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Diffstat (limited to 'src/lib/lapack/dsytrf.f')
| -rw-r--r-- | src/lib/lapack/dsytrf.f | 287 |
1 files changed, 0 insertions, 287 deletions
diff --git a/src/lib/lapack/dsytrf.f b/src/lib/lapack/dsytrf.f deleted file mode 100644 index 43a31248..00000000 --- a/src/lib/lapack/dsytrf.f +++ /dev/null @@ -1,287 +0,0 @@ - SUBROUTINE DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* DSYTRF computes the factorization of a real symmetric matrix A using -* the Bunch-Kaufman diagonal pivoting method. The form of the -* factorization is -* -* A = U*D*U**T or A = L*D*L**T -* -* where U (or L) is a product of permutation and unit upper (lower) -* triangular matrices, and D is symmetric and block diagonal with -* 1-by-1 and 2-by-2 diagonal blocks. -* -* This is the blocked version of the algorithm, calling Level 3 BLAS. -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* A (input/output) DOUBLE PRECISION 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, the block diagonal matrix D and the multipliers used -* to obtain the factor U or L (see below for further details). -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* IPIV (output) INTEGER array, dimension (N) -* Details of the interchanges and the block structure of D. -* If IPIV(k) > 0, then rows and columns k and IPIV(k) were -* interchanged and D(k,k) is a 1-by-1 diagonal block. -* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and -* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) -* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = -* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were -* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -* -* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -* -* LWORK (input) INTEGER -* The length of WORK. LWORK >=1. For best performance -* LWORK >= N*NB, where NB is the block size returned by ILAENV. -* -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: if INFO = i, D(i,i) is exactly zero. The factorization -* has been completed, but the block diagonal matrix D is -* exactly singular, and division by zero will occur if it -* is used to solve a system of equations. -* -* Further Details -* =============== -* -* If UPLO = 'U', then A = U*D*U', where -* U = P(n)*U(n)* ... *P(k)U(k)* ..., -* i.e., U is a product of terms P(k)*U(k), where k decreases from n to -* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 -* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as -* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such -* that if the diagonal block D(k) is of order s (s = 1 or 2), then -* -* ( I v 0 ) k-s -* U(k) = ( 0 I 0 ) s -* ( 0 0 I ) n-k -* k-s s n-k -* -* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). -* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), -* and A(k,k), and v overwrites A(1:k-2,k-1:k). -* -* If UPLO = 'L', then A = L*D*L', where -* L = P(1)*L(1)* ... *P(k)*L(k)* ..., -* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to -* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 -* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as -* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such -* that if the diagonal block D(k) is of order s (s = 1 or 2), then -* -* ( I 0 0 ) k-1 -* L(k) = ( 0 I 0 ) s -* ( 0 v I ) n-k-s+1 -* k-1 s n-k-s+1 -* -* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). -* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), -* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). -* -* ===================================================================== -* -* .. Local Scalars .. - LOGICAL LQUERY, UPPER - INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DLASYF, DSYTF2, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN - INFO = -7 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Determine the block size -* - NB = ILAENV( 1, 'DSYTRF', UPLO, N, -1, -1, -1 ) - LWKOPT = N*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYTRF', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* - NBMIN = 2 - LDWORK = N - IF( NB.GT.1 .AND. NB.LT.N ) THEN - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN - NB = MAX( LWORK / LDWORK, 1 ) - NBMIN = MAX( 2, ILAENV( 2, 'DSYTRF', UPLO, N, -1, -1, -1 ) ) - END IF - ELSE - IWS = 1 - END IF - IF( NB.LT.NBMIN ) - $ NB = N -* - IF( UPPER ) THEN -* -* Factorize A as U*D*U' using the upper triangle of A -* -* K is the main loop index, decreasing from N to 1 in steps of -* KB, where KB is the number of columns factorized by DLASYF; -* KB is either NB or NB-1, or K for the last block -* - K = N - 10 CONTINUE -* -* If K < 1, exit from loop -* - IF( K.LT.1 ) - $ GO TO 40 -* - IF( K.GT.NB ) THEN -* -* Factorize columns k-kb+1:k of A and use blocked code to -* update columns 1:k-kb -* - CALL DLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, LDWORK, - $ IINFO ) - ELSE -* -* Use unblocked code to factorize columns 1:k of A -* - CALL DSYTF2( UPLO, K, A, LDA, IPIV, IINFO ) - KB = K - END IF -* -* Set INFO on the first occurrence of a zero pivot -* - IF( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO -* -* Decrease K and return to the start of the main loop -* - K = K - KB - GO TO 10 -* - ELSE -* -* Factorize A as L*D*L' using the lower triangle of A -* -* K is the main loop index, increasing from 1 to N in steps of -* KB, where KB is the number of columns factorized by DLASYF; -* KB is either NB or NB-1, or N-K+1 for the last block -* - K = 1 - 20 CONTINUE -* -* If K > N, exit from loop -* - IF( K.GT.N ) - $ GO TO 40 -* - IF( K.LE.N-NB ) THEN -* -* Factorize columns k:k+kb-1 of A and use blocked code to -* update columns k+kb:n -* - CALL DLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ), - $ WORK, LDWORK, IINFO ) - ELSE -* -* Use unblocked code to factorize columns k:n of A -* - CALL DSYTF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO ) - KB = N - K + 1 - END IF -* -* Set INFO on the first occurrence of a zero pivot -* - IF( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO + K - 1 -* -* Adjust IPIV -* - DO 30 J = K, K + KB - 1 - IF( IPIV( J ).GT.0 ) THEN - IPIV( J ) = IPIV( J ) + K - 1 - ELSE - IPIV( J ) = IPIV( J ) - K + 1 - END IF - 30 CONTINUE -* -* Increase K and return to the start of the main loop -* - K = K + KB - GO TO 20 -* - END IF -* - 40 CONTINUE - WORK( 1 ) = LWKOPT - RETURN -* -* End of DSYTRF -* - END |