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---
:name: dlasdq
:md5sum: c377895c7b312038c22d75f7469b1c8c
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- sqre:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- ncvt:
:type: integer
:intent: input
- nru:
:type: integer
:intent: input
- ncc:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- e:
:type: doublereal
:intent: input/output
:dims:
- "sqre==0 ? n-1 : sqre==1 ? n : 0"
- vt:
:type: doublereal
:intent: input/output
:dims:
- ldvt
- ncvt
- ldvt:
:type: integer
:intent: input
- u:
:type: doublereal
:intent: input/output
:dims:
- ldu
- n
- ldu:
:type: integer
:intent: input
- c:
:type: doublereal
:intent: input/output
:dims:
- ldc
- ncc
- ldc:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: workspace
:dims:
- 4*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLASDQ computes the singular value decomposition (SVD) of a real\n\
* (upper or lower) bidiagonal matrix with diagonal D and offdiagonal\n\
* E, accumulating the transformations if desired. Letting B denote\n\
* the input bidiagonal matrix, the algorithm computes orthogonal\n\
* matrices Q and P such that B = Q * S * P' (P' denotes the transpose\n\
* of P). The singular values S are overwritten on D.\n\
*\n\
* The input matrix U is changed to U * Q if desired.\n\
* The input matrix VT is changed to P' * VT if desired.\n\
* The input matrix C is changed to Q' * C if desired.\n\
*\n\
* See \"Computing Small Singular Values of Bidiagonal Matrices With\n\
* Guaranteed High Relative Accuracy,\" by J. Demmel and W. Kahan,\n\
* LAPACK Working Note #3, for a detailed description of the algorithm.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* On entry, UPLO specifies whether the input bidiagonal matrix\n\
* is upper or lower bidiagonal, and whether it is square are\n\
* not.\n\
* UPLO = 'U' or 'u' B is upper bidiagonal.\n\
* UPLO = 'L' or 'l' B is lower bidiagonal.\n\
*\n\
* SQRE (input) INTEGER\n\
* = 0: then the input matrix is N-by-N.\n\
* = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and\n\
* (N+1)-by-N if UPLU = 'L'.\n\
*\n\
* The bidiagonal matrix has\n\
* N = NL + NR + 1 rows and\n\
* M = N + SQRE >= N columns.\n\
*\n\
* N (input) INTEGER\n\
* On entry, N specifies the number of rows and columns\n\
* in the matrix. N must be at least 0.\n\
*\n\
* NCVT (input) INTEGER\n\
* On entry, NCVT specifies the number of columns of\n\
* the matrix VT. NCVT must be at least 0.\n\
*\n\
* NRU (input) INTEGER\n\
* On entry, NRU specifies the number of rows of\n\
* the matrix U. NRU must be at least 0.\n\
*\n\
* NCC (input) INTEGER\n\
* On entry, NCC specifies the number of columns of\n\
* the matrix C. NCC must be at least 0.\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, D contains the diagonal entries of the\n\
* bidiagonal matrix whose SVD is desired. On normal exit,\n\
* D contains the singular values in ascending order.\n\
*\n\
* E (input/output) DOUBLE PRECISION array.\n\
* dimension is (N-1) if SQRE = 0 and N if SQRE = 1.\n\
* On entry, the entries of E contain the offdiagonal entries\n\
* of the bidiagonal matrix whose SVD is desired. On normal\n\
* exit, E will contain 0. If the algorithm does not converge,\n\
* D and E will contain the diagonal and superdiagonal entries\n\
* of a bidiagonal matrix orthogonally equivalent to the one\n\
* given as input.\n\
*\n\
* VT (input/output) DOUBLE PRECISION array, dimension (LDVT, NCVT)\n\
* On entry, contains a matrix which on exit has been\n\
* premultiplied by P', dimension N-by-NCVT if SQRE = 0\n\
* and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).\n\
*\n\
* LDVT (input) INTEGER\n\
* On entry, LDVT specifies the leading dimension of VT as\n\
* declared in the calling (sub) program. LDVT must be at\n\
* least 1. If NCVT is nonzero LDVT must also be at least N.\n\
*\n\
* U (input/output) DOUBLE PRECISION array, dimension (LDU, N)\n\
* On entry, contains a matrix which on exit has been\n\
* postmultiplied by Q, dimension NRU-by-N if SQRE = 0\n\
* and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).\n\
*\n\
* LDU (input) INTEGER\n\
* On entry, LDU specifies the leading dimension of U as\n\
* declared in the calling (sub) program. LDU must be at\n\
* least max( 1, NRU ) .\n\
*\n\
* C (input/output) DOUBLE PRECISION array, dimension (LDC, NCC)\n\
* On entry, contains an N-by-NCC matrix which on exit\n\
* has been premultiplied by Q' dimension N-by-NCC if SQRE = 0\n\
* and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).\n\
*\n\
* LDC (input) INTEGER\n\
* On entry, LDC specifies the leading dimension of C as\n\
* declared in the calling (sub) program. LDC must be at\n\
* least 1. If NCC is nonzero, LDC must also be at least N.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (4*N)\n\
* Workspace. Only referenced if one of NCVT, NRU, or NCC is\n\
* nonzero, and if N is at least 2.\n\
*\n\
* INFO (output) INTEGER\n\
* On exit, a value of 0 indicates a successful exit.\n\
* If INFO < 0, argument number -INFO is illegal.\n\
* If INFO > 0, the algorithm did not converge, and INFO\n\
* specifies how many superdiagonals did not converge.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Ming Gu and Huan Ren, Computer Science Division, University of\n\
* California at Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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