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---
:name: sbdsdc
:md5sum: 363562a2bf0038c64910ac814e09f1c7
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- compq:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- e:
:type: real
:intent: input/output
:dims:
- n-1
- u:
:type: real
:intent: output
:dims:
- "lsame_(&compq,\"I\") ? ldu : 0"
- "lsame_(&compq,\"I\") ? n : 0"
- ldu:
:type: integer
:intent: input
- vt:
:type: real
:intent: output
:dims:
- "lsame_(&compq,\"I\") ? ldvt : 0"
- "lsame_(&compq,\"I\") ? n : 0"
- ldvt:
:type: integer
:intent: input
- q:
:type: real
:intent: output
:dims:
- "lsame_(&compq,\"I\") ? ldq : 0"
- iq:
:type: integer
:intent: output
:dims:
- "lsame_(&compq,\"I\") ? ldiq : 0"
- work:
:type: real
:intent: workspace
:dims:
- MAX(1,lwork)
- iwork:
:type: integer
:intent: workspace
:dims:
- 8*n
- info:
:type: integer
:intent: output
:substitutions:
c__9: "9"
c__0: "0"
ldq: "lsame_(&compq,\"P\") ? n*(11+2*smlsiz+8*(int)(log(((double)n)/(smlsiz+1))/log(2.0))) : 0"
ldvt: "lsame_(&compq,\"I\") ? MAX(1,n) : 0"
ldiq: "lsame_(&compq,\"P\") ? n*(3+3*(int)(log(((double)n)/(smlsiz+1))/log(2.0))) : 0"
lwork: "lsame_(&compq,\"N\") ? 4*n : lsame_(&compq,\"P\") ? 6*n : lsame_(&compq,\"I\") ? 3*n*n+4*n : 0"
ldu: "lsame_(&compq,\"I\") ? MAX(1,n) : 0"
smlsiz: ilaenv_(&c__9, "SBDSDC", " ", &c__0, &c__0, &c__0, &c__0)
:fortran_help: " SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SBDSDC computes the singular value decomposition (SVD) of a real\n\
* N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,\n\
* using a divide and conquer method, where S is a diagonal matrix\n\
* with non-negative diagonal elements (the singular values of B), and\n\
* U and VT are orthogonal matrices of left and right singular vectors,\n\
* respectively. SBDSDC can be used to compute all singular values,\n\
* and optionally, singular vectors or singular vectors in compact form.\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 X-MP, Cray Y-MP, 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. See SLASD3 for details.\n\
*\n\
* The code currently calls SLASDQ if singular values only are desired.\n\
* However, it can be slightly modified to compute singular values\n\
* using the divide and conquer method.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': B is upper bidiagonal.\n\
* = 'L': B is lower bidiagonal.\n\
*\n\
* COMPQ (input) CHARACTER*1\n\
* Specifies whether singular vectors are to be computed\n\
* as follows:\n\
* = 'N': Compute singular values only;\n\
* = 'P': Compute singular values and compute singular\n\
* vectors in compact form;\n\
* = 'I': Compute singular values and singular vectors.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix B. N >= 0.\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry, the n diagonal elements of the bidiagonal matrix B.\n\
* On exit, if INFO=0, the singular values of B.\n\
*\n\
* E (input/output) REAL array, dimension (N-1)\n\
* On entry, the elements of E contain the offdiagonal\n\
* elements of the bidiagonal matrix whose SVD is desired.\n\
* On exit, E has been destroyed.\n\
*\n\
* U (output) REAL array, dimension (LDU,N)\n\
* If COMPQ = 'I', then:\n\
* On exit, if INFO = 0, U contains the left singular vectors\n\
* of the bidiagonal matrix.\n\
* For other values of COMPQ, U is not referenced.\n\
*\n\
* LDU (input) INTEGER\n\
* The leading dimension of the array U. LDU >= 1.\n\
* If singular vectors are desired, then LDU >= max( 1, N ).\n\
*\n\
* VT (output) REAL array, dimension (LDVT,N)\n\
* If COMPQ = 'I', then:\n\
* On exit, if INFO = 0, VT' contains the right singular\n\
* vectors of the bidiagonal matrix.\n\
* For other values of COMPQ, VT is not referenced.\n\
*\n\
* LDVT (input) INTEGER\n\
* The leading dimension of the array VT. LDVT >= 1.\n\
* If singular vectors are desired, then LDVT >= max( 1, N ).\n\
*\n\
* Q (output) REAL array, dimension (LDQ)\n\
* If COMPQ = 'P', then:\n\
* On exit, if INFO = 0, Q and IQ contain the left\n\
* and right singular vectors in a compact form,\n\
* requiring O(N log N) space instead of 2*N**2.\n\
* In particular, Q contains all the REAL data in\n\
* LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))\n\
* words of memory, where SMLSIZ is returned by ILAENV and\n\
* is equal to the maximum size of the subproblems at the\n\
* bottom of the computation tree (usually about 25).\n\
* For other values of COMPQ, Q is not referenced.\n\
*\n\
* IQ (output) INTEGER array, dimension (LDIQ)\n\
* If COMPQ = 'P', then:\n\
* On exit, if INFO = 0, Q and IQ contain the left\n\
* and right singular vectors in a compact form,\n\
* requiring O(N log N) space instead of 2*N**2.\n\
* In particular, IQ contains all INTEGER data in\n\
* LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))\n\
* words of memory, where SMLSIZ is returned by ILAENV and\n\
* is equal to the maximum size of the subproblems at the\n\
* bottom of the computation tree (usually about 25).\n\
* For other values of COMPQ, IQ is not referenced.\n\
*\n\
* WORK (workspace) REAL array, dimension (MAX(1,LWORK))\n\
* If COMPQ = 'N' then LWORK >= (4 * N).\n\
* If COMPQ = 'P' then LWORK >= (6 * N).\n\
* If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (8*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.\n\
* The update process of divide and conquer failed.\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\
* Changed dimension statement in comment describing E from (N) to\n\
* (N-1). Sven, 17 Feb 05.\n\
* =====================================================================\n\
*\n"
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