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---
:name: cgesdd
:md5sum: 22c0a1340de32a426796a6de2e6183b9
:category: :subroutine
:arguments:
- jobz:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- s:
:type: real
:intent: output
:dims:
- MIN(m,n)
- u:
:type: complex
:intent: output
:dims:
- ldu
- ucol
- ldu:
:type: integer
:intent: input
- vt:
:type: complex
:intent: output
:dims:
- ldvt
- n
- ldvt:
:type: integer
:intent: input
- work:
:type: complex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "lsame_(&jobz,\"N\") ? 2*MIN(m,n)+MAX(m,n) : lsame_(&jobz,\"O\") ? 2*MIN(m,n)*MIN(m,n)+2*MIN(m,n)+MAX(m,n) : (lsame_(&jobz,\"S\")||lsame_(&jobz,\"A\")) ? MIN(m,n)*MIN(m,n)+2*MIN(m,n)+MAX(m,n) : 0"
- rwork:
:type: real
:intent: workspace
:dims:
- "MAX(1, (lsame_(&jobz,\"N\") ? 5*MIN(m,n) : MIN(m,n)*MAX(5*MIN(m,n)+7,2*MAX(m,n)+2*MIN(m,n)+1)))"
- iwork:
:type: integer
:intent: workspace
:dims:
- 8*MIN(m,n)
- info:
:type: integer
:intent: output
:substitutions:
m: lda
ucol: "((lsame_(&jobz,\"A\")) || (((lsame_(&jobz,\"O\")) && (m < n)))) ? m : lsame_(&jobz,\"S\") ? MIN(m,n) : 0"
ldvt: "((lsame_(&jobz,\"A\")) || (((lsame_(&jobz,\"O\")) && (m >= n)))) ? n : lsame_(&jobz,\"S\") ? MIN(m,n) : 1"
ldu: "(lsame_(&jobz,\"S\") || lsame_(&jobz,\"A\") || (lsame_(&jobz,\"O\") && m < n)) ? m : 1"
:fortran_help: " SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CGESDD computes the singular value decomposition (SVD) of a complex\n\
* M-by-N matrix A, optionally computing the left and/or right singular\n\
* vectors, by using divide-and-conquer method. The SVD is written\n\
*\n\
* A = U * SIGMA * conjugate-transpose(V)\n\
*\n\
* where SIGMA is an M-by-N matrix which is zero except for its\n\
* min(m,n) diagonal elements, U is an M-by-M unitary matrix, and\n\
* V is an N-by-N unitary matrix. The diagonal elements of SIGMA\n\
* are the singular values of A; they are real and non-negative, and\n\
* are returned in descending order. The first min(m,n) columns of\n\
* U and V are the left and right singular vectors of A.\n\
*\n\
* Note that the routine returns VT = V**H, not V.\n\
*\n\
* The divide and conquer algorithm makes very mild assumptions about\n\
* floating point arithmetic. It will work on machines with a guard\n\
* digit in add/subtract, or on those binary machines without guard\n\
* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or\n\
* Cray-2. 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\
* JOBZ (input) CHARACTER*1\n\
* Specifies options for computing all or part of the matrix U:\n\
* = 'A': all M columns of U and all N rows of V**H are\n\
* returned in the arrays U and VT;\n\
* = 'S': the first min(M,N) columns of U and the first\n\
* min(M,N) rows of V**H are returned in the arrays U\n\
* and VT;\n\
* = 'O': If M >= N, the first N columns of U are overwritten\n\
* in the array A and all rows of V**H are returned in\n\
* the array VT;\n\
* otherwise, all columns of U are returned in the\n\
* array U and the first M rows of V**H are overwritten\n\
* in the array A;\n\
* = 'N': no columns of U or rows of V**H are computed.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the input matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the input matrix A. N >= 0.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA,N)\n\
* On entry, the M-by-N matrix A.\n\
* On exit,\n\
* if JOBZ = 'O', A is overwritten with the first N columns\n\
* of U (the left singular vectors, stored\n\
* columnwise) if M >= N;\n\
* A is overwritten with the first M rows\n\
* of V**H (the right singular vectors, stored\n\
* rowwise) otherwise.\n\
* if JOBZ .ne. 'O', the contents of A are destroyed.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* S (output) REAL array, dimension (min(M,N))\n\
* The singular values of A, sorted so that S(i) >= S(i+1).\n\
*\n\
* U (output) COMPLEX array, dimension (LDU,UCOL)\n\
* UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;\n\
* UCOL = min(M,N) if JOBZ = 'S'.\n\
* If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M\n\
* unitary matrix U;\n\
* if JOBZ = 'S', U contains the first min(M,N) columns of U\n\
* (the left singular vectors, stored columnwise);\n\
* if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.\n\
*\n\
* LDU (input) INTEGER\n\
* The leading dimension of the array U. LDU >= 1; if\n\
* JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.\n\
*\n\
* VT (output) COMPLEX array, dimension (LDVT,N)\n\
* If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the\n\
* N-by-N unitary matrix V**H;\n\
* if JOBZ = 'S', VT contains the first min(M,N) rows of\n\
* V**H (the right singular vectors, stored rowwise);\n\
* if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.\n\
*\n\
* LDVT (input) INTEGER\n\
* The leading dimension of the array VT. LDVT >= 1; if\n\
* JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;\n\
* if JOBZ = 'S', LDVT >= min(M,N).\n\
*\n\
* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= 1.\n\
* if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).\n\
* if JOBZ = 'O',\n\
* LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).\n\
* if JOBZ = 'S' or 'A',\n\
* LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).\n\
* For good performance, LWORK should generally be larger.\n\
*\n\
* If LWORK = -1, a workspace query is assumed. The optimal\n\
* size for the WORK array is calculated and stored in WORK(1),\n\
* and no other work except argument checking is performed.\n\
*\n\
* RWORK (workspace) REAL array, dimension (MAX(1,LRWORK))\n\
* If JOBZ = 'N', LRWORK >= 5*min(M,N).\n\
* Otherwise, \n\
* LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (8*min(M,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 updating process of SBDSDC 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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