diff options
Diffstat (limited to 'src/fortran/lapack/dsytrf.f')
| -rw-r--r-- | src/fortran/lapack/dsytrf.f | 287 |
1 files changed, 287 insertions, 0 deletions
diff --git a/src/fortran/lapack/dsytrf.f b/src/fortran/lapack/dsytrf.f new file mode 100644 index 0000000..43a3124 --- /dev/null +++ b/src/fortran/lapack/dsytrf.f @@ -0,0 +1,287 @@ + 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 |