lasd0 - lasd0: D&C step: top level solver

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subroutinedlasd0(integern,integersqre,doubleprecision,dimension(*)d,doubleprecision,dimension(*)e,doubleprecision,dimension(ldu,*)u,integerldu,doubleprecision,dimension(ldvt,*)vt,integerldvt,integersmlsiz,integer,dimension(*)iwork,doubleprecision,dimension(*)work,integerinfo)DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off- diagonal e. Used by sbdsdc. Purpose: Using a divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes orthogonal matrices U and VT such that B = U * S * VT. The singular values S are overwritten on D. A related subroutine, DLASDA, computes only the singular values, and optionally, the singular vectors in compact form. ParametersN N is INTEGER On entry, the row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D. SQRE SQRE is INTEGER Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N+1; D D is DOUBLE PRECISION array, dimension (N) On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values. E E is DOUBLE PRECISION array, dimension (M-1) Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed. U U is DOUBLE PRECISION array, dimension (LDU, N) On exit, U contains the left singular vectors, if U passed in as (N, N) Identity. LDU LDU is INTEGER On entry, leading dimension of U. VT VT is DOUBLE PRECISION array, dimension (LDVT, M) On exit, VT**T contains the right singular vectors, if VT passed in as (M, M) Identity. LDVT LDVT is INTEGER On entry, leading dimension of VT. SMLSIZ SMLSIZ is INTEGER On entry, maximum size of the subproblems at the bottom of the computation tree. IWORK IWORK is INTEGER array, dimension (8*N) WORK WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M) INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA subroutineslasd0(integern,integersqre,real,dimension(*)d,real,dimension(*)e,real,dimension(ldu,*)u,integerldu,real,dimension(ldvt,*)vt,integerldvt,integersmlsiz,integer,dimension(*)iwork,real,dimension(*)work,integerinfo)SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off- diagonal e. Used by sbdsdc. Purpose: Using a divide and conquer approach, SLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes orthogonal matrices U and VT such that B = U * S * VT. The singular values S are overwritten on D. A related subroutine, SLASDA, computes only the singular values, and optionally, the singular vectors in compact form. ParametersN N is INTEGER On entry, the row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D. SQRE SQRE is INTEGER Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N+1; D D is REAL array, dimension (N) On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values. E E is REAL array, dimension (M-1) Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed. U U is REAL array, dimension (LDU, N) On exit, U contains the left singular vectors, if U passed in as (N, N) Identity. LDU LDU is INTEGER On entry, leading dimension of U. VT VT is REAL array, dimension (LDVT, M) On exit, VT**T contains the right singular vectors, if VT passed in as (M, M) Identity. LDVT LDVT is INTEGER On entry, leading dimension of VT. SMLSIZ SMLSIZ is INTEGER On entry, maximum size of the subproblems at the bottom of the computation tree. IWORK IWORK is INTEGER array, dimension (8*N) WORK WORK is REAL array, dimension (3*M**2+2*M) INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

lasd0 - lasd0: D&C step: top level solver

Functions subroutine dlasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info) DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. subroutine slasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info) SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.