pstf2 - pstf2: triangular factor, with pivoting panel, level 2

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subroutinecpstf2(characteruplo,integern,complex,dimension(lda,*)a,integerlda,integer,dimension(n)piv,integerrank,realtol,real,dimension(2*n)work,integerinfo)CPSTF2 computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix. Purpose: CPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A. The factorization has the form P**T * A * P = U**H * U , if UPLO = 'U', P**T * A * P = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV. This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS. ParametersUPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX 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 INFO = 0, the factor U or L from the Cholesky factorization as above. PIV PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. RANK RANK is INTEGER The rank of A given by the number of steps the algorithm completed. TOL TOL is REAL User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). WORK WORK is REAL array, dimension (2*N) Work space. INFO INFO is INTEGER < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedpstf2(characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,integer,dimension(n)piv,integerrank,doubleprecisiontol,doubleprecision,dimension(2*n)work,integerinfo)DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. Purpose: DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A. The factorization has the form P**T * A * P = U**T * U , if UPLO = 'U', P**T * A * P = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV. This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS. ParametersUPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. A A is 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, if INFO = 0, the factor U or L from the Cholesky factorization as above. PIV PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. RANK RANK is INTEGER The rank of A given by the number of steps the algorithm completed. TOL TOL is DOUBLE PRECISION User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). WORK WORK is DOUBLE PRECISION array, dimension (2*N) Work space. INFO INFO is INTEGER < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinespstf2(characteruplo,integern,real,dimension(lda,*)a,integerlda,integer,dimension(n)piv,integerrank,realtol,real,dimension(2*n)work,integerinfo)SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. Purpose: SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A. The factorization has the form P**T * A * P = U**T * U , if UPLO = 'U', P**T * A * P = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV. This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS. ParametersUPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. A A is 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 INFO = 0, the factor U or L from the Cholesky factorization as above. PIV PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. RANK RANK is INTEGER The rank of A given by the number of steps the algorithm completed. TOL TOL is REAL User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). WORK WORK is REAL array, dimension (2*N) Work space. INFO INFO is INTEGER < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezpstf2(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,integer,dimension(n)piv,integerrank,doubleprecisiontol,doubleprecision,dimension(2*n)work,integerinfo)ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix. Purpose: ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A. The factorization has the form P**T * A * P = U**H * U , if UPLO = 'U', P**T * A * P = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular, and P is stored as vector PIV. This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 2 BLAS. ParametersUPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX*16 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 INFO = 0, the factor U or L from the Cholesky factorization as above. PIV PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. RANK RANK is INTEGER The rank of A given by the number of steps the algorithm completed. TOL TOL is DOUBLE PRECISION User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). WORK WORK is DOUBLE PRECISION array, dimension (2*N) Work space. INFO INFO is INTEGER < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is not positive semidefinite. See Section 7 of LAPACK Working Note #161 for further information. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

pstf2 - pstf2: triangular factor, with pivoting panel, level 2

Functions subroutine cpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) CPSTF2 computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix. subroutine dpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. subroutine spstf2 (uplo, n, a, lda, piv, rank, tol, work, info) SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. subroutine zpstf2 (uplo, n, a, lda, piv, rank, tol, work, info) ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.