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---
:name: zlalsd
:md5sum: 67b57ad9803fd57023c3c14223c42c05
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- smlsiz:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- e:
:type: doublereal
:intent: input/output
:dims:
- n-1
- b:
:type: doublecomplex
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- rcond:
:type: doublereal
:intent: input
- rank:
:type: integer
:intent: output
- work:
:type: doublecomplex
:intent: workspace
:dims:
- n * nrhs
- rwork:
:type: doublereal
:intent: workspace
:dims:
- 9*n+2*n*smlsiz+8*n*nlvl+3*smlsiz*nrhs+(smlsiz+1)*(smlsiz+1)
- iwork:
:type: integer
:intent: workspace
:dims:
- 3*n*nlvl + 11*n
- info:
:type: integer
:intent: output
:substitutions:
nlvl: ( (int)( log(((double)n)/(smlsiz+1))/log(2.0) ) ) + 1
:fortran_help: " SUBROUTINE ZLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZLALSD uses the singular value decomposition of A to solve the least\n\
* squares problem of finding X to minimize the Euclidean norm of each\n\
* column of A*X-B, where A is N-by-N upper bidiagonal, and X and B\n\
* are N-by-NRHS. The solution X overwrites B.\n\
*\n\
* The singular values of A smaller than RCOND times the largest\n\
* singular value are treated as zero in solving the least squares\n\
* problem; in this case a minimum norm solution is returned.\n\
* The actual singular values are returned in D in ascending order.\n\
*\n\
* This code makes very mild assumptions about floating point\n\
* arithmetic. It will work on machines with a guard digit in\n\
* add/subtract, or on those binary machines without guard digits\n\
* which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.\n\
* It could conceivably fail on hexadecimal or decimal machines\n\
* without guard digits, but we know of none.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': D and E define an upper bidiagonal matrix.\n\
* = 'L': D and E define a lower bidiagonal matrix.\n\
*\n\
* SMLSIZ (input) INTEGER\n\
* The maximum size of the subproblems at the bottom of the\n\
* computation tree.\n\
*\n\
* N (input) INTEGER\n\
* The dimension of the bidiagonal matrix. N >= 0.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of columns of B. NRHS must be at least 1.\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry D contains the main diagonal of the bidiagonal\n\
* matrix. On exit, if INFO = 0, D contains its singular values.\n\
*\n\
* E (input/output) DOUBLE PRECISION array, dimension (N-1)\n\
* Contains the super-diagonal entries of the bidiagonal matrix.\n\
* On exit, E has been destroyed.\n\
*\n\
* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)\n\
* On input, B contains the right hand sides of the least\n\
* squares problem. On output, B contains the solution X.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B in the calling subprogram.\n\
* LDB must be at least max(1,N).\n\
*\n\
* RCOND (input) DOUBLE PRECISION\n\
* The singular values of A less than or equal to RCOND times\n\
* the largest singular value are treated as zero in solving\n\
* the least squares problem. If RCOND is negative,\n\
* machine precision is used instead.\n\
* For example, if diag(S)*X=B were the least squares problem,\n\
* where diag(S) is a diagonal matrix of singular values, the\n\
* solution would be X(i) = B(i) / S(i) if S(i) is greater than\n\
* RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to\n\
* RCOND*max(S).\n\
*\n\
* RANK (output) INTEGER\n\
* The number of singular values of A greater than RCOND times\n\
* the largest singular value.\n\
*\n\
* WORK (workspace) COMPLEX*16 array, dimension at least\n\
* (N * NRHS).\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION array, dimension at least\n\
* (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +\n\
* MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),\n\
* where\n\
* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )\n\
*\n\
* IWORK (workspace) INTEGER array, dimension at least\n\
* (3*N*NLVL + 11*N).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: The algorithm failed to compute a singular value while\n\
* working on the submatrix lying in rows and columns\n\
* INFO/(N+1) through MOD(INFO,N+1).\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Ming Gu and Ren-Cang Li, Computer Science Division, University of\n\
* California at Berkeley, USA\n\
* Osni Marques, LBNL/NERSC, USA\n\
*\n\
* =====================================================================\n\
*\n"
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