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} |
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/* Increase K and return to the start of the main loop */ |
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k += kb; |
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goto L20; |
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} |
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L40: |
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work[1] = (doublereal) lwkopt; |
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return 0; |
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/* End of DSYTRF */ |
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} /* dsytrf_ */ |
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#undef a_ref |
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