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341 lines
10 KiB
341 lines
10 KiB
/* dsytrf.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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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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/* 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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/* 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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integer j, k, kb, nb, iws; |
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extern logical lsame_(char *, char *); |
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integer nbmin, iinfo; |
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logical upper; |
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extern /* Subroutine */ int dsytf2_(char *, integer *, doublereal *, |
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integer *, integer *, integer *), xerbla_(char *, integer |
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*); |
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
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integer *, integer *); |
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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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integer ldwork, lwkopt; |
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logical lquery; |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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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 (MAX(1,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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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1; |
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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); |
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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); |
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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[k + k * a_dim1], lda, &ipiv[k], |
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&work[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[k + k * a_dim1], 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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