.TH "gesdd" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gesdd \- gesdd: SVD, divide and conquer .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgesdd\fP (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, iwork, info)" .br .RI "\fBCGESDD\fP " .ti -1c .RI "subroutine \fBdgesdd\fP (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)" .br .RI "\fBDGESDD\fP " .ti -1c .RI "subroutine \fBsgesdd\fP (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)" .br .RI "\fBSGESDD\fP " .ti -1c .RI "subroutine \fBzgesdd\fP (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, iwork, info)" .br .RI "\fBZGESDD\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgesdd (character jobz, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)" .PP \fBCGESDD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method\&. The SVD is written A = U * SIGMA * conjugate-transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix\&. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order\&. The first min(m,n) columns of U and V are the left and right singular vectors of A\&. Note that the routine returns VT = V**H, not V\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**H are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**H are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten in the array A and all rows of V**H are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**H are overwritten in the array A; = 'N': no columns of U or rows of V**H are computed\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the input matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the input matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**H (the right singular vectors, stored rowwise) otherwise\&. if JOBZ \&.ne\&. 'O', the contents of A are destroyed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1)\&. .fi .PP .br \fIU\fP .PP .nf U is COMPLEX array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'\&. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced\&. .fi .PP .br \fILDU\fP .PP .nf LDU is INTEGER The leading dimension of the array U\&. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M\&. .fi .PP .br \fIVT\fP .PP .nf VT is COMPLEX array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER The leading dimension of the array VT\&. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 1\&. If LWORK = -1, a workspace query is assumed\&. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed\&. Let mx = max(M,N) and mn = min(M,N)\&. If JOBZ = 'N', LWORK >= 2*mn + mx\&. If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx\&. If JOBZ = 'S', LWORK >= mn*mn + 3*mn\&. If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx\&. These are not tight minimums in all cases; see comments inside code\&. For good performance, LWORK should generally be larger; a query is recommended\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (MAX(1,LRWORK)) Let mx = max(M,N) and mn = min(M,N)\&. If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3\&.6 needs 7*mn); else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; else LRWORK >= max( 5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn )\&. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (8*min(M,N)) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER < 0: if INFO = -i, the i-th argument had an illegal value\&. = -4: if A had a NAN entry\&. > 0: The updating process of SBDSDC did not converge\&. = 0: successful exit\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .RE .PP .SS "subroutine dgesdd (character jobz, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)" .PP \fBDGESDD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors\&. If singular vectors are desired, it uses a divide-and-conquer algorithm\&. The SVD is written A = U * SIGMA * transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix\&. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order\&. The first min(m,n) columns of U and V are the left and right singular vectors of A\&. Note that the routine returns VT = V**T, not V\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**T are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**T are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten on the array A and all rows of V**T are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**T are overwritten in the array A; = 'N': no columns of U or rows of V**T are computed\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the input matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the input matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**T (the right singular vectors, stored rowwise) otherwise\&. if JOBZ \&.ne\&. 'O', the contents of A are destroyed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1)\&. .fi .PP .br \fIU\fP .PP .nf U is DOUBLE PRECISION array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'\&. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M orthogonal matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced\&. .fi .PP .br \fILDU\fP .PP .nf LDU is INTEGER The leading dimension of the array U\&. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M\&. .fi .PP .br \fIVT\fP .PP .nf VT is DOUBLE PRECISION array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER The leading dimension of the array VT\&. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK; .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 1\&. If LWORK = -1, a workspace query is assumed\&. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed\&. Let mx = max(M,N) and mn = min(M,N)\&. If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn )\&. If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn )\&. If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn\&. If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx\&. These are not tight minimums in all cases; see comments inside code\&. For good performance, LWORK should generally be larger; a query is recommended\&. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (8*min(M,N)) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER < 0: if INFO = -i, the i-th argument had an illegal value\&. = -4: if A had a NAN entry\&. > 0: DBDSDC did not converge, updating process failed\&. = 0: successful exit\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .RE .PP .SS "subroutine sgesdd (character jobz, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)" .PP \fBSGESDD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors\&. If singular vectors are desired, it uses a divide-and-conquer algorithm\&. The SVD is written A = U * SIGMA * transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix\&. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order\&. The first min(m,n) columns of U and V are the left and right singular vectors of A\&. Note that the routine returns VT = V**T, not V\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**T are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**T are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten on the array A and all rows of V**T are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**T are overwritten in the array A; = 'N': no columns of U or rows of V**T are computed\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the input matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the input matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**T (the right singular vectors, stored rowwise) otherwise\&. if JOBZ \&.ne\&. 'O', the contents of A are destroyed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1)\&. .fi .PP .br \fIU\fP .PP .nf U is REAL array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'\&. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M orthogonal matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced\&. .fi .PP .br \fILDU\fP .PP .nf LDU is INTEGER The leading dimension of the array U\&. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M\&. .fi .PP .br \fIVT\fP .PP .nf VT is REAL array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER The leading dimension of the array VT\&. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK; .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 1\&. If LWORK = -1, a workspace query is assumed\&. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed\&. Let mx = max(M,N) and mn = min(M,N)\&. If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn )\&. If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn )\&. If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn\&. If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx\&. These are not tight minimums in all cases; see comments inside code\&. For good performance, LWORK should generally be larger; a query is recommended\&. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (8*min(M,N)) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER < 0: if INFO = -i, the i-th argument had an illegal value\&. = -4: if A had a NAN entry\&. > 0: SBDSDC did not converge, updating process failed\&. = 0: successful exit\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .RE .PP .SS "subroutine zgesdd (character jobz, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)" .PP \fBZGESDD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method\&. The SVD is written A = U * SIGMA * conjugate-transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix\&. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order\&. The first min(m,n) columns of U and V are the left and right singular vectors of A\&. Note that the routine returns VT = V**H, not V\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**H are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**H are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten in the array A and all rows of V**H are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**H are overwritten in the array A; = 'N': no columns of U or rows of V**H are computed\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the input matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the input matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**H (the right singular vectors, stored rowwise) otherwise\&. if JOBZ \&.ne\&. 'O', the contents of A are destroyed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1)\&. .fi .PP .br \fIU\fP .PP .nf U is COMPLEX*16 array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'\&. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M unitary matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced\&. .fi .PP .br \fILDU\fP .PP .nf LDU is INTEGER The leading dimension of the array U\&. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M\&. .fi .PP .br \fIVT\fP .PP .nf VT is COMPLEX*16 array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER The leading dimension of the array VT\&. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. .fi .PP .br \fILWORK\fP .PP .nf LWORK is INTEGER The dimension of the array WORK\&. LWORK >= 1\&. If LWORK = -1, a workspace query is assumed\&. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed\&. Let mx = max(M,N) and mn = min(M,N)\&. If JOBZ = 'N', LWORK >= 2*mn + mx\&. If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx\&. If JOBZ = 'S', LWORK >= mn*mn + 3*mn\&. If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx\&. These are not tight minimums in all cases; see comments inside code\&. For good performance, LWORK should generally be larger; a query is recommended\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) Let mx = max(M,N) and mn = min(M,N)\&. If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3\&.6 needs 7*mn); else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; else LRWORK >= max( 5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn )\&. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (8*min(M,N)) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER < 0: if INFO = -i, the i-th argument had an illegal value\&. = -4: if A had a NAN entry\&. > 0: The updating process of DBDSDC did not converge\&. = 0: successful exit\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.