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---
:name: slasd0
:md5sum: ee7a88d8d84c0475b3d0063f24187d61
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- sqre:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- e:
:type: real
:intent: input
:dims:
- m-1
- u:
:type: real
:intent: output
:dims:
- ldu
- n
- ldu:
:type: integer
:intent: input
- vt:
:type: real
:intent: output
:dims:
- ldvt
- m
- ldvt:
:type: integer
:intent: input
- smlsiz:
:type: integer
:intent: input
- iwork:
:type: integer
:intent: workspace
:dims:
- 8*n
- work:
:type: real
:intent: workspace
:dims:
- 3*pow(m,2)+2*m
- info:
:type: integer
:intent: output
:substitutions:
m: "sqre == 0 ? n : sqre == 1 ? n+1 : 0"
ldvt: m
ldu: n
:fortran_help: " SUBROUTINE SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* Using a divide and conquer approach, SLASD0 computes the singular\n\
* value decomposition (SVD) of a real upper bidiagonal N-by-M\n\
* matrix B with diagonal D and offdiagonal E, where M = N + SQRE.\n\
* The algorithm computes orthogonal matrices U and VT such that\n\
* B = U * S * VT. The singular values S are overwritten on D.\n\
*\n\
* A related subroutine, SLASDA, computes only the singular values,\n\
* and optionally, the singular vectors in compact form.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* On entry, the row dimension of the upper bidiagonal matrix.\n\
* This is also the dimension of the main diagonal array D.\n\
*\n\
* SQRE (input) INTEGER\n\
* Specifies the column dimension of the bidiagonal matrix.\n\
* = 0: The bidiagonal matrix has column dimension M = N;\n\
* = 1: The bidiagonal matrix has column dimension M = N+1;\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry D contains the main diagonal of the bidiagonal\n\
* matrix.\n\
* On exit D, if INFO = 0, contains its singular values.\n\
*\n\
* E (input) REAL array, dimension (M-1)\n\
* Contains the subdiagonal entries of the bidiagonal matrix.\n\
* On exit, E has been destroyed.\n\
*\n\
* U (output) REAL array, dimension at least (LDQ, N)\n\
* On exit, U contains the left singular vectors.\n\
*\n\
* LDU (input) INTEGER\n\
* On entry, leading dimension of U.\n\
*\n\
* VT (output) REAL array, dimension at least (LDVT, M)\n\
* On exit, VT' contains the right singular vectors.\n\
*\n\
* LDVT (input) INTEGER\n\
* On entry, leading dimension of VT.\n\
*\n\
* SMLSIZ (input) INTEGER\n\
* On entry, maximum size of the subproblems at the\n\
* bottom of the computation tree.\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (8*N)\n\
*\n\
* WORK (workspace) REAL array, dimension (3*M**2+2*M)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: if INFO = 1, a singular value 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\
* .. Local Scalars ..\n INTEGER I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,\n $ J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,\n $ NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI\n REAL ALPHA, BETA\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL SLASD1, SLASDQ, SLASDT, XERBLA\n\
* ..\n"
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